Pojoaque Valley SchoolsMathematics CCSS Pacing Guide
Grade 3 Skills adapted from
Kentucky Department of EducationMath Deconstructed Standards
Evidence of attainmentassessment Vocabulary Knowledge Skills and
Essential Elements adapted from Wisconsin Department of Education and
Standards Insights Computer-Based Program
Version 3 2015-2016 1
Version 3
2015-2016
Pojoaque Valley SchoolsMath Common Core Pacing Guide Introduction
The Pojoaque Valley Schools pacing guide documents are intended to guide teachersrsquo use of Common Core State Standards (CCSS) over the course of an instructional school year The guides identify the focus standards by quarter Teachers should understand that the focus standards emphasize deep instruction for that timeframe However because a certain quarter does not address specific standards it should be understood that previously taught standards should be reinforced while working on the focus standards for any designated quarter Some standards will recur across all quarters due to their importance and need to be addressed on an ongoing basis
The Math pacing guides are grounded in four key components the key fluency expectations for each grade level the critical areas designated in the CCSS Math Standards the Common Core Standards for Mathematics and the integration of the Standards for Mathematical Practice In planning instruction it is important that math teachers incorporate the 8 mathematical practices for mathematics to ensure that the Common Core standards are mastered by all students
The Math CCSS pacing guides contain the following elements Grade Level Identify the grade level of the intended standard Standard with code Defines the knowledge and skills for students The code contains the grade level
domain and standard number Domain Larger groups of related standards Standards from different domains may sometimes be
closely related Cluster Summarize groups of related standards Skills and Knowledge Identified as subsets of the standard and appear in one or more quarters Define
the skills and knowledge embedded in the standard to meet the full intent of the standard itself
Version 3 2015-2016
2
Version 2 of the Pojoaque Valley School District Pacing guides for Reading Language Arts and Mathematics are based on the done by staff and teachers of the school district using the Kentucky model and a synthesis of the excellent work done by Wisconsin Cooperative Educational Service Agency 7 (CESA 7) School Improvement Services Green Bay WI (2010) Standards Insight project
Standards Insight was developed to give educators a tool for in depth investigation of the Common Core State Standards (CCSS) The CCSS are ldquounpackedrdquo or dissected identifying specific knowledge skills vocabulary understandings and evidence of student attainment for each standard Standards Insight may be used by educators to gain a thorough grasp of the CCSS or as a powerful collaborative tool supporting educator teams through the essential conversations necessary for developing shared responsibility for student attainment of all CCSS serves as a high-powered vehicle to help educators examine the standards in a variety of ways
The Version 2 Pojoaque Valley School District Pacing guides present the standard with levels of detail and then the necessary skills by quarter based on the Kentucky model On the second page for each standard the synthesis of the Standards Insight project is presented in a way that further defines and refines the standard such that teachers may use the information to refine their teaching practices
Based on this synthesis of work and the purpose for the unpacking the following fields were selected as most helpful to aid in understanding of the Common Core Standards that will lead to shifts in instruction
1 Evidence of Student Attainment ldquoWhat could students do to show attainment of the standardrdquo
2 Vocabulary ldquoWhat are key terms in the standard that are essential for interpretation and understanding in order for students to learn the contentrdquo
3 Knowledge ldquoWhat does the student need to know in order to aid in attainment of this standardrdquo
4 Skills and Understanding ldquoWhat procedural skill(s) does the student need to demonstrate for attainment of this standardrdquo and ldquoWhat will students understand to attain the standardrdquo
The following fields are included in Version 2
Evidence of Student Attainment This field describes what the standard may look like in student work Specific expectations are listed in performance terms showing what students will say or do to demonstrate attainment of the standard
Standards Vocabulary This field lists words and phrases specific to each standard Shared interpretation and in depth understanding of standards vocabulary are essential for consistent instruction across and within grade levels and content areas
Knowledge The knowledge field lists what students will need to know in order to master each standard (facts vocabulary definitions)
Skills and Understanding The skills field identifies the procedural knowledge students apply in order to Version 3 2015-2016
3
master each standard (actions applications strategies) as well as the overarching understanding that connects the standard knowledge and skills Understandings included in Standards Insight synthesize ideas and have lasting value
Instructional Achievement Level Descriptors This field lists by level what a teacher can expect to see in a student who achieves at a particular level Additionally teachers can use this filed to differentiate instruction to provide further growth for studentrsquos in moving from one level to another This field can be used to provide specific teaching approaches to the standard in question
A Note About High School Standards The high school standards are listed in conceptual categories Conceptual categories portray a coherent view of high school instruction that crosses traditional course boundaries We have done everything possible with teacher input to link individual standards to the appropriate pacing guides
References to Tables References to tables within the standards in the Standards Insight tool refer to Tables 1-5 found in the glossary of the Mathematics Common Core State Standards document found at wwwcorestandardsorg
Version 3 2015-2016
4
Quarterly View of Standards 3 rd Grade Mathematics Pacing Guide
Quarter 1 2 3 43OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
X X
3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
X X
3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
X X
3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations8times = 48 5 = 1048781 divide 3 6 times 6 =
X X
3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication)Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)
X
3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when multiplied by 8 X X3OA7 Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division (eg knowing that 8 times 5 = 40 one knows 40 divide 5 = 8) or properties of operations By the end of Grade 3 know from memory all products of two one-digit numbers
X X
3OA8 Solve two-step word problems using the four operations Represent these problems using equations with a letter standing for the unknown quantity Assess the reasonableness of answers using mental computation and estimation strategies including rounding3
X X X
3OA9 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operationsFor example observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends
X X X
3NBT1 Use place value understanding to round whole numbers to the nearest 10 or 100 X3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtraction
X
3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operations
X
3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1b
X
Version 3 2015-2016 5
Quarter 1 2 3 43NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number line
X
3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction model
X
3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagram
X
3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7
X
3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 pets
X
3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quarters
X
3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units
X
3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units) X3MD7a Relate area to the operations of multiplication and addition a Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengths
X
3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoning
X
3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoning
X
3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problems
X
Version 3 2015-2016 6
Quarter 1 2 3 43MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters
X
3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategories
X
3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape
X
Version 3 2015-2016 7
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and division
Quarter 1 Quarter 2
Find the product of multiple groups of objects
Interpret products of whole numbers as a total number of objects in a number of groups
Quarter 3
Find the product of multiple groups of objects
Interpret products of whole numbers as a total number of objects in a number of groups
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 8
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven any multiplication problem in the form a x b = c
Represent the problem physically or pictorially and describe the relationship between the factors and the product in the equation and the attributes of the representation (ie given 3 x 5 = 15 students make 3 piles of buttons with 5 buttons in each pile They explain that 15 represents the total number of buttons 3 is the number of piles and 5 is the number of buttons in each pile)
Write a corresponding word problem containing a multiplication context
Students know
Characteristics of multiplication contexts
Students understand thatare able to
Represent quantities and operations (multiplication) physically pictorially or symbolically
Use mathematical language to communicate the connections between multiplication equations and related representations
Write word problems containing multiplication contexts
Putting together equal sized groups may be represented by multiplication equations and totals found through multiplication
EE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sum
Level IV Students willEE3OA1-2 Use repeated addition to find the total number of objects arranged in a square or rectangular arrayEx Using tiles in a template identify the total number of tiles by adding the tiles in the templateEx Fill space of squares and rectangles with 1-inch tiles add tiles in rows or columns to determine total number of tiles it takes to fill the shape (squarerectangle)Ex Use an abacus to find the total
Level III Students willEE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sumEx Two birds + two Birds + two birds = six birdsEx Given a repeated addition number sentence use a number line to find the sum
Level II Students willEE3OA1-2 Use addition to find the total number of objectsEx Three apples + four apples = six applesEx Add to find the total number of starsEx Skip count by twos to tell how many
Level I Students willEE3OA1-2 Identify which group has more or less when objects are added or taken awayEx When an object is added to a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoEx When an object is taken from a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 9
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and divisionQuarter 1 Quarter 2
Know what the numbers in a division problem represent
Explain what division means and how it relates to equal shares
Interpret quotients as the number of shares or the number of groups when a set of objects is divided equally
Quarter 3
Know what the numbers in a division problem represent
Explain what division means and how it relates to equal shares
Interpret quotients as the number of shares or the number of groups when a set of objects is divided equally
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 10
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven any division problem in the form a divide b = c
Represent the problem physically or pictorially and describe the relationship between the dividend divisor and quotient in the equation and the attributes of the representation (eg given 15 divide 3 = 5 students make 3 piles of buttons with 5 buttons in each pile and explain that 15 represents the total number of buttons 3 is the number of piles the total was shared among and 5 is the number of buttons in each pile)
Write a corresponding word problem containing a division context
Students know
Characteristics of division contexts
Students understand thatare able to
Represent quantities and operations (division) physically pictorially or symbolically
Use mathematical language to communicate the connections between division equations and related representations
Write word problems containing division contexts
Both partitioning into equal-sized shares and partitioning equally among a given number of groups may be modeled by division equations and the desired results found through division
EE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sum
Level IV Students willEE3OA1-2 Use repeated addition to find the total number of objects arranged in a square or rectangular arrayEx Using tiles in a template identify the total number of tiles by adding the tiles in the templateEx Fill space of squares and rectangles with 1-inch tiles add tiles in rows or columns to determine total number of tiles it takes to fill the shape (squarerectangle)Ex Use an abacus to find the total
Level III Students willEE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sumEx Two birds + two Birds + two birds = six birdsEx Given a repeated addition number sentence use a number line to find the sum
Level II Students willEE3OA1-2 Use addition to find the total number of objectsEx Three apples + four apples = six applesEx Add to find the total number of starsEx Skip count by twos to tell how many
Level I Students willEE3OA1-2 Identify which group has more or less when objects are added or taken awayEx When an object is added to a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoEx When an object is taken from a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 11
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and division
Quarter 1 Quarter 2
Multiply and divide within 100
Solve word problems in situations involving equal groups arrays and measurement quantities
Represent a word problem using a picture an equation with a symbol for the unknown number or in other ways
Quarter 3
Multiply and divide within 100
Solve word problems in situations involving equal groups arrays and measurement quantities
Represent a word problem using a picture an equation with a symbol for the unknown number or in other ways
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 12
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a variety of multiplication and division word problems within 100
Explain and justify solutions and solution paths using connections among a variety of representations (eg place value blocks drawings open arrays and equations with a symbol for the unknown)
See glossary for problem types (Table 2)
Students know
Characteristics of multiplication and division contexts
Multiplication and division strategies
Students understand thatare able to
Represent quantities and operations (multiplication and division) physically pictorially or symbolically
Strategically use a variety of representations to solve multiplication and division word problems
Use informal and mathematical language to communicate the connections among multiplication and division contexts and related physical pictorial or symbolic representations
Accurately compute products and quotients
Use symbols to represent unknown quantities in equations
EE3OA3 See EE3OA1 for repeated addition a foundational skill for multiplication and division (Multiplication begins in grade 4 and division begins in grade 5)
EE3OA3 See EE3OA1 for repeated addition a foundational skill for multiplication and division (Multiplication begins in grade 4 and division begins in grade 5)
Version 3 2015-2016 13
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8times = 48 5 = 1048781 divide 3 6 times 6 = Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and division
Quarter 1 Quarter 2
Multiply and divide within 100
Determine which operation (multiplication or division) is needed to determine the unknown whole number
Solve to find the unknown whole number in a multiplication or division equation
Quarter 3
Multiply and divide within 100
Determine which operation (multiplication or division) is needed to determine the unknown whole number
Solve to find the unknown whole number in a multiplication or division equation
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 14
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 15
Students
Solve single operation multiplicationdivision equations containing a single unknown (eg 8x = 48 5= __ divide3 6x6 = ___)
Students know
Strategies for solving simple equations with one unknown
Students understand thatare able to
Efficiently apply strategies for solving simple equations with one unknown
Justify solutions for single unknown equations
Multiplication is putting together equal sized groups and division is sharing into equal-sized shares or is sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models representations
Variables represent unknown quantities when representing mathematical situations algebraically
EE3OA4 Solve addition and subtraction problems when result is unknown with number 0-30
Level IV Students willEE3OA4 Solve addition and subtraction problems when any number in the problem is unknown (result start change difference) with numbers to 50Ex Using base-10 pieces add and subtract two-digit numbers to find the sum and the differenceEx Use pictures of numbers to add and subtract two-digit numbers to find the sum and the difference
Level III Students willEE3OA4 Solve addition and subtraction problems when result is unknown with number 0-30Ex Using base-10 pieces or counters add and subtractEx Use a 100s chart to find the sum or difference of given problemsEx Use count on strategies to add (eg When asked what is 5 + 2 the student says 5 6 7)
Level II Students willEE3OA4 Solve addition and subtraction problems with numbers 0-10Ex Use counters to add and subtractEx Use number lines to add or subtractEx Match the symbol to more or less thanEx Add one to a number by indicating the next number when asked (eg when the teacher says 3 4 5 the student says 6)
Level I Students willEE3OA4 Identify numbers 1 to 9Ex Given a set of five match it to the numberEx Given a set of three identify the number of objects on number linesRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 16
Grade Level 3rdStandard with code 3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2Multiply and divide within 100
Explain how the properties of operations work
Apply properties of operations as strategies to multiply and divide
Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 17
StudentsGiven multiplication and division problems within 100
Use the properties of operations and descriptive language for the property to justify their products and quotients (eg If I know that 8 x 5 is 40 and two more groups of 8 would be 16 then 8 x 7 must be 40 + 16 or 56)
Commutative Property of Multiplication
Associative Property of Multiplication
Distributive Property
Students know
Commutative Associative Identity and Zero Properties of Multiplication and the Distributive Property
Strategies for finding products and quotients
Students understand thatare able to
Strategically and efficiently apply properties of multiplication and division in order to find products and quotients
The order in which factors are multiplied does not change the product
EE3OA5 NA (Multiplication begins at grade 4)
EE3OA5 NA (Multiplication begins at grade 4)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 18
Grade Level 3rdStandard with code 3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when multiplied by 8Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 3
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 19
StudentsGiven a division problem with an unknown quotient
Use a pictorial or physical model to explain the connection between the division problem and the related unknown factor equation
Factor Students know
Strategies for finding quotients and products
Students understand thatare able to
Use symbols to represent unknown quantities in equations
Use mathematical language to communicate the connections between an unknown quotient problem and the related unknown factor problem
Use the inverse relationship between multiplication and division to find quotients
The relationship between multiplication and division (that one undoes the other) can be used to solve problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA6 NA (Division begins at grade 5)
EE3OA6 NA (Division begins at grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 20
Grade Level 3rdStandard with code 3OA7 Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division (eg knowing that 8 times 5 = 40 one knows 40 divide 5 = 8) or properties of operations By the end of Grade 3 know from memory all products of two one-digit numbersDomain Operations and Algebraic Thinking Cluster Multiply and divide within 100
Quarter 1 Quarter 2
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 3
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Version 3 2015-2016 21
AttainmentStudentsGiven any single digit multiplication problem or a division problem with a single digit divisor and an unknown single digit quotient
Use an efficient strategy (eg recall inverse operations arrays derived facts properties of operations etc) to name the product or quotient
Students know
Strategies for finding products and quotients
Students understand thatare able to
Use multiplication and division strategies efficiently based on the numbers in the problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 22
Grade Level 3rdStandard with code 3OA8 Solve two-step word problems using the four operations Represent these problems using equations with a letter standing for the unknown quantity Assess the reasonableness of answers using mental computation and estimation strategies including rounding3
Domain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmetic
Quarter 1
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 2
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 3
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 23
StudentsGiven a variety of two-step word problems involving all four operations
Apply their understanding of operations to explain and justify solutions and solution paths using the connections among a variety of representations including equations with symbols for unknown quantities
Apply their understanding of operations and estimation strategies including rounding to evaluate the reasonableness of their solutions (eg The answer had to be around 125 because its a put together problem and 72 is close to 75 and 56 is close to 50 and 75 plus 50 is 125)
Students know
Characteristics of addition subtraction multiplication and division situations
Addition subtraction multiplication and division strategies
Strategies for mentally computing and estimating sums differences products and quotients
Students understand thatare able to
Strategically use a variety of representations to solve two-step word problems involving all four operations
Use symbols to represent unknown quantities in equations that relate to word problem contexts
Use mathematical language and contextual situations to communicate the connections among the four operations and related physical pictorial or symbolic representations and justify solutionssolution paths
Accurately compute sums differences products and quotients
Use logical reasoning mental computation strategies and estimation strategies to justify the reasonableness of
EE3OA8 Add to solve real world one-step story problems from 0-30
Level IV Students willEE3OA8 Add to solve real world one-step story problems with sums up to 50 using various problem-solving modelsEx Solve by adding (eg ldquoThere are 25 birds in a tree and 10 more joined them How many birds are in a treerdquo)Ex Solve by adding (eg ldquoI have 15 snacks on the cart and 25 snacks in the cupboard how many snacks do I have all together)Ex Solve by adding (eg ldquoAdd the pencils in two boxes and tell how many pencils we haverdquo)
Level III Students willEE3OA8 Add to solve real world one-step story problems from 0-30 Represent the problem in pictures or with objectsEx Solve by adding (eg ldquoHere are 10 pencils We need 10 more for each person to get a pencil How many will we need in allrdquo)Ex Solve by adding (eg ldquoConnie had five marbles Juan gave her eight more marbles How many marbles does Connie have all togetherrdquo)Ex Solve by adding (eg ldquoAdd the crayons in these two boxes and show me how many we have in allrdquo)
Level II Students willEE3OA8 Add to solve word problems identified through symbol representationEx Complete word problems that have pictures rather than wordsEx Solve by adding (eg ldquoThere are three ducks in the pond two more joined How many ducks are in the pondrdquo [picture representation])
Level I Students willEE3OA8 Identify the object(s) that appear in a real world one-step story problemEx Given a simple word problem and asked ldquoWhat is the problem aboutrdquo point to an object from a choice of two that represents what the problem was about (eg box toy)Ex Indicate which object a word problem is about from an array of two choices
Version 3 2015-2016 24
solutions
Multiplication is putting together equal sized groups
Division is sharing into equal-sized shares or as sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models and representations
Solutions can be evaluated by using reasoning to compare the actual solution with estimated solutions
CCSS Math Pacing Guide
Version 3 2015-2016 25
Grade 3
Grade Level 3rdStandard with code 3OA9 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations For example observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addendsDomain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmeticQuarter 1
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 2
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 3
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 26
Students
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations (eg observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends)
Students know
Characteristics of numbers and properties of operations (eg odd even)
Properties from Table 3 etc
Students understand thatare able to
Identify arithmetic patterns in number sequences in the addition table or multiplication table
Use logical reasoning and properties of numbers and operations to explain arithmetic patterns
Characteristics of numbers and properties of operations justify patterns which can be used to reason about mathematical situations form conjectures and solve problems
EE3OA9 Identify arithmetic patterns
Level IV Students willEE3OA9 Complete a complex arithmetic patternEx Complete the pattern using more than two numbers (ie A B C A B C)Ex Using a 100s number chart complete the pattern identified
Level III Students willEE3OA9 Identify arithmetic patternsEx When provided arithmetic patterns on a 100s chart identify the next number in the patternEx When given two number stamps stamp an arithmetic pattern
Level II Students willEE3OA9 Identify a patternEx Make pattern jumps on a number lineEx Sing songs and identify the pattern in the song
Level I Students willEE3OA9 Follow patternsEx Sing ldquoHead Shoulders Knees and Toesrdquo and mimic the patternEx Using tactile objects (fur sand sand fur) in a pattern repeat the patternEx Using manipulatives mimic the teacher to create a pattern
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 27
Grade Level 3rdStandard with code 3NBT1 Use place value understanding to round whole numbers to the nearest 10 or 100Domain Number and Operations in Base Ten
Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 28
StudentsGiven any number less than 1000
Round it to the nearest 10 or 100 and justify the answer using place value vocabulary (eg Rounding 147 to the nearest 10 is 150 because 147 is between 140 and 150 and is more than half way to 150)
Students know
Place value (ones tens hundreds)
Rounding
Students understand thatare able to
Count by 10s and 100s
Determine what is halfway between two multiples of 10 or 100
Round to the nearest 10 or 100
Use place value vocabulary and logical reasoning to justify solutions to rounding problems
Rounding and place value can be used to estimate quantities by changing the original number to the closest multiple of a power of 10
EE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)
Level IV Students willEE3NBT1 Identify the two 10s a number comes in between and tell which is closest (numbers 0-50)Ex Use a color beaded number line to identify the number and round to the closest 10Ex Given a number line separated into tens (0-10 10-20 etc) stand on a number and identify the 10 that is closer
Level III Students willEE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)Ex Use a color beaded number line to identify the two 10s a number falls betweenEx Given the number 14 they would identify 10 and 20
Level II Students willEE3NBT1 Identify tens on a number lineEx Given a number line circle the tensEx Stand on a number chart on 10 20 30 etc
Level I Students willEE3NBT1 Identify a numberEx Point to any number from one to three on a number lineEx Participate in a cake walk When the music stops look to see if they are on the number that is called outEx Identify a number when point to or presented on a cardEx Given a number from one to three point to the number symbolRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 29
Grade Level 3rdStandard with code 3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtractionDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 30
Students
Fluently add and subtract within 1000 using strategies based on place values properties of operations andor the relationship between addition and subtraction
Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning
Students know
Tools for modeling addition and subtraction
Strategies for solving addition and subtraction problems
Methods for symbolically (numerically) recording strategies for solving addition and subtraction problems
Students understand thatare able to
Model addition and subtraction problems using appropriate tools
Record strategies for solving addition and subtraction problems
Communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems
Relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and solution strategies
EE3NBT2 Identify place value to tens
Level IV Students willEE3NBT2 Identify place value to 50Ex Build numbers with place value piecesEx Identify the number in the ones and tens place value (ie the price of an item)Ex Write the number in expanded form ndash 43 = 40 + 3
Level III Students willEE3NBT2 Identify place value to tensEx When given two-digit number cards identify the number in the tens place valueEx When given a group of 10 frame models arrange and count the value of the numberI saw three groups of 10 and five extras so three groups of 10 = 30 and 5 more makes 35
Level II Students willEE3NBT2 Count to 10 using one-to-one correspondenceEx Given a bag of Skittles pull 10 Skittles out of the bagEx Select a domino and tell what number the dots representEx Shown a set of 10 objects create a duplicate collectionEx Given a container of pennies count out 10 from the container
Level I Students willEE3NBT2 Identify more or lessEx Given two collections of objects (group of 10 group of 20) indicate ldquoWhich has morerdquoEx Given math manipulatives representing a single unit and multiple units point to the multiple unit representation when asked ldquowhich is morerdquoRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 31
Grade Level 3rdStandard with code 3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operationsDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 32
Students
Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers
Students know
Place value models for multiplying numbers (eg open arrays place value blocks)
Strategies for multiplying one-digit numbers
Strategies for mentally multiplying one-digit numbers by multiples of powers of 10
Students understand thatare able to
Use mental strategies based on an understanding of place value properties of operations and knowledge of one-digit multiplication to find products
Use a variety of place value models of multiplication problems to justify strategies and solutions
Patterns in the place value system and properties of operations can be used to efficiently compute products
EE3NBT3 Count by tens using money
Level IV Students willEE3NBT3 Compare the value of money based on place valueEx Use money (dimes and pennies) to represent place valueEx Given 15 pennies create a one group of 10 and a group of five ones
Level III Students willEE3NBT3 Count by tens using moneyEx Given three dimes count by 10 to determine totalEx Given five dimes count by 10 to determine total
Level II Students willEE3NBT3 Identify whole numbers to 10Ex Given sets of 10 pennies pair with numbersEx Given sets of 10 pennies pair with dimes
Level I Students willEE3NBT3 Count pennies to 10
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 33
Grade Level 3rdStandard with code 3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1bDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 34
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Pojoaque Valley SchoolsMath Common Core Pacing Guide Introduction
The Pojoaque Valley Schools pacing guide documents are intended to guide teachersrsquo use of Common Core State Standards (CCSS) over the course of an instructional school year The guides identify the focus standards by quarter Teachers should understand that the focus standards emphasize deep instruction for that timeframe However because a certain quarter does not address specific standards it should be understood that previously taught standards should be reinforced while working on the focus standards for any designated quarter Some standards will recur across all quarters due to their importance and need to be addressed on an ongoing basis
The Math pacing guides are grounded in four key components the key fluency expectations for each grade level the critical areas designated in the CCSS Math Standards the Common Core Standards for Mathematics and the integration of the Standards for Mathematical Practice In planning instruction it is important that math teachers incorporate the 8 mathematical practices for mathematics to ensure that the Common Core standards are mastered by all students
The Math CCSS pacing guides contain the following elements Grade Level Identify the grade level of the intended standard Standard with code Defines the knowledge and skills for students The code contains the grade level
domain and standard number Domain Larger groups of related standards Standards from different domains may sometimes be
closely related Cluster Summarize groups of related standards Skills and Knowledge Identified as subsets of the standard and appear in one or more quarters Define
the skills and knowledge embedded in the standard to meet the full intent of the standard itself
Version 3 2015-2016
2
Version 2 of the Pojoaque Valley School District Pacing guides for Reading Language Arts and Mathematics are based on the done by staff and teachers of the school district using the Kentucky model and a synthesis of the excellent work done by Wisconsin Cooperative Educational Service Agency 7 (CESA 7) School Improvement Services Green Bay WI (2010) Standards Insight project
Standards Insight was developed to give educators a tool for in depth investigation of the Common Core State Standards (CCSS) The CCSS are ldquounpackedrdquo or dissected identifying specific knowledge skills vocabulary understandings and evidence of student attainment for each standard Standards Insight may be used by educators to gain a thorough grasp of the CCSS or as a powerful collaborative tool supporting educator teams through the essential conversations necessary for developing shared responsibility for student attainment of all CCSS serves as a high-powered vehicle to help educators examine the standards in a variety of ways
The Version 2 Pojoaque Valley School District Pacing guides present the standard with levels of detail and then the necessary skills by quarter based on the Kentucky model On the second page for each standard the synthesis of the Standards Insight project is presented in a way that further defines and refines the standard such that teachers may use the information to refine their teaching practices
Based on this synthesis of work and the purpose for the unpacking the following fields were selected as most helpful to aid in understanding of the Common Core Standards that will lead to shifts in instruction
1 Evidence of Student Attainment ldquoWhat could students do to show attainment of the standardrdquo
2 Vocabulary ldquoWhat are key terms in the standard that are essential for interpretation and understanding in order for students to learn the contentrdquo
3 Knowledge ldquoWhat does the student need to know in order to aid in attainment of this standardrdquo
4 Skills and Understanding ldquoWhat procedural skill(s) does the student need to demonstrate for attainment of this standardrdquo and ldquoWhat will students understand to attain the standardrdquo
The following fields are included in Version 2
Evidence of Student Attainment This field describes what the standard may look like in student work Specific expectations are listed in performance terms showing what students will say or do to demonstrate attainment of the standard
Standards Vocabulary This field lists words and phrases specific to each standard Shared interpretation and in depth understanding of standards vocabulary are essential for consistent instruction across and within grade levels and content areas
Knowledge The knowledge field lists what students will need to know in order to master each standard (facts vocabulary definitions)
Skills and Understanding The skills field identifies the procedural knowledge students apply in order to Version 3 2015-2016
3
master each standard (actions applications strategies) as well as the overarching understanding that connects the standard knowledge and skills Understandings included in Standards Insight synthesize ideas and have lasting value
Instructional Achievement Level Descriptors This field lists by level what a teacher can expect to see in a student who achieves at a particular level Additionally teachers can use this filed to differentiate instruction to provide further growth for studentrsquos in moving from one level to another This field can be used to provide specific teaching approaches to the standard in question
A Note About High School Standards The high school standards are listed in conceptual categories Conceptual categories portray a coherent view of high school instruction that crosses traditional course boundaries We have done everything possible with teacher input to link individual standards to the appropriate pacing guides
References to Tables References to tables within the standards in the Standards Insight tool refer to Tables 1-5 found in the glossary of the Mathematics Common Core State Standards document found at wwwcorestandardsorg
Version 3 2015-2016
4
Quarterly View of Standards 3 rd Grade Mathematics Pacing Guide
Quarter 1 2 3 43OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
X X
3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
X X
3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
X X
3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations8times = 48 5 = 1048781 divide 3 6 times 6 =
X X
3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication)Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)
X
3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when multiplied by 8 X X3OA7 Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division (eg knowing that 8 times 5 = 40 one knows 40 divide 5 = 8) or properties of operations By the end of Grade 3 know from memory all products of two one-digit numbers
X X
3OA8 Solve two-step word problems using the four operations Represent these problems using equations with a letter standing for the unknown quantity Assess the reasonableness of answers using mental computation and estimation strategies including rounding3
X X X
3OA9 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operationsFor example observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends
X X X
3NBT1 Use place value understanding to round whole numbers to the nearest 10 or 100 X3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtraction
X
3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operations
X
3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1b
X
Version 3 2015-2016 5
Quarter 1 2 3 43NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number line
X
3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction model
X
3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagram
X
3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7
X
3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 pets
X
3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quarters
X
3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units
X
3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units) X3MD7a Relate area to the operations of multiplication and addition a Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengths
X
3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoning
X
3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoning
X
3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problems
X
Version 3 2015-2016 6
Quarter 1 2 3 43MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters
X
3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategories
X
3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape
X
Version 3 2015-2016 7
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and division
Quarter 1 Quarter 2
Find the product of multiple groups of objects
Interpret products of whole numbers as a total number of objects in a number of groups
Quarter 3
Find the product of multiple groups of objects
Interpret products of whole numbers as a total number of objects in a number of groups
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 8
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven any multiplication problem in the form a x b = c
Represent the problem physically or pictorially and describe the relationship between the factors and the product in the equation and the attributes of the representation (ie given 3 x 5 = 15 students make 3 piles of buttons with 5 buttons in each pile They explain that 15 represents the total number of buttons 3 is the number of piles and 5 is the number of buttons in each pile)
Write a corresponding word problem containing a multiplication context
Students know
Characteristics of multiplication contexts
Students understand thatare able to
Represent quantities and operations (multiplication) physically pictorially or symbolically
Use mathematical language to communicate the connections between multiplication equations and related representations
Write word problems containing multiplication contexts
Putting together equal sized groups may be represented by multiplication equations and totals found through multiplication
EE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sum
Level IV Students willEE3OA1-2 Use repeated addition to find the total number of objects arranged in a square or rectangular arrayEx Using tiles in a template identify the total number of tiles by adding the tiles in the templateEx Fill space of squares and rectangles with 1-inch tiles add tiles in rows or columns to determine total number of tiles it takes to fill the shape (squarerectangle)Ex Use an abacus to find the total
Level III Students willEE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sumEx Two birds + two Birds + two birds = six birdsEx Given a repeated addition number sentence use a number line to find the sum
Level II Students willEE3OA1-2 Use addition to find the total number of objectsEx Three apples + four apples = six applesEx Add to find the total number of starsEx Skip count by twos to tell how many
Level I Students willEE3OA1-2 Identify which group has more or less when objects are added or taken awayEx When an object is added to a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoEx When an object is taken from a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 9
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and divisionQuarter 1 Quarter 2
Know what the numbers in a division problem represent
Explain what division means and how it relates to equal shares
Interpret quotients as the number of shares or the number of groups when a set of objects is divided equally
Quarter 3
Know what the numbers in a division problem represent
Explain what division means and how it relates to equal shares
Interpret quotients as the number of shares or the number of groups when a set of objects is divided equally
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 10
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven any division problem in the form a divide b = c
Represent the problem physically or pictorially and describe the relationship between the dividend divisor and quotient in the equation and the attributes of the representation (eg given 15 divide 3 = 5 students make 3 piles of buttons with 5 buttons in each pile and explain that 15 represents the total number of buttons 3 is the number of piles the total was shared among and 5 is the number of buttons in each pile)
Write a corresponding word problem containing a division context
Students know
Characteristics of division contexts
Students understand thatare able to
Represent quantities and operations (division) physically pictorially or symbolically
Use mathematical language to communicate the connections between division equations and related representations
Write word problems containing division contexts
Both partitioning into equal-sized shares and partitioning equally among a given number of groups may be modeled by division equations and the desired results found through division
EE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sum
Level IV Students willEE3OA1-2 Use repeated addition to find the total number of objects arranged in a square or rectangular arrayEx Using tiles in a template identify the total number of tiles by adding the tiles in the templateEx Fill space of squares and rectangles with 1-inch tiles add tiles in rows or columns to determine total number of tiles it takes to fill the shape (squarerectangle)Ex Use an abacus to find the total
Level III Students willEE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sumEx Two birds + two Birds + two birds = six birdsEx Given a repeated addition number sentence use a number line to find the sum
Level II Students willEE3OA1-2 Use addition to find the total number of objectsEx Three apples + four apples = six applesEx Add to find the total number of starsEx Skip count by twos to tell how many
Level I Students willEE3OA1-2 Identify which group has more or less when objects are added or taken awayEx When an object is added to a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoEx When an object is taken from a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 11
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and division
Quarter 1 Quarter 2
Multiply and divide within 100
Solve word problems in situations involving equal groups arrays and measurement quantities
Represent a word problem using a picture an equation with a symbol for the unknown number or in other ways
Quarter 3
Multiply and divide within 100
Solve word problems in situations involving equal groups arrays and measurement quantities
Represent a word problem using a picture an equation with a symbol for the unknown number or in other ways
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 12
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a variety of multiplication and division word problems within 100
Explain and justify solutions and solution paths using connections among a variety of representations (eg place value blocks drawings open arrays and equations with a symbol for the unknown)
See glossary for problem types (Table 2)
Students know
Characteristics of multiplication and division contexts
Multiplication and division strategies
Students understand thatare able to
Represent quantities and operations (multiplication and division) physically pictorially or symbolically
Strategically use a variety of representations to solve multiplication and division word problems
Use informal and mathematical language to communicate the connections among multiplication and division contexts and related physical pictorial or symbolic representations
Accurately compute products and quotients
Use symbols to represent unknown quantities in equations
EE3OA3 See EE3OA1 for repeated addition a foundational skill for multiplication and division (Multiplication begins in grade 4 and division begins in grade 5)
EE3OA3 See EE3OA1 for repeated addition a foundational skill for multiplication and division (Multiplication begins in grade 4 and division begins in grade 5)
Version 3 2015-2016 13
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8times = 48 5 = 1048781 divide 3 6 times 6 = Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and division
Quarter 1 Quarter 2
Multiply and divide within 100
Determine which operation (multiplication or division) is needed to determine the unknown whole number
Solve to find the unknown whole number in a multiplication or division equation
Quarter 3
Multiply and divide within 100
Determine which operation (multiplication or division) is needed to determine the unknown whole number
Solve to find the unknown whole number in a multiplication or division equation
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 14
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 15
Students
Solve single operation multiplicationdivision equations containing a single unknown (eg 8x = 48 5= __ divide3 6x6 = ___)
Students know
Strategies for solving simple equations with one unknown
Students understand thatare able to
Efficiently apply strategies for solving simple equations with one unknown
Justify solutions for single unknown equations
Multiplication is putting together equal sized groups and division is sharing into equal-sized shares or is sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models representations
Variables represent unknown quantities when representing mathematical situations algebraically
EE3OA4 Solve addition and subtraction problems when result is unknown with number 0-30
Level IV Students willEE3OA4 Solve addition and subtraction problems when any number in the problem is unknown (result start change difference) with numbers to 50Ex Using base-10 pieces add and subtract two-digit numbers to find the sum and the differenceEx Use pictures of numbers to add and subtract two-digit numbers to find the sum and the difference
Level III Students willEE3OA4 Solve addition and subtraction problems when result is unknown with number 0-30Ex Using base-10 pieces or counters add and subtractEx Use a 100s chart to find the sum or difference of given problemsEx Use count on strategies to add (eg When asked what is 5 + 2 the student says 5 6 7)
Level II Students willEE3OA4 Solve addition and subtraction problems with numbers 0-10Ex Use counters to add and subtractEx Use number lines to add or subtractEx Match the symbol to more or less thanEx Add one to a number by indicating the next number when asked (eg when the teacher says 3 4 5 the student says 6)
Level I Students willEE3OA4 Identify numbers 1 to 9Ex Given a set of five match it to the numberEx Given a set of three identify the number of objects on number linesRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 16
Grade Level 3rdStandard with code 3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2Multiply and divide within 100
Explain how the properties of operations work
Apply properties of operations as strategies to multiply and divide
Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 17
StudentsGiven multiplication and division problems within 100
Use the properties of operations and descriptive language for the property to justify their products and quotients (eg If I know that 8 x 5 is 40 and two more groups of 8 would be 16 then 8 x 7 must be 40 + 16 or 56)
Commutative Property of Multiplication
Associative Property of Multiplication
Distributive Property
Students know
Commutative Associative Identity and Zero Properties of Multiplication and the Distributive Property
Strategies for finding products and quotients
Students understand thatare able to
Strategically and efficiently apply properties of multiplication and division in order to find products and quotients
The order in which factors are multiplied does not change the product
EE3OA5 NA (Multiplication begins at grade 4)
EE3OA5 NA (Multiplication begins at grade 4)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 18
Grade Level 3rdStandard with code 3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when multiplied by 8Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 3
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 19
StudentsGiven a division problem with an unknown quotient
Use a pictorial or physical model to explain the connection between the division problem and the related unknown factor equation
Factor Students know
Strategies for finding quotients and products
Students understand thatare able to
Use symbols to represent unknown quantities in equations
Use mathematical language to communicate the connections between an unknown quotient problem and the related unknown factor problem
Use the inverse relationship between multiplication and division to find quotients
The relationship between multiplication and division (that one undoes the other) can be used to solve problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA6 NA (Division begins at grade 5)
EE3OA6 NA (Division begins at grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 20
Grade Level 3rdStandard with code 3OA7 Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division (eg knowing that 8 times 5 = 40 one knows 40 divide 5 = 8) or properties of operations By the end of Grade 3 know from memory all products of two one-digit numbersDomain Operations and Algebraic Thinking Cluster Multiply and divide within 100
Quarter 1 Quarter 2
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 3
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Version 3 2015-2016 21
AttainmentStudentsGiven any single digit multiplication problem or a division problem with a single digit divisor and an unknown single digit quotient
Use an efficient strategy (eg recall inverse operations arrays derived facts properties of operations etc) to name the product or quotient
Students know
Strategies for finding products and quotients
Students understand thatare able to
Use multiplication and division strategies efficiently based on the numbers in the problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 22
Grade Level 3rdStandard with code 3OA8 Solve two-step word problems using the four operations Represent these problems using equations with a letter standing for the unknown quantity Assess the reasonableness of answers using mental computation and estimation strategies including rounding3
Domain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmetic
Quarter 1
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 2
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 3
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 23
StudentsGiven a variety of two-step word problems involving all four operations
Apply their understanding of operations to explain and justify solutions and solution paths using the connections among a variety of representations including equations with symbols for unknown quantities
Apply their understanding of operations and estimation strategies including rounding to evaluate the reasonableness of their solutions (eg The answer had to be around 125 because its a put together problem and 72 is close to 75 and 56 is close to 50 and 75 plus 50 is 125)
Students know
Characteristics of addition subtraction multiplication and division situations
Addition subtraction multiplication and division strategies
Strategies for mentally computing and estimating sums differences products and quotients
Students understand thatare able to
Strategically use a variety of representations to solve two-step word problems involving all four operations
Use symbols to represent unknown quantities in equations that relate to word problem contexts
Use mathematical language and contextual situations to communicate the connections among the four operations and related physical pictorial or symbolic representations and justify solutionssolution paths
Accurately compute sums differences products and quotients
Use logical reasoning mental computation strategies and estimation strategies to justify the reasonableness of
EE3OA8 Add to solve real world one-step story problems from 0-30
Level IV Students willEE3OA8 Add to solve real world one-step story problems with sums up to 50 using various problem-solving modelsEx Solve by adding (eg ldquoThere are 25 birds in a tree and 10 more joined them How many birds are in a treerdquo)Ex Solve by adding (eg ldquoI have 15 snacks on the cart and 25 snacks in the cupboard how many snacks do I have all together)Ex Solve by adding (eg ldquoAdd the pencils in two boxes and tell how many pencils we haverdquo)
Level III Students willEE3OA8 Add to solve real world one-step story problems from 0-30 Represent the problem in pictures or with objectsEx Solve by adding (eg ldquoHere are 10 pencils We need 10 more for each person to get a pencil How many will we need in allrdquo)Ex Solve by adding (eg ldquoConnie had five marbles Juan gave her eight more marbles How many marbles does Connie have all togetherrdquo)Ex Solve by adding (eg ldquoAdd the crayons in these two boxes and show me how many we have in allrdquo)
Level II Students willEE3OA8 Add to solve word problems identified through symbol representationEx Complete word problems that have pictures rather than wordsEx Solve by adding (eg ldquoThere are three ducks in the pond two more joined How many ducks are in the pondrdquo [picture representation])
Level I Students willEE3OA8 Identify the object(s) that appear in a real world one-step story problemEx Given a simple word problem and asked ldquoWhat is the problem aboutrdquo point to an object from a choice of two that represents what the problem was about (eg box toy)Ex Indicate which object a word problem is about from an array of two choices
Version 3 2015-2016 24
solutions
Multiplication is putting together equal sized groups
Division is sharing into equal-sized shares or as sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models and representations
Solutions can be evaluated by using reasoning to compare the actual solution with estimated solutions
CCSS Math Pacing Guide
Version 3 2015-2016 25
Grade 3
Grade Level 3rdStandard with code 3OA9 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations For example observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addendsDomain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmeticQuarter 1
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 2
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 3
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 26
Students
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations (eg observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends)
Students know
Characteristics of numbers and properties of operations (eg odd even)
Properties from Table 3 etc
Students understand thatare able to
Identify arithmetic patterns in number sequences in the addition table or multiplication table
Use logical reasoning and properties of numbers and operations to explain arithmetic patterns
Characteristics of numbers and properties of operations justify patterns which can be used to reason about mathematical situations form conjectures and solve problems
EE3OA9 Identify arithmetic patterns
Level IV Students willEE3OA9 Complete a complex arithmetic patternEx Complete the pattern using more than two numbers (ie A B C A B C)Ex Using a 100s number chart complete the pattern identified
Level III Students willEE3OA9 Identify arithmetic patternsEx When provided arithmetic patterns on a 100s chart identify the next number in the patternEx When given two number stamps stamp an arithmetic pattern
Level II Students willEE3OA9 Identify a patternEx Make pattern jumps on a number lineEx Sing songs and identify the pattern in the song
Level I Students willEE3OA9 Follow patternsEx Sing ldquoHead Shoulders Knees and Toesrdquo and mimic the patternEx Using tactile objects (fur sand sand fur) in a pattern repeat the patternEx Using manipulatives mimic the teacher to create a pattern
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 27
Grade Level 3rdStandard with code 3NBT1 Use place value understanding to round whole numbers to the nearest 10 or 100Domain Number and Operations in Base Ten
Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 28
StudentsGiven any number less than 1000
Round it to the nearest 10 or 100 and justify the answer using place value vocabulary (eg Rounding 147 to the nearest 10 is 150 because 147 is between 140 and 150 and is more than half way to 150)
Students know
Place value (ones tens hundreds)
Rounding
Students understand thatare able to
Count by 10s and 100s
Determine what is halfway between two multiples of 10 or 100
Round to the nearest 10 or 100
Use place value vocabulary and logical reasoning to justify solutions to rounding problems
Rounding and place value can be used to estimate quantities by changing the original number to the closest multiple of a power of 10
EE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)
Level IV Students willEE3NBT1 Identify the two 10s a number comes in between and tell which is closest (numbers 0-50)Ex Use a color beaded number line to identify the number and round to the closest 10Ex Given a number line separated into tens (0-10 10-20 etc) stand on a number and identify the 10 that is closer
Level III Students willEE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)Ex Use a color beaded number line to identify the two 10s a number falls betweenEx Given the number 14 they would identify 10 and 20
Level II Students willEE3NBT1 Identify tens on a number lineEx Given a number line circle the tensEx Stand on a number chart on 10 20 30 etc
Level I Students willEE3NBT1 Identify a numberEx Point to any number from one to three on a number lineEx Participate in a cake walk When the music stops look to see if they are on the number that is called outEx Identify a number when point to or presented on a cardEx Given a number from one to three point to the number symbolRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 29
Grade Level 3rdStandard with code 3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtractionDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 30
Students
Fluently add and subtract within 1000 using strategies based on place values properties of operations andor the relationship between addition and subtraction
Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning
Students know
Tools for modeling addition and subtraction
Strategies for solving addition and subtraction problems
Methods for symbolically (numerically) recording strategies for solving addition and subtraction problems
Students understand thatare able to
Model addition and subtraction problems using appropriate tools
Record strategies for solving addition and subtraction problems
Communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems
Relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and solution strategies
EE3NBT2 Identify place value to tens
Level IV Students willEE3NBT2 Identify place value to 50Ex Build numbers with place value piecesEx Identify the number in the ones and tens place value (ie the price of an item)Ex Write the number in expanded form ndash 43 = 40 + 3
Level III Students willEE3NBT2 Identify place value to tensEx When given two-digit number cards identify the number in the tens place valueEx When given a group of 10 frame models arrange and count the value of the numberI saw three groups of 10 and five extras so three groups of 10 = 30 and 5 more makes 35
Level II Students willEE3NBT2 Count to 10 using one-to-one correspondenceEx Given a bag of Skittles pull 10 Skittles out of the bagEx Select a domino and tell what number the dots representEx Shown a set of 10 objects create a duplicate collectionEx Given a container of pennies count out 10 from the container
Level I Students willEE3NBT2 Identify more or lessEx Given two collections of objects (group of 10 group of 20) indicate ldquoWhich has morerdquoEx Given math manipulatives representing a single unit and multiple units point to the multiple unit representation when asked ldquowhich is morerdquoRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 31
Grade Level 3rdStandard with code 3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operationsDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 32
Students
Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers
Students know
Place value models for multiplying numbers (eg open arrays place value blocks)
Strategies for multiplying one-digit numbers
Strategies for mentally multiplying one-digit numbers by multiples of powers of 10
Students understand thatare able to
Use mental strategies based on an understanding of place value properties of operations and knowledge of one-digit multiplication to find products
Use a variety of place value models of multiplication problems to justify strategies and solutions
Patterns in the place value system and properties of operations can be used to efficiently compute products
EE3NBT3 Count by tens using money
Level IV Students willEE3NBT3 Compare the value of money based on place valueEx Use money (dimes and pennies) to represent place valueEx Given 15 pennies create a one group of 10 and a group of five ones
Level III Students willEE3NBT3 Count by tens using moneyEx Given three dimes count by 10 to determine totalEx Given five dimes count by 10 to determine total
Level II Students willEE3NBT3 Identify whole numbers to 10Ex Given sets of 10 pennies pair with numbersEx Given sets of 10 pennies pair with dimes
Level I Students willEE3NBT3 Count pennies to 10
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 33
Grade Level 3rdStandard with code 3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1bDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 34
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Version 2 of the Pojoaque Valley School District Pacing guides for Reading Language Arts and Mathematics are based on the done by staff and teachers of the school district using the Kentucky model and a synthesis of the excellent work done by Wisconsin Cooperative Educational Service Agency 7 (CESA 7) School Improvement Services Green Bay WI (2010) Standards Insight project
Standards Insight was developed to give educators a tool for in depth investigation of the Common Core State Standards (CCSS) The CCSS are ldquounpackedrdquo or dissected identifying specific knowledge skills vocabulary understandings and evidence of student attainment for each standard Standards Insight may be used by educators to gain a thorough grasp of the CCSS or as a powerful collaborative tool supporting educator teams through the essential conversations necessary for developing shared responsibility for student attainment of all CCSS serves as a high-powered vehicle to help educators examine the standards in a variety of ways
The Version 2 Pojoaque Valley School District Pacing guides present the standard with levels of detail and then the necessary skills by quarter based on the Kentucky model On the second page for each standard the synthesis of the Standards Insight project is presented in a way that further defines and refines the standard such that teachers may use the information to refine their teaching practices
Based on this synthesis of work and the purpose for the unpacking the following fields were selected as most helpful to aid in understanding of the Common Core Standards that will lead to shifts in instruction
1 Evidence of Student Attainment ldquoWhat could students do to show attainment of the standardrdquo
2 Vocabulary ldquoWhat are key terms in the standard that are essential for interpretation and understanding in order for students to learn the contentrdquo
3 Knowledge ldquoWhat does the student need to know in order to aid in attainment of this standardrdquo
4 Skills and Understanding ldquoWhat procedural skill(s) does the student need to demonstrate for attainment of this standardrdquo and ldquoWhat will students understand to attain the standardrdquo
The following fields are included in Version 2
Evidence of Student Attainment This field describes what the standard may look like in student work Specific expectations are listed in performance terms showing what students will say or do to demonstrate attainment of the standard
Standards Vocabulary This field lists words and phrases specific to each standard Shared interpretation and in depth understanding of standards vocabulary are essential for consistent instruction across and within grade levels and content areas
Knowledge The knowledge field lists what students will need to know in order to master each standard (facts vocabulary definitions)
Skills and Understanding The skills field identifies the procedural knowledge students apply in order to Version 3 2015-2016
3
master each standard (actions applications strategies) as well as the overarching understanding that connects the standard knowledge and skills Understandings included in Standards Insight synthesize ideas and have lasting value
Instructional Achievement Level Descriptors This field lists by level what a teacher can expect to see in a student who achieves at a particular level Additionally teachers can use this filed to differentiate instruction to provide further growth for studentrsquos in moving from one level to another This field can be used to provide specific teaching approaches to the standard in question
A Note About High School Standards The high school standards are listed in conceptual categories Conceptual categories portray a coherent view of high school instruction that crosses traditional course boundaries We have done everything possible with teacher input to link individual standards to the appropriate pacing guides
References to Tables References to tables within the standards in the Standards Insight tool refer to Tables 1-5 found in the glossary of the Mathematics Common Core State Standards document found at wwwcorestandardsorg
Version 3 2015-2016
4
Quarterly View of Standards 3 rd Grade Mathematics Pacing Guide
Quarter 1 2 3 43OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
X X
3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
X X
3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
X X
3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations8times = 48 5 = 1048781 divide 3 6 times 6 =
X X
3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication)Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)
X
3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when multiplied by 8 X X3OA7 Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division (eg knowing that 8 times 5 = 40 one knows 40 divide 5 = 8) or properties of operations By the end of Grade 3 know from memory all products of two one-digit numbers
X X
3OA8 Solve two-step word problems using the four operations Represent these problems using equations with a letter standing for the unknown quantity Assess the reasonableness of answers using mental computation and estimation strategies including rounding3
X X X
3OA9 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operationsFor example observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends
X X X
3NBT1 Use place value understanding to round whole numbers to the nearest 10 or 100 X3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtraction
X
3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operations
X
3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1b
X
Version 3 2015-2016 5
Quarter 1 2 3 43NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number line
X
3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction model
X
3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagram
X
3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7
X
3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 pets
X
3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quarters
X
3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units
X
3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units) X3MD7a Relate area to the operations of multiplication and addition a Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengths
X
3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoning
X
3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoning
X
3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problems
X
Version 3 2015-2016 6
Quarter 1 2 3 43MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters
X
3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategories
X
3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape
X
Version 3 2015-2016 7
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and division
Quarter 1 Quarter 2
Find the product of multiple groups of objects
Interpret products of whole numbers as a total number of objects in a number of groups
Quarter 3
Find the product of multiple groups of objects
Interpret products of whole numbers as a total number of objects in a number of groups
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 8
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven any multiplication problem in the form a x b = c
Represent the problem physically or pictorially and describe the relationship between the factors and the product in the equation and the attributes of the representation (ie given 3 x 5 = 15 students make 3 piles of buttons with 5 buttons in each pile They explain that 15 represents the total number of buttons 3 is the number of piles and 5 is the number of buttons in each pile)
Write a corresponding word problem containing a multiplication context
Students know
Characteristics of multiplication contexts
Students understand thatare able to
Represent quantities and operations (multiplication) physically pictorially or symbolically
Use mathematical language to communicate the connections between multiplication equations and related representations
Write word problems containing multiplication contexts
Putting together equal sized groups may be represented by multiplication equations and totals found through multiplication
EE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sum
Level IV Students willEE3OA1-2 Use repeated addition to find the total number of objects arranged in a square or rectangular arrayEx Using tiles in a template identify the total number of tiles by adding the tiles in the templateEx Fill space of squares and rectangles with 1-inch tiles add tiles in rows or columns to determine total number of tiles it takes to fill the shape (squarerectangle)Ex Use an abacus to find the total
Level III Students willEE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sumEx Two birds + two Birds + two birds = six birdsEx Given a repeated addition number sentence use a number line to find the sum
Level II Students willEE3OA1-2 Use addition to find the total number of objectsEx Three apples + four apples = six applesEx Add to find the total number of starsEx Skip count by twos to tell how many
Level I Students willEE3OA1-2 Identify which group has more or less when objects are added or taken awayEx When an object is added to a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoEx When an object is taken from a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 9
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and divisionQuarter 1 Quarter 2
Know what the numbers in a division problem represent
Explain what division means and how it relates to equal shares
Interpret quotients as the number of shares or the number of groups when a set of objects is divided equally
Quarter 3
Know what the numbers in a division problem represent
Explain what division means and how it relates to equal shares
Interpret quotients as the number of shares or the number of groups when a set of objects is divided equally
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 10
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven any division problem in the form a divide b = c
Represent the problem physically or pictorially and describe the relationship between the dividend divisor and quotient in the equation and the attributes of the representation (eg given 15 divide 3 = 5 students make 3 piles of buttons with 5 buttons in each pile and explain that 15 represents the total number of buttons 3 is the number of piles the total was shared among and 5 is the number of buttons in each pile)
Write a corresponding word problem containing a division context
Students know
Characteristics of division contexts
Students understand thatare able to
Represent quantities and operations (division) physically pictorially or symbolically
Use mathematical language to communicate the connections between division equations and related representations
Write word problems containing division contexts
Both partitioning into equal-sized shares and partitioning equally among a given number of groups may be modeled by division equations and the desired results found through division
EE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sum
Level IV Students willEE3OA1-2 Use repeated addition to find the total number of objects arranged in a square or rectangular arrayEx Using tiles in a template identify the total number of tiles by adding the tiles in the templateEx Fill space of squares and rectangles with 1-inch tiles add tiles in rows or columns to determine total number of tiles it takes to fill the shape (squarerectangle)Ex Use an abacus to find the total
Level III Students willEE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sumEx Two birds + two Birds + two birds = six birdsEx Given a repeated addition number sentence use a number line to find the sum
Level II Students willEE3OA1-2 Use addition to find the total number of objectsEx Three apples + four apples = six applesEx Add to find the total number of starsEx Skip count by twos to tell how many
Level I Students willEE3OA1-2 Identify which group has more or less when objects are added or taken awayEx When an object is added to a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoEx When an object is taken from a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 11
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and division
Quarter 1 Quarter 2
Multiply and divide within 100
Solve word problems in situations involving equal groups arrays and measurement quantities
Represent a word problem using a picture an equation with a symbol for the unknown number or in other ways
Quarter 3
Multiply and divide within 100
Solve word problems in situations involving equal groups arrays and measurement quantities
Represent a word problem using a picture an equation with a symbol for the unknown number or in other ways
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 12
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a variety of multiplication and division word problems within 100
Explain and justify solutions and solution paths using connections among a variety of representations (eg place value blocks drawings open arrays and equations with a symbol for the unknown)
See glossary for problem types (Table 2)
Students know
Characteristics of multiplication and division contexts
Multiplication and division strategies
Students understand thatare able to
Represent quantities and operations (multiplication and division) physically pictorially or symbolically
Strategically use a variety of representations to solve multiplication and division word problems
Use informal and mathematical language to communicate the connections among multiplication and division contexts and related physical pictorial or symbolic representations
Accurately compute products and quotients
Use symbols to represent unknown quantities in equations
EE3OA3 See EE3OA1 for repeated addition a foundational skill for multiplication and division (Multiplication begins in grade 4 and division begins in grade 5)
EE3OA3 See EE3OA1 for repeated addition a foundational skill for multiplication and division (Multiplication begins in grade 4 and division begins in grade 5)
Version 3 2015-2016 13
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8times = 48 5 = 1048781 divide 3 6 times 6 = Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and division
Quarter 1 Quarter 2
Multiply and divide within 100
Determine which operation (multiplication or division) is needed to determine the unknown whole number
Solve to find the unknown whole number in a multiplication or division equation
Quarter 3
Multiply and divide within 100
Determine which operation (multiplication or division) is needed to determine the unknown whole number
Solve to find the unknown whole number in a multiplication or division equation
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 14
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 15
Students
Solve single operation multiplicationdivision equations containing a single unknown (eg 8x = 48 5= __ divide3 6x6 = ___)
Students know
Strategies for solving simple equations with one unknown
Students understand thatare able to
Efficiently apply strategies for solving simple equations with one unknown
Justify solutions for single unknown equations
Multiplication is putting together equal sized groups and division is sharing into equal-sized shares or is sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models representations
Variables represent unknown quantities when representing mathematical situations algebraically
EE3OA4 Solve addition and subtraction problems when result is unknown with number 0-30
Level IV Students willEE3OA4 Solve addition and subtraction problems when any number in the problem is unknown (result start change difference) with numbers to 50Ex Using base-10 pieces add and subtract two-digit numbers to find the sum and the differenceEx Use pictures of numbers to add and subtract two-digit numbers to find the sum and the difference
Level III Students willEE3OA4 Solve addition and subtraction problems when result is unknown with number 0-30Ex Using base-10 pieces or counters add and subtractEx Use a 100s chart to find the sum or difference of given problemsEx Use count on strategies to add (eg When asked what is 5 + 2 the student says 5 6 7)
Level II Students willEE3OA4 Solve addition and subtraction problems with numbers 0-10Ex Use counters to add and subtractEx Use number lines to add or subtractEx Match the symbol to more or less thanEx Add one to a number by indicating the next number when asked (eg when the teacher says 3 4 5 the student says 6)
Level I Students willEE3OA4 Identify numbers 1 to 9Ex Given a set of five match it to the numberEx Given a set of three identify the number of objects on number linesRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 16
Grade Level 3rdStandard with code 3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2Multiply and divide within 100
Explain how the properties of operations work
Apply properties of operations as strategies to multiply and divide
Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 17
StudentsGiven multiplication and division problems within 100
Use the properties of operations and descriptive language for the property to justify their products and quotients (eg If I know that 8 x 5 is 40 and two more groups of 8 would be 16 then 8 x 7 must be 40 + 16 or 56)
Commutative Property of Multiplication
Associative Property of Multiplication
Distributive Property
Students know
Commutative Associative Identity and Zero Properties of Multiplication and the Distributive Property
Strategies for finding products and quotients
Students understand thatare able to
Strategically and efficiently apply properties of multiplication and division in order to find products and quotients
The order in which factors are multiplied does not change the product
EE3OA5 NA (Multiplication begins at grade 4)
EE3OA5 NA (Multiplication begins at grade 4)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 18
Grade Level 3rdStandard with code 3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when multiplied by 8Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 3
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 19
StudentsGiven a division problem with an unknown quotient
Use a pictorial or physical model to explain the connection between the division problem and the related unknown factor equation
Factor Students know
Strategies for finding quotients and products
Students understand thatare able to
Use symbols to represent unknown quantities in equations
Use mathematical language to communicate the connections between an unknown quotient problem and the related unknown factor problem
Use the inverse relationship between multiplication and division to find quotients
The relationship between multiplication and division (that one undoes the other) can be used to solve problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA6 NA (Division begins at grade 5)
EE3OA6 NA (Division begins at grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 20
Grade Level 3rdStandard with code 3OA7 Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division (eg knowing that 8 times 5 = 40 one knows 40 divide 5 = 8) or properties of operations By the end of Grade 3 know from memory all products of two one-digit numbersDomain Operations and Algebraic Thinking Cluster Multiply and divide within 100
Quarter 1 Quarter 2
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 3
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Version 3 2015-2016 21
AttainmentStudentsGiven any single digit multiplication problem or a division problem with a single digit divisor and an unknown single digit quotient
Use an efficient strategy (eg recall inverse operations arrays derived facts properties of operations etc) to name the product or quotient
Students know
Strategies for finding products and quotients
Students understand thatare able to
Use multiplication and division strategies efficiently based on the numbers in the problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 22
Grade Level 3rdStandard with code 3OA8 Solve two-step word problems using the four operations Represent these problems using equations with a letter standing for the unknown quantity Assess the reasonableness of answers using mental computation and estimation strategies including rounding3
Domain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmetic
Quarter 1
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 2
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 3
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 23
StudentsGiven a variety of two-step word problems involving all four operations
Apply their understanding of operations to explain and justify solutions and solution paths using the connections among a variety of representations including equations with symbols for unknown quantities
Apply their understanding of operations and estimation strategies including rounding to evaluate the reasonableness of their solutions (eg The answer had to be around 125 because its a put together problem and 72 is close to 75 and 56 is close to 50 and 75 plus 50 is 125)
Students know
Characteristics of addition subtraction multiplication and division situations
Addition subtraction multiplication and division strategies
Strategies for mentally computing and estimating sums differences products and quotients
Students understand thatare able to
Strategically use a variety of representations to solve two-step word problems involving all four operations
Use symbols to represent unknown quantities in equations that relate to word problem contexts
Use mathematical language and contextual situations to communicate the connections among the four operations and related physical pictorial or symbolic representations and justify solutionssolution paths
Accurately compute sums differences products and quotients
Use logical reasoning mental computation strategies and estimation strategies to justify the reasonableness of
EE3OA8 Add to solve real world one-step story problems from 0-30
Level IV Students willEE3OA8 Add to solve real world one-step story problems with sums up to 50 using various problem-solving modelsEx Solve by adding (eg ldquoThere are 25 birds in a tree and 10 more joined them How many birds are in a treerdquo)Ex Solve by adding (eg ldquoI have 15 snacks on the cart and 25 snacks in the cupboard how many snacks do I have all together)Ex Solve by adding (eg ldquoAdd the pencils in two boxes and tell how many pencils we haverdquo)
Level III Students willEE3OA8 Add to solve real world one-step story problems from 0-30 Represent the problem in pictures or with objectsEx Solve by adding (eg ldquoHere are 10 pencils We need 10 more for each person to get a pencil How many will we need in allrdquo)Ex Solve by adding (eg ldquoConnie had five marbles Juan gave her eight more marbles How many marbles does Connie have all togetherrdquo)Ex Solve by adding (eg ldquoAdd the crayons in these two boxes and show me how many we have in allrdquo)
Level II Students willEE3OA8 Add to solve word problems identified through symbol representationEx Complete word problems that have pictures rather than wordsEx Solve by adding (eg ldquoThere are three ducks in the pond two more joined How many ducks are in the pondrdquo [picture representation])
Level I Students willEE3OA8 Identify the object(s) that appear in a real world one-step story problemEx Given a simple word problem and asked ldquoWhat is the problem aboutrdquo point to an object from a choice of two that represents what the problem was about (eg box toy)Ex Indicate which object a word problem is about from an array of two choices
Version 3 2015-2016 24
solutions
Multiplication is putting together equal sized groups
Division is sharing into equal-sized shares or as sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models and representations
Solutions can be evaluated by using reasoning to compare the actual solution with estimated solutions
CCSS Math Pacing Guide
Version 3 2015-2016 25
Grade 3
Grade Level 3rdStandard with code 3OA9 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations For example observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addendsDomain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmeticQuarter 1
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 2
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 3
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 26
Students
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations (eg observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends)
Students know
Characteristics of numbers and properties of operations (eg odd even)
Properties from Table 3 etc
Students understand thatare able to
Identify arithmetic patterns in number sequences in the addition table or multiplication table
Use logical reasoning and properties of numbers and operations to explain arithmetic patterns
Characteristics of numbers and properties of operations justify patterns which can be used to reason about mathematical situations form conjectures and solve problems
EE3OA9 Identify arithmetic patterns
Level IV Students willEE3OA9 Complete a complex arithmetic patternEx Complete the pattern using more than two numbers (ie A B C A B C)Ex Using a 100s number chart complete the pattern identified
Level III Students willEE3OA9 Identify arithmetic patternsEx When provided arithmetic patterns on a 100s chart identify the next number in the patternEx When given two number stamps stamp an arithmetic pattern
Level II Students willEE3OA9 Identify a patternEx Make pattern jumps on a number lineEx Sing songs and identify the pattern in the song
Level I Students willEE3OA9 Follow patternsEx Sing ldquoHead Shoulders Knees and Toesrdquo and mimic the patternEx Using tactile objects (fur sand sand fur) in a pattern repeat the patternEx Using manipulatives mimic the teacher to create a pattern
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 27
Grade Level 3rdStandard with code 3NBT1 Use place value understanding to round whole numbers to the nearest 10 or 100Domain Number and Operations in Base Ten
Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 28
StudentsGiven any number less than 1000
Round it to the nearest 10 or 100 and justify the answer using place value vocabulary (eg Rounding 147 to the nearest 10 is 150 because 147 is between 140 and 150 and is more than half way to 150)
Students know
Place value (ones tens hundreds)
Rounding
Students understand thatare able to
Count by 10s and 100s
Determine what is halfway between two multiples of 10 or 100
Round to the nearest 10 or 100
Use place value vocabulary and logical reasoning to justify solutions to rounding problems
Rounding and place value can be used to estimate quantities by changing the original number to the closest multiple of a power of 10
EE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)
Level IV Students willEE3NBT1 Identify the two 10s a number comes in between and tell which is closest (numbers 0-50)Ex Use a color beaded number line to identify the number and round to the closest 10Ex Given a number line separated into tens (0-10 10-20 etc) stand on a number and identify the 10 that is closer
Level III Students willEE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)Ex Use a color beaded number line to identify the two 10s a number falls betweenEx Given the number 14 they would identify 10 and 20
Level II Students willEE3NBT1 Identify tens on a number lineEx Given a number line circle the tensEx Stand on a number chart on 10 20 30 etc
Level I Students willEE3NBT1 Identify a numberEx Point to any number from one to three on a number lineEx Participate in a cake walk When the music stops look to see if they are on the number that is called outEx Identify a number when point to or presented on a cardEx Given a number from one to three point to the number symbolRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 29
Grade Level 3rdStandard with code 3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtractionDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 30
Students
Fluently add and subtract within 1000 using strategies based on place values properties of operations andor the relationship between addition and subtraction
Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning
Students know
Tools for modeling addition and subtraction
Strategies for solving addition and subtraction problems
Methods for symbolically (numerically) recording strategies for solving addition and subtraction problems
Students understand thatare able to
Model addition and subtraction problems using appropriate tools
Record strategies for solving addition and subtraction problems
Communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems
Relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and solution strategies
EE3NBT2 Identify place value to tens
Level IV Students willEE3NBT2 Identify place value to 50Ex Build numbers with place value piecesEx Identify the number in the ones and tens place value (ie the price of an item)Ex Write the number in expanded form ndash 43 = 40 + 3
Level III Students willEE3NBT2 Identify place value to tensEx When given two-digit number cards identify the number in the tens place valueEx When given a group of 10 frame models arrange and count the value of the numberI saw three groups of 10 and five extras so three groups of 10 = 30 and 5 more makes 35
Level II Students willEE3NBT2 Count to 10 using one-to-one correspondenceEx Given a bag of Skittles pull 10 Skittles out of the bagEx Select a domino and tell what number the dots representEx Shown a set of 10 objects create a duplicate collectionEx Given a container of pennies count out 10 from the container
Level I Students willEE3NBT2 Identify more or lessEx Given two collections of objects (group of 10 group of 20) indicate ldquoWhich has morerdquoEx Given math manipulatives representing a single unit and multiple units point to the multiple unit representation when asked ldquowhich is morerdquoRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 31
Grade Level 3rdStandard with code 3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operationsDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 32
Students
Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers
Students know
Place value models for multiplying numbers (eg open arrays place value blocks)
Strategies for multiplying one-digit numbers
Strategies for mentally multiplying one-digit numbers by multiples of powers of 10
Students understand thatare able to
Use mental strategies based on an understanding of place value properties of operations and knowledge of one-digit multiplication to find products
Use a variety of place value models of multiplication problems to justify strategies and solutions
Patterns in the place value system and properties of operations can be used to efficiently compute products
EE3NBT3 Count by tens using money
Level IV Students willEE3NBT3 Compare the value of money based on place valueEx Use money (dimes and pennies) to represent place valueEx Given 15 pennies create a one group of 10 and a group of five ones
Level III Students willEE3NBT3 Count by tens using moneyEx Given three dimes count by 10 to determine totalEx Given five dimes count by 10 to determine total
Level II Students willEE3NBT3 Identify whole numbers to 10Ex Given sets of 10 pennies pair with numbersEx Given sets of 10 pennies pair with dimes
Level I Students willEE3NBT3 Count pennies to 10
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 33
Grade Level 3rdStandard with code 3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1bDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 34
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
master each standard (actions applications strategies) as well as the overarching understanding that connects the standard knowledge and skills Understandings included in Standards Insight synthesize ideas and have lasting value
Instructional Achievement Level Descriptors This field lists by level what a teacher can expect to see in a student who achieves at a particular level Additionally teachers can use this filed to differentiate instruction to provide further growth for studentrsquos in moving from one level to another This field can be used to provide specific teaching approaches to the standard in question
A Note About High School Standards The high school standards are listed in conceptual categories Conceptual categories portray a coherent view of high school instruction that crosses traditional course boundaries We have done everything possible with teacher input to link individual standards to the appropriate pacing guides
References to Tables References to tables within the standards in the Standards Insight tool refer to Tables 1-5 found in the glossary of the Mathematics Common Core State Standards document found at wwwcorestandardsorg
Version 3 2015-2016
4
Quarterly View of Standards 3 rd Grade Mathematics Pacing Guide
Quarter 1 2 3 43OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
X X
3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
X X
3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
X X
3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations8times = 48 5 = 1048781 divide 3 6 times 6 =
X X
3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication)Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)
X
3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when multiplied by 8 X X3OA7 Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division (eg knowing that 8 times 5 = 40 one knows 40 divide 5 = 8) or properties of operations By the end of Grade 3 know from memory all products of two one-digit numbers
X X
3OA8 Solve two-step word problems using the four operations Represent these problems using equations with a letter standing for the unknown quantity Assess the reasonableness of answers using mental computation and estimation strategies including rounding3
X X X
3OA9 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operationsFor example observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends
X X X
3NBT1 Use place value understanding to round whole numbers to the nearest 10 or 100 X3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtraction
X
3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operations
X
3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1b
X
Version 3 2015-2016 5
Quarter 1 2 3 43NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number line
X
3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction model
X
3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagram
X
3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7
X
3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 pets
X
3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quarters
X
3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units
X
3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units) X3MD7a Relate area to the operations of multiplication and addition a Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengths
X
3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoning
X
3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoning
X
3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problems
X
Version 3 2015-2016 6
Quarter 1 2 3 43MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters
X
3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategories
X
3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape
X
Version 3 2015-2016 7
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and division
Quarter 1 Quarter 2
Find the product of multiple groups of objects
Interpret products of whole numbers as a total number of objects in a number of groups
Quarter 3
Find the product of multiple groups of objects
Interpret products of whole numbers as a total number of objects in a number of groups
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 8
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven any multiplication problem in the form a x b = c
Represent the problem physically or pictorially and describe the relationship between the factors and the product in the equation and the attributes of the representation (ie given 3 x 5 = 15 students make 3 piles of buttons with 5 buttons in each pile They explain that 15 represents the total number of buttons 3 is the number of piles and 5 is the number of buttons in each pile)
Write a corresponding word problem containing a multiplication context
Students know
Characteristics of multiplication contexts
Students understand thatare able to
Represent quantities and operations (multiplication) physically pictorially or symbolically
Use mathematical language to communicate the connections between multiplication equations and related representations
Write word problems containing multiplication contexts
Putting together equal sized groups may be represented by multiplication equations and totals found through multiplication
EE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sum
Level IV Students willEE3OA1-2 Use repeated addition to find the total number of objects arranged in a square or rectangular arrayEx Using tiles in a template identify the total number of tiles by adding the tiles in the templateEx Fill space of squares and rectangles with 1-inch tiles add tiles in rows or columns to determine total number of tiles it takes to fill the shape (squarerectangle)Ex Use an abacus to find the total
Level III Students willEE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sumEx Two birds + two Birds + two birds = six birdsEx Given a repeated addition number sentence use a number line to find the sum
Level II Students willEE3OA1-2 Use addition to find the total number of objectsEx Three apples + four apples = six applesEx Add to find the total number of starsEx Skip count by twos to tell how many
Level I Students willEE3OA1-2 Identify which group has more or less when objects are added or taken awayEx When an object is added to a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoEx When an object is taken from a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 9
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and divisionQuarter 1 Quarter 2
Know what the numbers in a division problem represent
Explain what division means and how it relates to equal shares
Interpret quotients as the number of shares or the number of groups when a set of objects is divided equally
Quarter 3
Know what the numbers in a division problem represent
Explain what division means and how it relates to equal shares
Interpret quotients as the number of shares or the number of groups when a set of objects is divided equally
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 10
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven any division problem in the form a divide b = c
Represent the problem physically or pictorially and describe the relationship between the dividend divisor and quotient in the equation and the attributes of the representation (eg given 15 divide 3 = 5 students make 3 piles of buttons with 5 buttons in each pile and explain that 15 represents the total number of buttons 3 is the number of piles the total was shared among and 5 is the number of buttons in each pile)
Write a corresponding word problem containing a division context
Students know
Characteristics of division contexts
Students understand thatare able to
Represent quantities and operations (division) physically pictorially or symbolically
Use mathematical language to communicate the connections between division equations and related representations
Write word problems containing division contexts
Both partitioning into equal-sized shares and partitioning equally among a given number of groups may be modeled by division equations and the desired results found through division
EE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sum
Level IV Students willEE3OA1-2 Use repeated addition to find the total number of objects arranged in a square or rectangular arrayEx Using tiles in a template identify the total number of tiles by adding the tiles in the templateEx Fill space of squares and rectangles with 1-inch tiles add tiles in rows or columns to determine total number of tiles it takes to fill the shape (squarerectangle)Ex Use an abacus to find the total
Level III Students willEE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sumEx Two birds + two Birds + two birds = six birdsEx Given a repeated addition number sentence use a number line to find the sum
Level II Students willEE3OA1-2 Use addition to find the total number of objectsEx Three apples + four apples = six applesEx Add to find the total number of starsEx Skip count by twos to tell how many
Level I Students willEE3OA1-2 Identify which group has more or less when objects are added or taken awayEx When an object is added to a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoEx When an object is taken from a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 11
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and division
Quarter 1 Quarter 2
Multiply and divide within 100
Solve word problems in situations involving equal groups arrays and measurement quantities
Represent a word problem using a picture an equation with a symbol for the unknown number or in other ways
Quarter 3
Multiply and divide within 100
Solve word problems in situations involving equal groups arrays and measurement quantities
Represent a word problem using a picture an equation with a symbol for the unknown number or in other ways
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 12
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a variety of multiplication and division word problems within 100
Explain and justify solutions and solution paths using connections among a variety of representations (eg place value blocks drawings open arrays and equations with a symbol for the unknown)
See glossary for problem types (Table 2)
Students know
Characteristics of multiplication and division contexts
Multiplication and division strategies
Students understand thatare able to
Represent quantities and operations (multiplication and division) physically pictorially or symbolically
Strategically use a variety of representations to solve multiplication and division word problems
Use informal and mathematical language to communicate the connections among multiplication and division contexts and related physical pictorial or symbolic representations
Accurately compute products and quotients
Use symbols to represent unknown quantities in equations
EE3OA3 See EE3OA1 for repeated addition a foundational skill for multiplication and division (Multiplication begins in grade 4 and division begins in grade 5)
EE3OA3 See EE3OA1 for repeated addition a foundational skill for multiplication and division (Multiplication begins in grade 4 and division begins in grade 5)
Version 3 2015-2016 13
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8times = 48 5 = 1048781 divide 3 6 times 6 = Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and division
Quarter 1 Quarter 2
Multiply and divide within 100
Determine which operation (multiplication or division) is needed to determine the unknown whole number
Solve to find the unknown whole number in a multiplication or division equation
Quarter 3
Multiply and divide within 100
Determine which operation (multiplication or division) is needed to determine the unknown whole number
Solve to find the unknown whole number in a multiplication or division equation
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 14
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 15
Students
Solve single operation multiplicationdivision equations containing a single unknown (eg 8x = 48 5= __ divide3 6x6 = ___)
Students know
Strategies for solving simple equations with one unknown
Students understand thatare able to
Efficiently apply strategies for solving simple equations with one unknown
Justify solutions for single unknown equations
Multiplication is putting together equal sized groups and division is sharing into equal-sized shares or is sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models representations
Variables represent unknown quantities when representing mathematical situations algebraically
EE3OA4 Solve addition and subtraction problems when result is unknown with number 0-30
Level IV Students willEE3OA4 Solve addition and subtraction problems when any number in the problem is unknown (result start change difference) with numbers to 50Ex Using base-10 pieces add and subtract two-digit numbers to find the sum and the differenceEx Use pictures of numbers to add and subtract two-digit numbers to find the sum and the difference
Level III Students willEE3OA4 Solve addition and subtraction problems when result is unknown with number 0-30Ex Using base-10 pieces or counters add and subtractEx Use a 100s chart to find the sum or difference of given problemsEx Use count on strategies to add (eg When asked what is 5 + 2 the student says 5 6 7)
Level II Students willEE3OA4 Solve addition and subtraction problems with numbers 0-10Ex Use counters to add and subtractEx Use number lines to add or subtractEx Match the symbol to more or less thanEx Add one to a number by indicating the next number when asked (eg when the teacher says 3 4 5 the student says 6)
Level I Students willEE3OA4 Identify numbers 1 to 9Ex Given a set of five match it to the numberEx Given a set of three identify the number of objects on number linesRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 16
Grade Level 3rdStandard with code 3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2Multiply and divide within 100
Explain how the properties of operations work
Apply properties of operations as strategies to multiply and divide
Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 17
StudentsGiven multiplication and division problems within 100
Use the properties of operations and descriptive language for the property to justify their products and quotients (eg If I know that 8 x 5 is 40 and two more groups of 8 would be 16 then 8 x 7 must be 40 + 16 or 56)
Commutative Property of Multiplication
Associative Property of Multiplication
Distributive Property
Students know
Commutative Associative Identity and Zero Properties of Multiplication and the Distributive Property
Strategies for finding products and quotients
Students understand thatare able to
Strategically and efficiently apply properties of multiplication and division in order to find products and quotients
The order in which factors are multiplied does not change the product
EE3OA5 NA (Multiplication begins at grade 4)
EE3OA5 NA (Multiplication begins at grade 4)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 18
Grade Level 3rdStandard with code 3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when multiplied by 8Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 3
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 19
StudentsGiven a division problem with an unknown quotient
Use a pictorial or physical model to explain the connection between the division problem and the related unknown factor equation
Factor Students know
Strategies for finding quotients and products
Students understand thatare able to
Use symbols to represent unknown quantities in equations
Use mathematical language to communicate the connections between an unknown quotient problem and the related unknown factor problem
Use the inverse relationship between multiplication and division to find quotients
The relationship between multiplication and division (that one undoes the other) can be used to solve problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA6 NA (Division begins at grade 5)
EE3OA6 NA (Division begins at grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 20
Grade Level 3rdStandard with code 3OA7 Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division (eg knowing that 8 times 5 = 40 one knows 40 divide 5 = 8) or properties of operations By the end of Grade 3 know from memory all products of two one-digit numbersDomain Operations and Algebraic Thinking Cluster Multiply and divide within 100
Quarter 1 Quarter 2
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 3
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Version 3 2015-2016 21
AttainmentStudentsGiven any single digit multiplication problem or a division problem with a single digit divisor and an unknown single digit quotient
Use an efficient strategy (eg recall inverse operations arrays derived facts properties of operations etc) to name the product or quotient
Students know
Strategies for finding products and quotients
Students understand thatare able to
Use multiplication and division strategies efficiently based on the numbers in the problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 22
Grade Level 3rdStandard with code 3OA8 Solve two-step word problems using the four operations Represent these problems using equations with a letter standing for the unknown quantity Assess the reasonableness of answers using mental computation and estimation strategies including rounding3
Domain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmetic
Quarter 1
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 2
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 3
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 23
StudentsGiven a variety of two-step word problems involving all four operations
Apply their understanding of operations to explain and justify solutions and solution paths using the connections among a variety of representations including equations with symbols for unknown quantities
Apply their understanding of operations and estimation strategies including rounding to evaluate the reasonableness of their solutions (eg The answer had to be around 125 because its a put together problem and 72 is close to 75 and 56 is close to 50 and 75 plus 50 is 125)
Students know
Characteristics of addition subtraction multiplication and division situations
Addition subtraction multiplication and division strategies
Strategies for mentally computing and estimating sums differences products and quotients
Students understand thatare able to
Strategically use a variety of representations to solve two-step word problems involving all four operations
Use symbols to represent unknown quantities in equations that relate to word problem contexts
Use mathematical language and contextual situations to communicate the connections among the four operations and related physical pictorial or symbolic representations and justify solutionssolution paths
Accurately compute sums differences products and quotients
Use logical reasoning mental computation strategies and estimation strategies to justify the reasonableness of
EE3OA8 Add to solve real world one-step story problems from 0-30
Level IV Students willEE3OA8 Add to solve real world one-step story problems with sums up to 50 using various problem-solving modelsEx Solve by adding (eg ldquoThere are 25 birds in a tree and 10 more joined them How many birds are in a treerdquo)Ex Solve by adding (eg ldquoI have 15 snacks on the cart and 25 snacks in the cupboard how many snacks do I have all together)Ex Solve by adding (eg ldquoAdd the pencils in two boxes and tell how many pencils we haverdquo)
Level III Students willEE3OA8 Add to solve real world one-step story problems from 0-30 Represent the problem in pictures or with objectsEx Solve by adding (eg ldquoHere are 10 pencils We need 10 more for each person to get a pencil How many will we need in allrdquo)Ex Solve by adding (eg ldquoConnie had five marbles Juan gave her eight more marbles How many marbles does Connie have all togetherrdquo)Ex Solve by adding (eg ldquoAdd the crayons in these two boxes and show me how many we have in allrdquo)
Level II Students willEE3OA8 Add to solve word problems identified through symbol representationEx Complete word problems that have pictures rather than wordsEx Solve by adding (eg ldquoThere are three ducks in the pond two more joined How many ducks are in the pondrdquo [picture representation])
Level I Students willEE3OA8 Identify the object(s) that appear in a real world one-step story problemEx Given a simple word problem and asked ldquoWhat is the problem aboutrdquo point to an object from a choice of two that represents what the problem was about (eg box toy)Ex Indicate which object a word problem is about from an array of two choices
Version 3 2015-2016 24
solutions
Multiplication is putting together equal sized groups
Division is sharing into equal-sized shares or as sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models and representations
Solutions can be evaluated by using reasoning to compare the actual solution with estimated solutions
CCSS Math Pacing Guide
Version 3 2015-2016 25
Grade 3
Grade Level 3rdStandard with code 3OA9 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations For example observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addendsDomain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmeticQuarter 1
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 2
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 3
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 26
Students
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations (eg observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends)
Students know
Characteristics of numbers and properties of operations (eg odd even)
Properties from Table 3 etc
Students understand thatare able to
Identify arithmetic patterns in number sequences in the addition table or multiplication table
Use logical reasoning and properties of numbers and operations to explain arithmetic patterns
Characteristics of numbers and properties of operations justify patterns which can be used to reason about mathematical situations form conjectures and solve problems
EE3OA9 Identify arithmetic patterns
Level IV Students willEE3OA9 Complete a complex arithmetic patternEx Complete the pattern using more than two numbers (ie A B C A B C)Ex Using a 100s number chart complete the pattern identified
Level III Students willEE3OA9 Identify arithmetic patternsEx When provided arithmetic patterns on a 100s chart identify the next number in the patternEx When given two number stamps stamp an arithmetic pattern
Level II Students willEE3OA9 Identify a patternEx Make pattern jumps on a number lineEx Sing songs and identify the pattern in the song
Level I Students willEE3OA9 Follow patternsEx Sing ldquoHead Shoulders Knees and Toesrdquo and mimic the patternEx Using tactile objects (fur sand sand fur) in a pattern repeat the patternEx Using manipulatives mimic the teacher to create a pattern
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 27
Grade Level 3rdStandard with code 3NBT1 Use place value understanding to round whole numbers to the nearest 10 or 100Domain Number and Operations in Base Ten
Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 28
StudentsGiven any number less than 1000
Round it to the nearest 10 or 100 and justify the answer using place value vocabulary (eg Rounding 147 to the nearest 10 is 150 because 147 is between 140 and 150 and is more than half way to 150)
Students know
Place value (ones tens hundreds)
Rounding
Students understand thatare able to
Count by 10s and 100s
Determine what is halfway between two multiples of 10 or 100
Round to the nearest 10 or 100
Use place value vocabulary and logical reasoning to justify solutions to rounding problems
Rounding and place value can be used to estimate quantities by changing the original number to the closest multiple of a power of 10
EE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)
Level IV Students willEE3NBT1 Identify the two 10s a number comes in between and tell which is closest (numbers 0-50)Ex Use a color beaded number line to identify the number and round to the closest 10Ex Given a number line separated into tens (0-10 10-20 etc) stand on a number and identify the 10 that is closer
Level III Students willEE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)Ex Use a color beaded number line to identify the two 10s a number falls betweenEx Given the number 14 they would identify 10 and 20
Level II Students willEE3NBT1 Identify tens on a number lineEx Given a number line circle the tensEx Stand on a number chart on 10 20 30 etc
Level I Students willEE3NBT1 Identify a numberEx Point to any number from one to three on a number lineEx Participate in a cake walk When the music stops look to see if they are on the number that is called outEx Identify a number when point to or presented on a cardEx Given a number from one to three point to the number symbolRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 29
Grade Level 3rdStandard with code 3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtractionDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 30
Students
Fluently add and subtract within 1000 using strategies based on place values properties of operations andor the relationship between addition and subtraction
Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning
Students know
Tools for modeling addition and subtraction
Strategies for solving addition and subtraction problems
Methods for symbolically (numerically) recording strategies for solving addition and subtraction problems
Students understand thatare able to
Model addition and subtraction problems using appropriate tools
Record strategies for solving addition and subtraction problems
Communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems
Relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and solution strategies
EE3NBT2 Identify place value to tens
Level IV Students willEE3NBT2 Identify place value to 50Ex Build numbers with place value piecesEx Identify the number in the ones and tens place value (ie the price of an item)Ex Write the number in expanded form ndash 43 = 40 + 3
Level III Students willEE3NBT2 Identify place value to tensEx When given two-digit number cards identify the number in the tens place valueEx When given a group of 10 frame models arrange and count the value of the numberI saw three groups of 10 and five extras so three groups of 10 = 30 and 5 more makes 35
Level II Students willEE3NBT2 Count to 10 using one-to-one correspondenceEx Given a bag of Skittles pull 10 Skittles out of the bagEx Select a domino and tell what number the dots representEx Shown a set of 10 objects create a duplicate collectionEx Given a container of pennies count out 10 from the container
Level I Students willEE3NBT2 Identify more or lessEx Given two collections of objects (group of 10 group of 20) indicate ldquoWhich has morerdquoEx Given math manipulatives representing a single unit and multiple units point to the multiple unit representation when asked ldquowhich is morerdquoRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 31
Grade Level 3rdStandard with code 3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operationsDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 32
Students
Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers
Students know
Place value models for multiplying numbers (eg open arrays place value blocks)
Strategies for multiplying one-digit numbers
Strategies for mentally multiplying one-digit numbers by multiples of powers of 10
Students understand thatare able to
Use mental strategies based on an understanding of place value properties of operations and knowledge of one-digit multiplication to find products
Use a variety of place value models of multiplication problems to justify strategies and solutions
Patterns in the place value system and properties of operations can be used to efficiently compute products
EE3NBT3 Count by tens using money
Level IV Students willEE3NBT3 Compare the value of money based on place valueEx Use money (dimes and pennies) to represent place valueEx Given 15 pennies create a one group of 10 and a group of five ones
Level III Students willEE3NBT3 Count by tens using moneyEx Given three dimes count by 10 to determine totalEx Given five dimes count by 10 to determine total
Level II Students willEE3NBT3 Identify whole numbers to 10Ex Given sets of 10 pennies pair with numbersEx Given sets of 10 pennies pair with dimes
Level I Students willEE3NBT3 Count pennies to 10
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 33
Grade Level 3rdStandard with code 3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1bDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 34
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Quarterly View of Standards 3 rd Grade Mathematics Pacing Guide
Quarter 1 2 3 43OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
X X
3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8
X X
3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
X X
3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations8times = 48 5 = 1048781 divide 3 6 times 6 =
X X
3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication)Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)
X
3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when multiplied by 8 X X3OA7 Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division (eg knowing that 8 times 5 = 40 one knows 40 divide 5 = 8) or properties of operations By the end of Grade 3 know from memory all products of two one-digit numbers
X X
3OA8 Solve two-step word problems using the four operations Represent these problems using equations with a letter standing for the unknown quantity Assess the reasonableness of answers using mental computation and estimation strategies including rounding3
X X X
3OA9 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operationsFor example observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends
X X X
3NBT1 Use place value understanding to round whole numbers to the nearest 10 or 100 X3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtraction
X
3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operations
X
3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1b
X
Version 3 2015-2016 5
Quarter 1 2 3 43NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number line
X
3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction model
X
3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagram
X
3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7
X
3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 pets
X
3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quarters
X
3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units
X
3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units) X3MD7a Relate area to the operations of multiplication and addition a Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengths
X
3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoning
X
3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoning
X
3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problems
X
Version 3 2015-2016 6
Quarter 1 2 3 43MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters
X
3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategories
X
3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape
X
Version 3 2015-2016 7
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and division
Quarter 1 Quarter 2
Find the product of multiple groups of objects
Interpret products of whole numbers as a total number of objects in a number of groups
Quarter 3
Find the product of multiple groups of objects
Interpret products of whole numbers as a total number of objects in a number of groups
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 8
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven any multiplication problem in the form a x b = c
Represent the problem physically or pictorially and describe the relationship between the factors and the product in the equation and the attributes of the representation (ie given 3 x 5 = 15 students make 3 piles of buttons with 5 buttons in each pile They explain that 15 represents the total number of buttons 3 is the number of piles and 5 is the number of buttons in each pile)
Write a corresponding word problem containing a multiplication context
Students know
Characteristics of multiplication contexts
Students understand thatare able to
Represent quantities and operations (multiplication) physically pictorially or symbolically
Use mathematical language to communicate the connections between multiplication equations and related representations
Write word problems containing multiplication contexts
Putting together equal sized groups may be represented by multiplication equations and totals found through multiplication
EE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sum
Level IV Students willEE3OA1-2 Use repeated addition to find the total number of objects arranged in a square or rectangular arrayEx Using tiles in a template identify the total number of tiles by adding the tiles in the templateEx Fill space of squares and rectangles with 1-inch tiles add tiles in rows or columns to determine total number of tiles it takes to fill the shape (squarerectangle)Ex Use an abacus to find the total
Level III Students willEE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sumEx Two birds + two Birds + two birds = six birdsEx Given a repeated addition number sentence use a number line to find the sum
Level II Students willEE3OA1-2 Use addition to find the total number of objectsEx Three apples + four apples = six applesEx Add to find the total number of starsEx Skip count by twos to tell how many
Level I Students willEE3OA1-2 Identify which group has more or less when objects are added or taken awayEx When an object is added to a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoEx When an object is taken from a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 9
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and divisionQuarter 1 Quarter 2
Know what the numbers in a division problem represent
Explain what division means and how it relates to equal shares
Interpret quotients as the number of shares or the number of groups when a set of objects is divided equally
Quarter 3
Know what the numbers in a division problem represent
Explain what division means and how it relates to equal shares
Interpret quotients as the number of shares or the number of groups when a set of objects is divided equally
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 10
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven any division problem in the form a divide b = c
Represent the problem physically or pictorially and describe the relationship between the dividend divisor and quotient in the equation and the attributes of the representation (eg given 15 divide 3 = 5 students make 3 piles of buttons with 5 buttons in each pile and explain that 15 represents the total number of buttons 3 is the number of piles the total was shared among and 5 is the number of buttons in each pile)
Write a corresponding word problem containing a division context
Students know
Characteristics of division contexts
Students understand thatare able to
Represent quantities and operations (division) physically pictorially or symbolically
Use mathematical language to communicate the connections between division equations and related representations
Write word problems containing division contexts
Both partitioning into equal-sized shares and partitioning equally among a given number of groups may be modeled by division equations and the desired results found through division
EE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sum
Level IV Students willEE3OA1-2 Use repeated addition to find the total number of objects arranged in a square or rectangular arrayEx Using tiles in a template identify the total number of tiles by adding the tiles in the templateEx Fill space of squares and rectangles with 1-inch tiles add tiles in rows or columns to determine total number of tiles it takes to fill the shape (squarerectangle)Ex Use an abacus to find the total
Level III Students willEE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sumEx Two birds + two Birds + two birds = six birdsEx Given a repeated addition number sentence use a number line to find the sum
Level II Students willEE3OA1-2 Use addition to find the total number of objectsEx Three apples + four apples = six applesEx Add to find the total number of starsEx Skip count by twos to tell how many
Level I Students willEE3OA1-2 Identify which group has more or less when objects are added or taken awayEx When an object is added to a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoEx When an object is taken from a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 11
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and division
Quarter 1 Quarter 2
Multiply and divide within 100
Solve word problems in situations involving equal groups arrays and measurement quantities
Represent a word problem using a picture an equation with a symbol for the unknown number or in other ways
Quarter 3
Multiply and divide within 100
Solve word problems in situations involving equal groups arrays and measurement quantities
Represent a word problem using a picture an equation with a symbol for the unknown number or in other ways
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 12
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a variety of multiplication and division word problems within 100
Explain and justify solutions and solution paths using connections among a variety of representations (eg place value blocks drawings open arrays and equations with a symbol for the unknown)
See glossary for problem types (Table 2)
Students know
Characteristics of multiplication and division contexts
Multiplication and division strategies
Students understand thatare able to
Represent quantities and operations (multiplication and division) physically pictorially or symbolically
Strategically use a variety of representations to solve multiplication and division word problems
Use informal and mathematical language to communicate the connections among multiplication and division contexts and related physical pictorial or symbolic representations
Accurately compute products and quotients
Use symbols to represent unknown quantities in equations
EE3OA3 See EE3OA1 for repeated addition a foundational skill for multiplication and division (Multiplication begins in grade 4 and division begins in grade 5)
EE3OA3 See EE3OA1 for repeated addition a foundational skill for multiplication and division (Multiplication begins in grade 4 and division begins in grade 5)
Version 3 2015-2016 13
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8times = 48 5 = 1048781 divide 3 6 times 6 = Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and division
Quarter 1 Quarter 2
Multiply and divide within 100
Determine which operation (multiplication or division) is needed to determine the unknown whole number
Solve to find the unknown whole number in a multiplication or division equation
Quarter 3
Multiply and divide within 100
Determine which operation (multiplication or division) is needed to determine the unknown whole number
Solve to find the unknown whole number in a multiplication or division equation
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 14
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 15
Students
Solve single operation multiplicationdivision equations containing a single unknown (eg 8x = 48 5= __ divide3 6x6 = ___)
Students know
Strategies for solving simple equations with one unknown
Students understand thatare able to
Efficiently apply strategies for solving simple equations with one unknown
Justify solutions for single unknown equations
Multiplication is putting together equal sized groups and division is sharing into equal-sized shares or is sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models representations
Variables represent unknown quantities when representing mathematical situations algebraically
EE3OA4 Solve addition and subtraction problems when result is unknown with number 0-30
Level IV Students willEE3OA4 Solve addition and subtraction problems when any number in the problem is unknown (result start change difference) with numbers to 50Ex Using base-10 pieces add and subtract two-digit numbers to find the sum and the differenceEx Use pictures of numbers to add and subtract two-digit numbers to find the sum and the difference
Level III Students willEE3OA4 Solve addition and subtraction problems when result is unknown with number 0-30Ex Using base-10 pieces or counters add and subtractEx Use a 100s chart to find the sum or difference of given problemsEx Use count on strategies to add (eg When asked what is 5 + 2 the student says 5 6 7)
Level II Students willEE3OA4 Solve addition and subtraction problems with numbers 0-10Ex Use counters to add and subtractEx Use number lines to add or subtractEx Match the symbol to more or less thanEx Add one to a number by indicating the next number when asked (eg when the teacher says 3 4 5 the student says 6)
Level I Students willEE3OA4 Identify numbers 1 to 9Ex Given a set of five match it to the numberEx Given a set of three identify the number of objects on number linesRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 16
Grade Level 3rdStandard with code 3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2Multiply and divide within 100
Explain how the properties of operations work
Apply properties of operations as strategies to multiply and divide
Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 17
StudentsGiven multiplication and division problems within 100
Use the properties of operations and descriptive language for the property to justify their products and quotients (eg If I know that 8 x 5 is 40 and two more groups of 8 would be 16 then 8 x 7 must be 40 + 16 or 56)
Commutative Property of Multiplication
Associative Property of Multiplication
Distributive Property
Students know
Commutative Associative Identity and Zero Properties of Multiplication and the Distributive Property
Strategies for finding products and quotients
Students understand thatare able to
Strategically and efficiently apply properties of multiplication and division in order to find products and quotients
The order in which factors are multiplied does not change the product
EE3OA5 NA (Multiplication begins at grade 4)
EE3OA5 NA (Multiplication begins at grade 4)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 18
Grade Level 3rdStandard with code 3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when multiplied by 8Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 3
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 19
StudentsGiven a division problem with an unknown quotient
Use a pictorial or physical model to explain the connection between the division problem and the related unknown factor equation
Factor Students know
Strategies for finding quotients and products
Students understand thatare able to
Use symbols to represent unknown quantities in equations
Use mathematical language to communicate the connections between an unknown quotient problem and the related unknown factor problem
Use the inverse relationship between multiplication and division to find quotients
The relationship between multiplication and division (that one undoes the other) can be used to solve problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA6 NA (Division begins at grade 5)
EE3OA6 NA (Division begins at grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 20
Grade Level 3rdStandard with code 3OA7 Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division (eg knowing that 8 times 5 = 40 one knows 40 divide 5 = 8) or properties of operations By the end of Grade 3 know from memory all products of two one-digit numbersDomain Operations and Algebraic Thinking Cluster Multiply and divide within 100
Quarter 1 Quarter 2
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 3
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Version 3 2015-2016 21
AttainmentStudentsGiven any single digit multiplication problem or a division problem with a single digit divisor and an unknown single digit quotient
Use an efficient strategy (eg recall inverse operations arrays derived facts properties of operations etc) to name the product or quotient
Students know
Strategies for finding products and quotients
Students understand thatare able to
Use multiplication and division strategies efficiently based on the numbers in the problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 22
Grade Level 3rdStandard with code 3OA8 Solve two-step word problems using the four operations Represent these problems using equations with a letter standing for the unknown quantity Assess the reasonableness of answers using mental computation and estimation strategies including rounding3
Domain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmetic
Quarter 1
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 2
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 3
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 23
StudentsGiven a variety of two-step word problems involving all four operations
Apply their understanding of operations to explain and justify solutions and solution paths using the connections among a variety of representations including equations with symbols for unknown quantities
Apply their understanding of operations and estimation strategies including rounding to evaluate the reasonableness of their solutions (eg The answer had to be around 125 because its a put together problem and 72 is close to 75 and 56 is close to 50 and 75 plus 50 is 125)
Students know
Characteristics of addition subtraction multiplication and division situations
Addition subtraction multiplication and division strategies
Strategies for mentally computing and estimating sums differences products and quotients
Students understand thatare able to
Strategically use a variety of representations to solve two-step word problems involving all four operations
Use symbols to represent unknown quantities in equations that relate to word problem contexts
Use mathematical language and contextual situations to communicate the connections among the four operations and related physical pictorial or symbolic representations and justify solutionssolution paths
Accurately compute sums differences products and quotients
Use logical reasoning mental computation strategies and estimation strategies to justify the reasonableness of
EE3OA8 Add to solve real world one-step story problems from 0-30
Level IV Students willEE3OA8 Add to solve real world one-step story problems with sums up to 50 using various problem-solving modelsEx Solve by adding (eg ldquoThere are 25 birds in a tree and 10 more joined them How many birds are in a treerdquo)Ex Solve by adding (eg ldquoI have 15 snacks on the cart and 25 snacks in the cupboard how many snacks do I have all together)Ex Solve by adding (eg ldquoAdd the pencils in two boxes and tell how many pencils we haverdquo)
Level III Students willEE3OA8 Add to solve real world one-step story problems from 0-30 Represent the problem in pictures or with objectsEx Solve by adding (eg ldquoHere are 10 pencils We need 10 more for each person to get a pencil How many will we need in allrdquo)Ex Solve by adding (eg ldquoConnie had five marbles Juan gave her eight more marbles How many marbles does Connie have all togetherrdquo)Ex Solve by adding (eg ldquoAdd the crayons in these two boxes and show me how many we have in allrdquo)
Level II Students willEE3OA8 Add to solve word problems identified through symbol representationEx Complete word problems that have pictures rather than wordsEx Solve by adding (eg ldquoThere are three ducks in the pond two more joined How many ducks are in the pondrdquo [picture representation])
Level I Students willEE3OA8 Identify the object(s) that appear in a real world one-step story problemEx Given a simple word problem and asked ldquoWhat is the problem aboutrdquo point to an object from a choice of two that represents what the problem was about (eg box toy)Ex Indicate which object a word problem is about from an array of two choices
Version 3 2015-2016 24
solutions
Multiplication is putting together equal sized groups
Division is sharing into equal-sized shares or as sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models and representations
Solutions can be evaluated by using reasoning to compare the actual solution with estimated solutions
CCSS Math Pacing Guide
Version 3 2015-2016 25
Grade 3
Grade Level 3rdStandard with code 3OA9 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations For example observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addendsDomain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmeticQuarter 1
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 2
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 3
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 26
Students
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations (eg observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends)
Students know
Characteristics of numbers and properties of operations (eg odd even)
Properties from Table 3 etc
Students understand thatare able to
Identify arithmetic patterns in number sequences in the addition table or multiplication table
Use logical reasoning and properties of numbers and operations to explain arithmetic patterns
Characteristics of numbers and properties of operations justify patterns which can be used to reason about mathematical situations form conjectures and solve problems
EE3OA9 Identify arithmetic patterns
Level IV Students willEE3OA9 Complete a complex arithmetic patternEx Complete the pattern using more than two numbers (ie A B C A B C)Ex Using a 100s number chart complete the pattern identified
Level III Students willEE3OA9 Identify arithmetic patternsEx When provided arithmetic patterns on a 100s chart identify the next number in the patternEx When given two number stamps stamp an arithmetic pattern
Level II Students willEE3OA9 Identify a patternEx Make pattern jumps on a number lineEx Sing songs and identify the pattern in the song
Level I Students willEE3OA9 Follow patternsEx Sing ldquoHead Shoulders Knees and Toesrdquo and mimic the patternEx Using tactile objects (fur sand sand fur) in a pattern repeat the patternEx Using manipulatives mimic the teacher to create a pattern
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 27
Grade Level 3rdStandard with code 3NBT1 Use place value understanding to round whole numbers to the nearest 10 or 100Domain Number and Operations in Base Ten
Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 28
StudentsGiven any number less than 1000
Round it to the nearest 10 or 100 and justify the answer using place value vocabulary (eg Rounding 147 to the nearest 10 is 150 because 147 is between 140 and 150 and is more than half way to 150)
Students know
Place value (ones tens hundreds)
Rounding
Students understand thatare able to
Count by 10s and 100s
Determine what is halfway between two multiples of 10 or 100
Round to the nearest 10 or 100
Use place value vocabulary and logical reasoning to justify solutions to rounding problems
Rounding and place value can be used to estimate quantities by changing the original number to the closest multiple of a power of 10
EE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)
Level IV Students willEE3NBT1 Identify the two 10s a number comes in between and tell which is closest (numbers 0-50)Ex Use a color beaded number line to identify the number and round to the closest 10Ex Given a number line separated into tens (0-10 10-20 etc) stand on a number and identify the 10 that is closer
Level III Students willEE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)Ex Use a color beaded number line to identify the two 10s a number falls betweenEx Given the number 14 they would identify 10 and 20
Level II Students willEE3NBT1 Identify tens on a number lineEx Given a number line circle the tensEx Stand on a number chart on 10 20 30 etc
Level I Students willEE3NBT1 Identify a numberEx Point to any number from one to three on a number lineEx Participate in a cake walk When the music stops look to see if they are on the number that is called outEx Identify a number when point to or presented on a cardEx Given a number from one to three point to the number symbolRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 29
Grade Level 3rdStandard with code 3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtractionDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 30
Students
Fluently add and subtract within 1000 using strategies based on place values properties of operations andor the relationship between addition and subtraction
Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning
Students know
Tools for modeling addition and subtraction
Strategies for solving addition and subtraction problems
Methods for symbolically (numerically) recording strategies for solving addition and subtraction problems
Students understand thatare able to
Model addition and subtraction problems using appropriate tools
Record strategies for solving addition and subtraction problems
Communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems
Relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and solution strategies
EE3NBT2 Identify place value to tens
Level IV Students willEE3NBT2 Identify place value to 50Ex Build numbers with place value piecesEx Identify the number in the ones and tens place value (ie the price of an item)Ex Write the number in expanded form ndash 43 = 40 + 3
Level III Students willEE3NBT2 Identify place value to tensEx When given two-digit number cards identify the number in the tens place valueEx When given a group of 10 frame models arrange and count the value of the numberI saw three groups of 10 and five extras so three groups of 10 = 30 and 5 more makes 35
Level II Students willEE3NBT2 Count to 10 using one-to-one correspondenceEx Given a bag of Skittles pull 10 Skittles out of the bagEx Select a domino and tell what number the dots representEx Shown a set of 10 objects create a duplicate collectionEx Given a container of pennies count out 10 from the container
Level I Students willEE3NBT2 Identify more or lessEx Given two collections of objects (group of 10 group of 20) indicate ldquoWhich has morerdquoEx Given math manipulatives representing a single unit and multiple units point to the multiple unit representation when asked ldquowhich is morerdquoRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 31
Grade Level 3rdStandard with code 3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operationsDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 32
Students
Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers
Students know
Place value models for multiplying numbers (eg open arrays place value blocks)
Strategies for multiplying one-digit numbers
Strategies for mentally multiplying one-digit numbers by multiples of powers of 10
Students understand thatare able to
Use mental strategies based on an understanding of place value properties of operations and knowledge of one-digit multiplication to find products
Use a variety of place value models of multiplication problems to justify strategies and solutions
Patterns in the place value system and properties of operations can be used to efficiently compute products
EE3NBT3 Count by tens using money
Level IV Students willEE3NBT3 Compare the value of money based on place valueEx Use money (dimes and pennies) to represent place valueEx Given 15 pennies create a one group of 10 and a group of five ones
Level III Students willEE3NBT3 Count by tens using moneyEx Given three dimes count by 10 to determine totalEx Given five dimes count by 10 to determine total
Level II Students willEE3NBT3 Identify whole numbers to 10Ex Given sets of 10 pennies pair with numbersEx Given sets of 10 pennies pair with dimes
Level I Students willEE3NBT3 Count pennies to 10
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 33
Grade Level 3rdStandard with code 3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1bDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 34
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Quarter 1 2 3 43NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number line
X
3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction model
X
3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagram
X
3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7
X
3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 pets
X
3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quarters
X
3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units
X
3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units) X3MD7a Relate area to the operations of multiplication and addition a Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengths
X
3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoning
X
3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoning
X
3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problems
X
Version 3 2015-2016 6
Quarter 1 2 3 43MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters
X
3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategories
X
3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape
X
Version 3 2015-2016 7
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and division
Quarter 1 Quarter 2
Find the product of multiple groups of objects
Interpret products of whole numbers as a total number of objects in a number of groups
Quarter 3
Find the product of multiple groups of objects
Interpret products of whole numbers as a total number of objects in a number of groups
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 8
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven any multiplication problem in the form a x b = c
Represent the problem physically or pictorially and describe the relationship between the factors and the product in the equation and the attributes of the representation (ie given 3 x 5 = 15 students make 3 piles of buttons with 5 buttons in each pile They explain that 15 represents the total number of buttons 3 is the number of piles and 5 is the number of buttons in each pile)
Write a corresponding word problem containing a multiplication context
Students know
Characteristics of multiplication contexts
Students understand thatare able to
Represent quantities and operations (multiplication) physically pictorially or symbolically
Use mathematical language to communicate the connections between multiplication equations and related representations
Write word problems containing multiplication contexts
Putting together equal sized groups may be represented by multiplication equations and totals found through multiplication
EE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sum
Level IV Students willEE3OA1-2 Use repeated addition to find the total number of objects arranged in a square or rectangular arrayEx Using tiles in a template identify the total number of tiles by adding the tiles in the templateEx Fill space of squares and rectangles with 1-inch tiles add tiles in rows or columns to determine total number of tiles it takes to fill the shape (squarerectangle)Ex Use an abacus to find the total
Level III Students willEE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sumEx Two birds + two Birds + two birds = six birdsEx Given a repeated addition number sentence use a number line to find the sum
Level II Students willEE3OA1-2 Use addition to find the total number of objectsEx Three apples + four apples = six applesEx Add to find the total number of starsEx Skip count by twos to tell how many
Level I Students willEE3OA1-2 Identify which group has more or less when objects are added or taken awayEx When an object is added to a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoEx When an object is taken from a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 9
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and divisionQuarter 1 Quarter 2
Know what the numbers in a division problem represent
Explain what division means and how it relates to equal shares
Interpret quotients as the number of shares or the number of groups when a set of objects is divided equally
Quarter 3
Know what the numbers in a division problem represent
Explain what division means and how it relates to equal shares
Interpret quotients as the number of shares or the number of groups when a set of objects is divided equally
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 10
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven any division problem in the form a divide b = c
Represent the problem physically or pictorially and describe the relationship between the dividend divisor and quotient in the equation and the attributes of the representation (eg given 15 divide 3 = 5 students make 3 piles of buttons with 5 buttons in each pile and explain that 15 represents the total number of buttons 3 is the number of piles the total was shared among and 5 is the number of buttons in each pile)
Write a corresponding word problem containing a division context
Students know
Characteristics of division contexts
Students understand thatare able to
Represent quantities and operations (division) physically pictorially or symbolically
Use mathematical language to communicate the connections between division equations and related representations
Write word problems containing division contexts
Both partitioning into equal-sized shares and partitioning equally among a given number of groups may be modeled by division equations and the desired results found through division
EE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sum
Level IV Students willEE3OA1-2 Use repeated addition to find the total number of objects arranged in a square or rectangular arrayEx Using tiles in a template identify the total number of tiles by adding the tiles in the templateEx Fill space of squares and rectangles with 1-inch tiles add tiles in rows or columns to determine total number of tiles it takes to fill the shape (squarerectangle)Ex Use an abacus to find the total
Level III Students willEE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sumEx Two birds + two Birds + two birds = six birdsEx Given a repeated addition number sentence use a number line to find the sum
Level II Students willEE3OA1-2 Use addition to find the total number of objectsEx Three apples + four apples = six applesEx Add to find the total number of starsEx Skip count by twos to tell how many
Level I Students willEE3OA1-2 Identify which group has more or less when objects are added or taken awayEx When an object is added to a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoEx When an object is taken from a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 11
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and division
Quarter 1 Quarter 2
Multiply and divide within 100
Solve word problems in situations involving equal groups arrays and measurement quantities
Represent a word problem using a picture an equation with a symbol for the unknown number or in other ways
Quarter 3
Multiply and divide within 100
Solve word problems in situations involving equal groups arrays and measurement quantities
Represent a word problem using a picture an equation with a symbol for the unknown number or in other ways
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 12
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a variety of multiplication and division word problems within 100
Explain and justify solutions and solution paths using connections among a variety of representations (eg place value blocks drawings open arrays and equations with a symbol for the unknown)
See glossary for problem types (Table 2)
Students know
Characteristics of multiplication and division contexts
Multiplication and division strategies
Students understand thatare able to
Represent quantities and operations (multiplication and division) physically pictorially or symbolically
Strategically use a variety of representations to solve multiplication and division word problems
Use informal and mathematical language to communicate the connections among multiplication and division contexts and related physical pictorial or symbolic representations
Accurately compute products and quotients
Use symbols to represent unknown quantities in equations
EE3OA3 See EE3OA1 for repeated addition a foundational skill for multiplication and division (Multiplication begins in grade 4 and division begins in grade 5)
EE3OA3 See EE3OA1 for repeated addition a foundational skill for multiplication and division (Multiplication begins in grade 4 and division begins in grade 5)
Version 3 2015-2016 13
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8times = 48 5 = 1048781 divide 3 6 times 6 = Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and division
Quarter 1 Quarter 2
Multiply and divide within 100
Determine which operation (multiplication or division) is needed to determine the unknown whole number
Solve to find the unknown whole number in a multiplication or division equation
Quarter 3
Multiply and divide within 100
Determine which operation (multiplication or division) is needed to determine the unknown whole number
Solve to find the unknown whole number in a multiplication or division equation
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 14
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 15
Students
Solve single operation multiplicationdivision equations containing a single unknown (eg 8x = 48 5= __ divide3 6x6 = ___)
Students know
Strategies for solving simple equations with one unknown
Students understand thatare able to
Efficiently apply strategies for solving simple equations with one unknown
Justify solutions for single unknown equations
Multiplication is putting together equal sized groups and division is sharing into equal-sized shares or is sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models representations
Variables represent unknown quantities when representing mathematical situations algebraically
EE3OA4 Solve addition and subtraction problems when result is unknown with number 0-30
Level IV Students willEE3OA4 Solve addition and subtraction problems when any number in the problem is unknown (result start change difference) with numbers to 50Ex Using base-10 pieces add and subtract two-digit numbers to find the sum and the differenceEx Use pictures of numbers to add and subtract two-digit numbers to find the sum and the difference
Level III Students willEE3OA4 Solve addition and subtraction problems when result is unknown with number 0-30Ex Using base-10 pieces or counters add and subtractEx Use a 100s chart to find the sum or difference of given problemsEx Use count on strategies to add (eg When asked what is 5 + 2 the student says 5 6 7)
Level II Students willEE3OA4 Solve addition and subtraction problems with numbers 0-10Ex Use counters to add and subtractEx Use number lines to add or subtractEx Match the symbol to more or less thanEx Add one to a number by indicating the next number when asked (eg when the teacher says 3 4 5 the student says 6)
Level I Students willEE3OA4 Identify numbers 1 to 9Ex Given a set of five match it to the numberEx Given a set of three identify the number of objects on number linesRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 16
Grade Level 3rdStandard with code 3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2Multiply and divide within 100
Explain how the properties of operations work
Apply properties of operations as strategies to multiply and divide
Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 17
StudentsGiven multiplication and division problems within 100
Use the properties of operations and descriptive language for the property to justify their products and quotients (eg If I know that 8 x 5 is 40 and two more groups of 8 would be 16 then 8 x 7 must be 40 + 16 or 56)
Commutative Property of Multiplication
Associative Property of Multiplication
Distributive Property
Students know
Commutative Associative Identity and Zero Properties of Multiplication and the Distributive Property
Strategies for finding products and quotients
Students understand thatare able to
Strategically and efficiently apply properties of multiplication and division in order to find products and quotients
The order in which factors are multiplied does not change the product
EE3OA5 NA (Multiplication begins at grade 4)
EE3OA5 NA (Multiplication begins at grade 4)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 18
Grade Level 3rdStandard with code 3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when multiplied by 8Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 3
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 19
StudentsGiven a division problem with an unknown quotient
Use a pictorial or physical model to explain the connection between the division problem and the related unknown factor equation
Factor Students know
Strategies for finding quotients and products
Students understand thatare able to
Use symbols to represent unknown quantities in equations
Use mathematical language to communicate the connections between an unknown quotient problem and the related unknown factor problem
Use the inverse relationship between multiplication and division to find quotients
The relationship between multiplication and division (that one undoes the other) can be used to solve problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA6 NA (Division begins at grade 5)
EE3OA6 NA (Division begins at grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 20
Grade Level 3rdStandard with code 3OA7 Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division (eg knowing that 8 times 5 = 40 one knows 40 divide 5 = 8) or properties of operations By the end of Grade 3 know from memory all products of two one-digit numbersDomain Operations and Algebraic Thinking Cluster Multiply and divide within 100
Quarter 1 Quarter 2
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 3
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Version 3 2015-2016 21
AttainmentStudentsGiven any single digit multiplication problem or a division problem with a single digit divisor and an unknown single digit quotient
Use an efficient strategy (eg recall inverse operations arrays derived facts properties of operations etc) to name the product or quotient
Students know
Strategies for finding products and quotients
Students understand thatare able to
Use multiplication and division strategies efficiently based on the numbers in the problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 22
Grade Level 3rdStandard with code 3OA8 Solve two-step word problems using the four operations Represent these problems using equations with a letter standing for the unknown quantity Assess the reasonableness of answers using mental computation and estimation strategies including rounding3
Domain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmetic
Quarter 1
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 2
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 3
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 23
StudentsGiven a variety of two-step word problems involving all four operations
Apply their understanding of operations to explain and justify solutions and solution paths using the connections among a variety of representations including equations with symbols for unknown quantities
Apply their understanding of operations and estimation strategies including rounding to evaluate the reasonableness of their solutions (eg The answer had to be around 125 because its a put together problem and 72 is close to 75 and 56 is close to 50 and 75 plus 50 is 125)
Students know
Characteristics of addition subtraction multiplication and division situations
Addition subtraction multiplication and division strategies
Strategies for mentally computing and estimating sums differences products and quotients
Students understand thatare able to
Strategically use a variety of representations to solve two-step word problems involving all four operations
Use symbols to represent unknown quantities in equations that relate to word problem contexts
Use mathematical language and contextual situations to communicate the connections among the four operations and related physical pictorial or symbolic representations and justify solutionssolution paths
Accurately compute sums differences products and quotients
Use logical reasoning mental computation strategies and estimation strategies to justify the reasonableness of
EE3OA8 Add to solve real world one-step story problems from 0-30
Level IV Students willEE3OA8 Add to solve real world one-step story problems with sums up to 50 using various problem-solving modelsEx Solve by adding (eg ldquoThere are 25 birds in a tree and 10 more joined them How many birds are in a treerdquo)Ex Solve by adding (eg ldquoI have 15 snacks on the cart and 25 snacks in the cupboard how many snacks do I have all together)Ex Solve by adding (eg ldquoAdd the pencils in two boxes and tell how many pencils we haverdquo)
Level III Students willEE3OA8 Add to solve real world one-step story problems from 0-30 Represent the problem in pictures or with objectsEx Solve by adding (eg ldquoHere are 10 pencils We need 10 more for each person to get a pencil How many will we need in allrdquo)Ex Solve by adding (eg ldquoConnie had five marbles Juan gave her eight more marbles How many marbles does Connie have all togetherrdquo)Ex Solve by adding (eg ldquoAdd the crayons in these two boxes and show me how many we have in allrdquo)
Level II Students willEE3OA8 Add to solve word problems identified through symbol representationEx Complete word problems that have pictures rather than wordsEx Solve by adding (eg ldquoThere are three ducks in the pond two more joined How many ducks are in the pondrdquo [picture representation])
Level I Students willEE3OA8 Identify the object(s) that appear in a real world one-step story problemEx Given a simple word problem and asked ldquoWhat is the problem aboutrdquo point to an object from a choice of two that represents what the problem was about (eg box toy)Ex Indicate which object a word problem is about from an array of two choices
Version 3 2015-2016 24
solutions
Multiplication is putting together equal sized groups
Division is sharing into equal-sized shares or as sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models and representations
Solutions can be evaluated by using reasoning to compare the actual solution with estimated solutions
CCSS Math Pacing Guide
Version 3 2015-2016 25
Grade 3
Grade Level 3rdStandard with code 3OA9 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations For example observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addendsDomain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmeticQuarter 1
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 2
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 3
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 26
Students
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations (eg observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends)
Students know
Characteristics of numbers and properties of operations (eg odd even)
Properties from Table 3 etc
Students understand thatare able to
Identify arithmetic patterns in number sequences in the addition table or multiplication table
Use logical reasoning and properties of numbers and operations to explain arithmetic patterns
Characteristics of numbers and properties of operations justify patterns which can be used to reason about mathematical situations form conjectures and solve problems
EE3OA9 Identify arithmetic patterns
Level IV Students willEE3OA9 Complete a complex arithmetic patternEx Complete the pattern using more than two numbers (ie A B C A B C)Ex Using a 100s number chart complete the pattern identified
Level III Students willEE3OA9 Identify arithmetic patternsEx When provided arithmetic patterns on a 100s chart identify the next number in the patternEx When given two number stamps stamp an arithmetic pattern
Level II Students willEE3OA9 Identify a patternEx Make pattern jumps on a number lineEx Sing songs and identify the pattern in the song
Level I Students willEE3OA9 Follow patternsEx Sing ldquoHead Shoulders Knees and Toesrdquo and mimic the patternEx Using tactile objects (fur sand sand fur) in a pattern repeat the patternEx Using manipulatives mimic the teacher to create a pattern
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 27
Grade Level 3rdStandard with code 3NBT1 Use place value understanding to round whole numbers to the nearest 10 or 100Domain Number and Operations in Base Ten
Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 28
StudentsGiven any number less than 1000
Round it to the nearest 10 or 100 and justify the answer using place value vocabulary (eg Rounding 147 to the nearest 10 is 150 because 147 is between 140 and 150 and is more than half way to 150)
Students know
Place value (ones tens hundreds)
Rounding
Students understand thatare able to
Count by 10s and 100s
Determine what is halfway between two multiples of 10 or 100
Round to the nearest 10 or 100
Use place value vocabulary and logical reasoning to justify solutions to rounding problems
Rounding and place value can be used to estimate quantities by changing the original number to the closest multiple of a power of 10
EE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)
Level IV Students willEE3NBT1 Identify the two 10s a number comes in between and tell which is closest (numbers 0-50)Ex Use a color beaded number line to identify the number and round to the closest 10Ex Given a number line separated into tens (0-10 10-20 etc) stand on a number and identify the 10 that is closer
Level III Students willEE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)Ex Use a color beaded number line to identify the two 10s a number falls betweenEx Given the number 14 they would identify 10 and 20
Level II Students willEE3NBT1 Identify tens on a number lineEx Given a number line circle the tensEx Stand on a number chart on 10 20 30 etc
Level I Students willEE3NBT1 Identify a numberEx Point to any number from one to three on a number lineEx Participate in a cake walk When the music stops look to see if they are on the number that is called outEx Identify a number when point to or presented on a cardEx Given a number from one to three point to the number symbolRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 29
Grade Level 3rdStandard with code 3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtractionDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 30
Students
Fluently add and subtract within 1000 using strategies based on place values properties of operations andor the relationship between addition and subtraction
Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning
Students know
Tools for modeling addition and subtraction
Strategies for solving addition and subtraction problems
Methods for symbolically (numerically) recording strategies for solving addition and subtraction problems
Students understand thatare able to
Model addition and subtraction problems using appropriate tools
Record strategies for solving addition and subtraction problems
Communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems
Relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and solution strategies
EE3NBT2 Identify place value to tens
Level IV Students willEE3NBT2 Identify place value to 50Ex Build numbers with place value piecesEx Identify the number in the ones and tens place value (ie the price of an item)Ex Write the number in expanded form ndash 43 = 40 + 3
Level III Students willEE3NBT2 Identify place value to tensEx When given two-digit number cards identify the number in the tens place valueEx When given a group of 10 frame models arrange and count the value of the numberI saw three groups of 10 and five extras so three groups of 10 = 30 and 5 more makes 35
Level II Students willEE3NBT2 Count to 10 using one-to-one correspondenceEx Given a bag of Skittles pull 10 Skittles out of the bagEx Select a domino and tell what number the dots representEx Shown a set of 10 objects create a duplicate collectionEx Given a container of pennies count out 10 from the container
Level I Students willEE3NBT2 Identify more or lessEx Given two collections of objects (group of 10 group of 20) indicate ldquoWhich has morerdquoEx Given math manipulatives representing a single unit and multiple units point to the multiple unit representation when asked ldquowhich is morerdquoRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 31
Grade Level 3rdStandard with code 3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operationsDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 32
Students
Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers
Students know
Place value models for multiplying numbers (eg open arrays place value blocks)
Strategies for multiplying one-digit numbers
Strategies for mentally multiplying one-digit numbers by multiples of powers of 10
Students understand thatare able to
Use mental strategies based on an understanding of place value properties of operations and knowledge of one-digit multiplication to find products
Use a variety of place value models of multiplication problems to justify strategies and solutions
Patterns in the place value system and properties of operations can be used to efficiently compute products
EE3NBT3 Count by tens using money
Level IV Students willEE3NBT3 Compare the value of money based on place valueEx Use money (dimes and pennies) to represent place valueEx Given 15 pennies create a one group of 10 and a group of five ones
Level III Students willEE3NBT3 Count by tens using moneyEx Given three dimes count by 10 to determine totalEx Given five dimes count by 10 to determine total
Level II Students willEE3NBT3 Identify whole numbers to 10Ex Given sets of 10 pennies pair with numbersEx Given sets of 10 pennies pair with dimes
Level I Students willEE3NBT3 Count pennies to 10
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 33
Grade Level 3rdStandard with code 3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1bDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 34
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Quarter 1 2 3 43MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters
X
3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategories
X
3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape
X
Version 3 2015-2016 7
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and division
Quarter 1 Quarter 2
Find the product of multiple groups of objects
Interpret products of whole numbers as a total number of objects in a number of groups
Quarter 3
Find the product of multiple groups of objects
Interpret products of whole numbers as a total number of objects in a number of groups
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 8
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven any multiplication problem in the form a x b = c
Represent the problem physically or pictorially and describe the relationship between the factors and the product in the equation and the attributes of the representation (ie given 3 x 5 = 15 students make 3 piles of buttons with 5 buttons in each pile They explain that 15 represents the total number of buttons 3 is the number of piles and 5 is the number of buttons in each pile)
Write a corresponding word problem containing a multiplication context
Students know
Characteristics of multiplication contexts
Students understand thatare able to
Represent quantities and operations (multiplication) physically pictorially or symbolically
Use mathematical language to communicate the connections between multiplication equations and related representations
Write word problems containing multiplication contexts
Putting together equal sized groups may be represented by multiplication equations and totals found through multiplication
EE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sum
Level IV Students willEE3OA1-2 Use repeated addition to find the total number of objects arranged in a square or rectangular arrayEx Using tiles in a template identify the total number of tiles by adding the tiles in the templateEx Fill space of squares and rectangles with 1-inch tiles add tiles in rows or columns to determine total number of tiles it takes to fill the shape (squarerectangle)Ex Use an abacus to find the total
Level III Students willEE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sumEx Two birds + two Birds + two birds = six birdsEx Given a repeated addition number sentence use a number line to find the sum
Level II Students willEE3OA1-2 Use addition to find the total number of objectsEx Three apples + four apples = six applesEx Add to find the total number of starsEx Skip count by twos to tell how many
Level I Students willEE3OA1-2 Identify which group has more or less when objects are added or taken awayEx When an object is added to a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoEx When an object is taken from a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 9
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and divisionQuarter 1 Quarter 2
Know what the numbers in a division problem represent
Explain what division means and how it relates to equal shares
Interpret quotients as the number of shares or the number of groups when a set of objects is divided equally
Quarter 3
Know what the numbers in a division problem represent
Explain what division means and how it relates to equal shares
Interpret quotients as the number of shares or the number of groups when a set of objects is divided equally
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 10
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven any division problem in the form a divide b = c
Represent the problem physically or pictorially and describe the relationship between the dividend divisor and quotient in the equation and the attributes of the representation (eg given 15 divide 3 = 5 students make 3 piles of buttons with 5 buttons in each pile and explain that 15 represents the total number of buttons 3 is the number of piles the total was shared among and 5 is the number of buttons in each pile)
Write a corresponding word problem containing a division context
Students know
Characteristics of division contexts
Students understand thatare able to
Represent quantities and operations (division) physically pictorially or symbolically
Use mathematical language to communicate the connections between division equations and related representations
Write word problems containing division contexts
Both partitioning into equal-sized shares and partitioning equally among a given number of groups may be modeled by division equations and the desired results found through division
EE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sum
Level IV Students willEE3OA1-2 Use repeated addition to find the total number of objects arranged in a square or rectangular arrayEx Using tiles in a template identify the total number of tiles by adding the tiles in the templateEx Fill space of squares and rectangles with 1-inch tiles add tiles in rows or columns to determine total number of tiles it takes to fill the shape (squarerectangle)Ex Use an abacus to find the total
Level III Students willEE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sumEx Two birds + two Birds + two birds = six birdsEx Given a repeated addition number sentence use a number line to find the sum
Level II Students willEE3OA1-2 Use addition to find the total number of objectsEx Three apples + four apples = six applesEx Add to find the total number of starsEx Skip count by twos to tell how many
Level I Students willEE3OA1-2 Identify which group has more or less when objects are added or taken awayEx When an object is added to a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoEx When an object is taken from a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 11
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and division
Quarter 1 Quarter 2
Multiply and divide within 100
Solve word problems in situations involving equal groups arrays and measurement quantities
Represent a word problem using a picture an equation with a symbol for the unknown number or in other ways
Quarter 3
Multiply and divide within 100
Solve word problems in situations involving equal groups arrays and measurement quantities
Represent a word problem using a picture an equation with a symbol for the unknown number or in other ways
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 12
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a variety of multiplication and division word problems within 100
Explain and justify solutions and solution paths using connections among a variety of representations (eg place value blocks drawings open arrays and equations with a symbol for the unknown)
See glossary for problem types (Table 2)
Students know
Characteristics of multiplication and division contexts
Multiplication and division strategies
Students understand thatare able to
Represent quantities and operations (multiplication and division) physically pictorially or symbolically
Strategically use a variety of representations to solve multiplication and division word problems
Use informal and mathematical language to communicate the connections among multiplication and division contexts and related physical pictorial or symbolic representations
Accurately compute products and quotients
Use symbols to represent unknown quantities in equations
EE3OA3 See EE3OA1 for repeated addition a foundational skill for multiplication and division (Multiplication begins in grade 4 and division begins in grade 5)
EE3OA3 See EE3OA1 for repeated addition a foundational skill for multiplication and division (Multiplication begins in grade 4 and division begins in grade 5)
Version 3 2015-2016 13
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8times = 48 5 = 1048781 divide 3 6 times 6 = Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and division
Quarter 1 Quarter 2
Multiply and divide within 100
Determine which operation (multiplication or division) is needed to determine the unknown whole number
Solve to find the unknown whole number in a multiplication or division equation
Quarter 3
Multiply and divide within 100
Determine which operation (multiplication or division) is needed to determine the unknown whole number
Solve to find the unknown whole number in a multiplication or division equation
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 14
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 15
Students
Solve single operation multiplicationdivision equations containing a single unknown (eg 8x = 48 5= __ divide3 6x6 = ___)
Students know
Strategies for solving simple equations with one unknown
Students understand thatare able to
Efficiently apply strategies for solving simple equations with one unknown
Justify solutions for single unknown equations
Multiplication is putting together equal sized groups and division is sharing into equal-sized shares or is sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models representations
Variables represent unknown quantities when representing mathematical situations algebraically
EE3OA4 Solve addition and subtraction problems when result is unknown with number 0-30
Level IV Students willEE3OA4 Solve addition and subtraction problems when any number in the problem is unknown (result start change difference) with numbers to 50Ex Using base-10 pieces add and subtract two-digit numbers to find the sum and the differenceEx Use pictures of numbers to add and subtract two-digit numbers to find the sum and the difference
Level III Students willEE3OA4 Solve addition and subtraction problems when result is unknown with number 0-30Ex Using base-10 pieces or counters add and subtractEx Use a 100s chart to find the sum or difference of given problemsEx Use count on strategies to add (eg When asked what is 5 + 2 the student says 5 6 7)
Level II Students willEE3OA4 Solve addition and subtraction problems with numbers 0-10Ex Use counters to add and subtractEx Use number lines to add or subtractEx Match the symbol to more or less thanEx Add one to a number by indicating the next number when asked (eg when the teacher says 3 4 5 the student says 6)
Level I Students willEE3OA4 Identify numbers 1 to 9Ex Given a set of five match it to the numberEx Given a set of three identify the number of objects on number linesRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 16
Grade Level 3rdStandard with code 3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2Multiply and divide within 100
Explain how the properties of operations work
Apply properties of operations as strategies to multiply and divide
Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 17
StudentsGiven multiplication and division problems within 100
Use the properties of operations and descriptive language for the property to justify their products and quotients (eg If I know that 8 x 5 is 40 and two more groups of 8 would be 16 then 8 x 7 must be 40 + 16 or 56)
Commutative Property of Multiplication
Associative Property of Multiplication
Distributive Property
Students know
Commutative Associative Identity and Zero Properties of Multiplication and the Distributive Property
Strategies for finding products and quotients
Students understand thatare able to
Strategically and efficiently apply properties of multiplication and division in order to find products and quotients
The order in which factors are multiplied does not change the product
EE3OA5 NA (Multiplication begins at grade 4)
EE3OA5 NA (Multiplication begins at grade 4)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 18
Grade Level 3rdStandard with code 3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when multiplied by 8Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 3
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 19
StudentsGiven a division problem with an unknown quotient
Use a pictorial or physical model to explain the connection between the division problem and the related unknown factor equation
Factor Students know
Strategies for finding quotients and products
Students understand thatare able to
Use symbols to represent unknown quantities in equations
Use mathematical language to communicate the connections between an unknown quotient problem and the related unknown factor problem
Use the inverse relationship between multiplication and division to find quotients
The relationship between multiplication and division (that one undoes the other) can be used to solve problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA6 NA (Division begins at grade 5)
EE3OA6 NA (Division begins at grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 20
Grade Level 3rdStandard with code 3OA7 Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division (eg knowing that 8 times 5 = 40 one knows 40 divide 5 = 8) or properties of operations By the end of Grade 3 know from memory all products of two one-digit numbersDomain Operations and Algebraic Thinking Cluster Multiply and divide within 100
Quarter 1 Quarter 2
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 3
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Version 3 2015-2016 21
AttainmentStudentsGiven any single digit multiplication problem or a division problem with a single digit divisor and an unknown single digit quotient
Use an efficient strategy (eg recall inverse operations arrays derived facts properties of operations etc) to name the product or quotient
Students know
Strategies for finding products and quotients
Students understand thatare able to
Use multiplication and division strategies efficiently based on the numbers in the problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 22
Grade Level 3rdStandard with code 3OA8 Solve two-step word problems using the four operations Represent these problems using equations with a letter standing for the unknown quantity Assess the reasonableness of answers using mental computation and estimation strategies including rounding3
Domain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmetic
Quarter 1
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 2
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 3
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 23
StudentsGiven a variety of two-step word problems involving all four operations
Apply their understanding of operations to explain and justify solutions and solution paths using the connections among a variety of representations including equations with symbols for unknown quantities
Apply their understanding of operations and estimation strategies including rounding to evaluate the reasonableness of their solutions (eg The answer had to be around 125 because its a put together problem and 72 is close to 75 and 56 is close to 50 and 75 plus 50 is 125)
Students know
Characteristics of addition subtraction multiplication and division situations
Addition subtraction multiplication and division strategies
Strategies for mentally computing and estimating sums differences products and quotients
Students understand thatare able to
Strategically use a variety of representations to solve two-step word problems involving all four operations
Use symbols to represent unknown quantities in equations that relate to word problem contexts
Use mathematical language and contextual situations to communicate the connections among the four operations and related physical pictorial or symbolic representations and justify solutionssolution paths
Accurately compute sums differences products and quotients
Use logical reasoning mental computation strategies and estimation strategies to justify the reasonableness of
EE3OA8 Add to solve real world one-step story problems from 0-30
Level IV Students willEE3OA8 Add to solve real world one-step story problems with sums up to 50 using various problem-solving modelsEx Solve by adding (eg ldquoThere are 25 birds in a tree and 10 more joined them How many birds are in a treerdquo)Ex Solve by adding (eg ldquoI have 15 snacks on the cart and 25 snacks in the cupboard how many snacks do I have all together)Ex Solve by adding (eg ldquoAdd the pencils in two boxes and tell how many pencils we haverdquo)
Level III Students willEE3OA8 Add to solve real world one-step story problems from 0-30 Represent the problem in pictures or with objectsEx Solve by adding (eg ldquoHere are 10 pencils We need 10 more for each person to get a pencil How many will we need in allrdquo)Ex Solve by adding (eg ldquoConnie had five marbles Juan gave her eight more marbles How many marbles does Connie have all togetherrdquo)Ex Solve by adding (eg ldquoAdd the crayons in these two boxes and show me how many we have in allrdquo)
Level II Students willEE3OA8 Add to solve word problems identified through symbol representationEx Complete word problems that have pictures rather than wordsEx Solve by adding (eg ldquoThere are three ducks in the pond two more joined How many ducks are in the pondrdquo [picture representation])
Level I Students willEE3OA8 Identify the object(s) that appear in a real world one-step story problemEx Given a simple word problem and asked ldquoWhat is the problem aboutrdquo point to an object from a choice of two that represents what the problem was about (eg box toy)Ex Indicate which object a word problem is about from an array of two choices
Version 3 2015-2016 24
solutions
Multiplication is putting together equal sized groups
Division is sharing into equal-sized shares or as sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models and representations
Solutions can be evaluated by using reasoning to compare the actual solution with estimated solutions
CCSS Math Pacing Guide
Version 3 2015-2016 25
Grade 3
Grade Level 3rdStandard with code 3OA9 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations For example observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addendsDomain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmeticQuarter 1
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 2
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 3
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 26
Students
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations (eg observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends)
Students know
Characteristics of numbers and properties of operations (eg odd even)
Properties from Table 3 etc
Students understand thatare able to
Identify arithmetic patterns in number sequences in the addition table or multiplication table
Use logical reasoning and properties of numbers and operations to explain arithmetic patterns
Characteristics of numbers and properties of operations justify patterns which can be used to reason about mathematical situations form conjectures and solve problems
EE3OA9 Identify arithmetic patterns
Level IV Students willEE3OA9 Complete a complex arithmetic patternEx Complete the pattern using more than two numbers (ie A B C A B C)Ex Using a 100s number chart complete the pattern identified
Level III Students willEE3OA9 Identify arithmetic patternsEx When provided arithmetic patterns on a 100s chart identify the next number in the patternEx When given two number stamps stamp an arithmetic pattern
Level II Students willEE3OA9 Identify a patternEx Make pattern jumps on a number lineEx Sing songs and identify the pattern in the song
Level I Students willEE3OA9 Follow patternsEx Sing ldquoHead Shoulders Knees and Toesrdquo and mimic the patternEx Using tactile objects (fur sand sand fur) in a pattern repeat the patternEx Using manipulatives mimic the teacher to create a pattern
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 27
Grade Level 3rdStandard with code 3NBT1 Use place value understanding to round whole numbers to the nearest 10 or 100Domain Number and Operations in Base Ten
Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 28
StudentsGiven any number less than 1000
Round it to the nearest 10 or 100 and justify the answer using place value vocabulary (eg Rounding 147 to the nearest 10 is 150 because 147 is between 140 and 150 and is more than half way to 150)
Students know
Place value (ones tens hundreds)
Rounding
Students understand thatare able to
Count by 10s and 100s
Determine what is halfway between two multiples of 10 or 100
Round to the nearest 10 or 100
Use place value vocabulary and logical reasoning to justify solutions to rounding problems
Rounding and place value can be used to estimate quantities by changing the original number to the closest multiple of a power of 10
EE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)
Level IV Students willEE3NBT1 Identify the two 10s a number comes in between and tell which is closest (numbers 0-50)Ex Use a color beaded number line to identify the number and round to the closest 10Ex Given a number line separated into tens (0-10 10-20 etc) stand on a number and identify the 10 that is closer
Level III Students willEE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)Ex Use a color beaded number line to identify the two 10s a number falls betweenEx Given the number 14 they would identify 10 and 20
Level II Students willEE3NBT1 Identify tens on a number lineEx Given a number line circle the tensEx Stand on a number chart on 10 20 30 etc
Level I Students willEE3NBT1 Identify a numberEx Point to any number from one to three on a number lineEx Participate in a cake walk When the music stops look to see if they are on the number that is called outEx Identify a number when point to or presented on a cardEx Given a number from one to three point to the number symbolRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 29
Grade Level 3rdStandard with code 3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtractionDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 30
Students
Fluently add and subtract within 1000 using strategies based on place values properties of operations andor the relationship between addition and subtraction
Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning
Students know
Tools for modeling addition and subtraction
Strategies for solving addition and subtraction problems
Methods for symbolically (numerically) recording strategies for solving addition and subtraction problems
Students understand thatare able to
Model addition and subtraction problems using appropriate tools
Record strategies for solving addition and subtraction problems
Communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems
Relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and solution strategies
EE3NBT2 Identify place value to tens
Level IV Students willEE3NBT2 Identify place value to 50Ex Build numbers with place value piecesEx Identify the number in the ones and tens place value (ie the price of an item)Ex Write the number in expanded form ndash 43 = 40 + 3
Level III Students willEE3NBT2 Identify place value to tensEx When given two-digit number cards identify the number in the tens place valueEx When given a group of 10 frame models arrange and count the value of the numberI saw three groups of 10 and five extras so three groups of 10 = 30 and 5 more makes 35
Level II Students willEE3NBT2 Count to 10 using one-to-one correspondenceEx Given a bag of Skittles pull 10 Skittles out of the bagEx Select a domino and tell what number the dots representEx Shown a set of 10 objects create a duplicate collectionEx Given a container of pennies count out 10 from the container
Level I Students willEE3NBT2 Identify more or lessEx Given two collections of objects (group of 10 group of 20) indicate ldquoWhich has morerdquoEx Given math manipulatives representing a single unit and multiple units point to the multiple unit representation when asked ldquowhich is morerdquoRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 31
Grade Level 3rdStandard with code 3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operationsDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 32
Students
Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers
Students know
Place value models for multiplying numbers (eg open arrays place value blocks)
Strategies for multiplying one-digit numbers
Strategies for mentally multiplying one-digit numbers by multiples of powers of 10
Students understand thatare able to
Use mental strategies based on an understanding of place value properties of operations and knowledge of one-digit multiplication to find products
Use a variety of place value models of multiplication problems to justify strategies and solutions
Patterns in the place value system and properties of operations can be used to efficiently compute products
EE3NBT3 Count by tens using money
Level IV Students willEE3NBT3 Compare the value of money based on place valueEx Use money (dimes and pennies) to represent place valueEx Given 15 pennies create a one group of 10 and a group of five ones
Level III Students willEE3NBT3 Count by tens using moneyEx Given three dimes count by 10 to determine totalEx Given five dimes count by 10 to determine total
Level II Students willEE3NBT3 Identify whole numbers to 10Ex Given sets of 10 pennies pair with numbersEx Given sets of 10 pennies pair with dimes
Level I Students willEE3NBT3 Count pennies to 10
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 33
Grade Level 3rdStandard with code 3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1bDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 34
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7
Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and division
Quarter 1 Quarter 2
Find the product of multiple groups of objects
Interpret products of whole numbers as a total number of objects in a number of groups
Quarter 3
Find the product of multiple groups of objects
Interpret products of whole numbers as a total number of objects in a number of groups
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 8
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven any multiplication problem in the form a x b = c
Represent the problem physically or pictorially and describe the relationship between the factors and the product in the equation and the attributes of the representation (ie given 3 x 5 = 15 students make 3 piles of buttons with 5 buttons in each pile They explain that 15 represents the total number of buttons 3 is the number of piles and 5 is the number of buttons in each pile)
Write a corresponding word problem containing a multiplication context
Students know
Characteristics of multiplication contexts
Students understand thatare able to
Represent quantities and operations (multiplication) physically pictorially or symbolically
Use mathematical language to communicate the connections between multiplication equations and related representations
Write word problems containing multiplication contexts
Putting together equal sized groups may be represented by multiplication equations and totals found through multiplication
EE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sum
Level IV Students willEE3OA1-2 Use repeated addition to find the total number of objects arranged in a square or rectangular arrayEx Using tiles in a template identify the total number of tiles by adding the tiles in the templateEx Fill space of squares and rectangles with 1-inch tiles add tiles in rows or columns to determine total number of tiles it takes to fill the shape (squarerectangle)Ex Use an abacus to find the total
Level III Students willEE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sumEx Two birds + two Birds + two birds = six birdsEx Given a repeated addition number sentence use a number line to find the sum
Level II Students willEE3OA1-2 Use addition to find the total number of objectsEx Three apples + four apples = six applesEx Add to find the total number of starsEx Skip count by twos to tell how many
Level I Students willEE3OA1-2 Identify which group has more or less when objects are added or taken awayEx When an object is added to a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoEx When an object is taken from a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 9
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and divisionQuarter 1 Quarter 2
Know what the numbers in a division problem represent
Explain what division means and how it relates to equal shares
Interpret quotients as the number of shares or the number of groups when a set of objects is divided equally
Quarter 3
Know what the numbers in a division problem represent
Explain what division means and how it relates to equal shares
Interpret quotients as the number of shares or the number of groups when a set of objects is divided equally
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 10
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven any division problem in the form a divide b = c
Represent the problem physically or pictorially and describe the relationship between the dividend divisor and quotient in the equation and the attributes of the representation (eg given 15 divide 3 = 5 students make 3 piles of buttons with 5 buttons in each pile and explain that 15 represents the total number of buttons 3 is the number of piles the total was shared among and 5 is the number of buttons in each pile)
Write a corresponding word problem containing a division context
Students know
Characteristics of division contexts
Students understand thatare able to
Represent quantities and operations (division) physically pictorially or symbolically
Use mathematical language to communicate the connections between division equations and related representations
Write word problems containing division contexts
Both partitioning into equal-sized shares and partitioning equally among a given number of groups may be modeled by division equations and the desired results found through division
EE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sum
Level IV Students willEE3OA1-2 Use repeated addition to find the total number of objects arranged in a square or rectangular arrayEx Using tiles in a template identify the total number of tiles by adding the tiles in the templateEx Fill space of squares and rectangles with 1-inch tiles add tiles in rows or columns to determine total number of tiles it takes to fill the shape (squarerectangle)Ex Use an abacus to find the total
Level III Students willEE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sumEx Two birds + two Birds + two birds = six birdsEx Given a repeated addition number sentence use a number line to find the sum
Level II Students willEE3OA1-2 Use addition to find the total number of objectsEx Three apples + four apples = six applesEx Add to find the total number of starsEx Skip count by twos to tell how many
Level I Students willEE3OA1-2 Identify which group has more or less when objects are added or taken awayEx When an object is added to a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoEx When an object is taken from a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 11
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and division
Quarter 1 Quarter 2
Multiply and divide within 100
Solve word problems in situations involving equal groups arrays and measurement quantities
Represent a word problem using a picture an equation with a symbol for the unknown number or in other ways
Quarter 3
Multiply and divide within 100
Solve word problems in situations involving equal groups arrays and measurement quantities
Represent a word problem using a picture an equation with a symbol for the unknown number or in other ways
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 12
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a variety of multiplication and division word problems within 100
Explain and justify solutions and solution paths using connections among a variety of representations (eg place value blocks drawings open arrays and equations with a symbol for the unknown)
See glossary for problem types (Table 2)
Students know
Characteristics of multiplication and division contexts
Multiplication and division strategies
Students understand thatare able to
Represent quantities and operations (multiplication and division) physically pictorially or symbolically
Strategically use a variety of representations to solve multiplication and division word problems
Use informal and mathematical language to communicate the connections among multiplication and division contexts and related physical pictorial or symbolic representations
Accurately compute products and quotients
Use symbols to represent unknown quantities in equations
EE3OA3 See EE3OA1 for repeated addition a foundational skill for multiplication and division (Multiplication begins in grade 4 and division begins in grade 5)
EE3OA3 See EE3OA1 for repeated addition a foundational skill for multiplication and division (Multiplication begins in grade 4 and division begins in grade 5)
Version 3 2015-2016 13
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8times = 48 5 = 1048781 divide 3 6 times 6 = Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and division
Quarter 1 Quarter 2
Multiply and divide within 100
Determine which operation (multiplication or division) is needed to determine the unknown whole number
Solve to find the unknown whole number in a multiplication or division equation
Quarter 3
Multiply and divide within 100
Determine which operation (multiplication or division) is needed to determine the unknown whole number
Solve to find the unknown whole number in a multiplication or division equation
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 14
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 15
Students
Solve single operation multiplicationdivision equations containing a single unknown (eg 8x = 48 5= __ divide3 6x6 = ___)
Students know
Strategies for solving simple equations with one unknown
Students understand thatare able to
Efficiently apply strategies for solving simple equations with one unknown
Justify solutions for single unknown equations
Multiplication is putting together equal sized groups and division is sharing into equal-sized shares or is sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models representations
Variables represent unknown quantities when representing mathematical situations algebraically
EE3OA4 Solve addition and subtraction problems when result is unknown with number 0-30
Level IV Students willEE3OA4 Solve addition and subtraction problems when any number in the problem is unknown (result start change difference) with numbers to 50Ex Using base-10 pieces add and subtract two-digit numbers to find the sum and the differenceEx Use pictures of numbers to add and subtract two-digit numbers to find the sum and the difference
Level III Students willEE3OA4 Solve addition and subtraction problems when result is unknown with number 0-30Ex Using base-10 pieces or counters add and subtractEx Use a 100s chart to find the sum or difference of given problemsEx Use count on strategies to add (eg When asked what is 5 + 2 the student says 5 6 7)
Level II Students willEE3OA4 Solve addition and subtraction problems with numbers 0-10Ex Use counters to add and subtractEx Use number lines to add or subtractEx Match the symbol to more or less thanEx Add one to a number by indicating the next number when asked (eg when the teacher says 3 4 5 the student says 6)
Level I Students willEE3OA4 Identify numbers 1 to 9Ex Given a set of five match it to the numberEx Given a set of three identify the number of objects on number linesRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 16
Grade Level 3rdStandard with code 3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2Multiply and divide within 100
Explain how the properties of operations work
Apply properties of operations as strategies to multiply and divide
Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 17
StudentsGiven multiplication and division problems within 100
Use the properties of operations and descriptive language for the property to justify their products and quotients (eg If I know that 8 x 5 is 40 and two more groups of 8 would be 16 then 8 x 7 must be 40 + 16 or 56)
Commutative Property of Multiplication
Associative Property of Multiplication
Distributive Property
Students know
Commutative Associative Identity and Zero Properties of Multiplication and the Distributive Property
Strategies for finding products and quotients
Students understand thatare able to
Strategically and efficiently apply properties of multiplication and division in order to find products and quotients
The order in which factors are multiplied does not change the product
EE3OA5 NA (Multiplication begins at grade 4)
EE3OA5 NA (Multiplication begins at grade 4)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 18
Grade Level 3rdStandard with code 3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when multiplied by 8Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 3
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 19
StudentsGiven a division problem with an unknown quotient
Use a pictorial or physical model to explain the connection between the division problem and the related unknown factor equation
Factor Students know
Strategies for finding quotients and products
Students understand thatare able to
Use symbols to represent unknown quantities in equations
Use mathematical language to communicate the connections between an unknown quotient problem and the related unknown factor problem
Use the inverse relationship between multiplication and division to find quotients
The relationship between multiplication and division (that one undoes the other) can be used to solve problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA6 NA (Division begins at grade 5)
EE3OA6 NA (Division begins at grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 20
Grade Level 3rdStandard with code 3OA7 Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division (eg knowing that 8 times 5 = 40 one knows 40 divide 5 = 8) or properties of operations By the end of Grade 3 know from memory all products of two one-digit numbersDomain Operations and Algebraic Thinking Cluster Multiply and divide within 100
Quarter 1 Quarter 2
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 3
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Version 3 2015-2016 21
AttainmentStudentsGiven any single digit multiplication problem or a division problem with a single digit divisor and an unknown single digit quotient
Use an efficient strategy (eg recall inverse operations arrays derived facts properties of operations etc) to name the product or quotient
Students know
Strategies for finding products and quotients
Students understand thatare able to
Use multiplication and division strategies efficiently based on the numbers in the problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 22
Grade Level 3rdStandard with code 3OA8 Solve two-step word problems using the four operations Represent these problems using equations with a letter standing for the unknown quantity Assess the reasonableness of answers using mental computation and estimation strategies including rounding3
Domain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmetic
Quarter 1
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 2
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 3
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 23
StudentsGiven a variety of two-step word problems involving all four operations
Apply their understanding of operations to explain and justify solutions and solution paths using the connections among a variety of representations including equations with symbols for unknown quantities
Apply their understanding of operations and estimation strategies including rounding to evaluate the reasonableness of their solutions (eg The answer had to be around 125 because its a put together problem and 72 is close to 75 and 56 is close to 50 and 75 plus 50 is 125)
Students know
Characteristics of addition subtraction multiplication and division situations
Addition subtraction multiplication and division strategies
Strategies for mentally computing and estimating sums differences products and quotients
Students understand thatare able to
Strategically use a variety of representations to solve two-step word problems involving all four operations
Use symbols to represent unknown quantities in equations that relate to word problem contexts
Use mathematical language and contextual situations to communicate the connections among the four operations and related physical pictorial or symbolic representations and justify solutionssolution paths
Accurately compute sums differences products and quotients
Use logical reasoning mental computation strategies and estimation strategies to justify the reasonableness of
EE3OA8 Add to solve real world one-step story problems from 0-30
Level IV Students willEE3OA8 Add to solve real world one-step story problems with sums up to 50 using various problem-solving modelsEx Solve by adding (eg ldquoThere are 25 birds in a tree and 10 more joined them How many birds are in a treerdquo)Ex Solve by adding (eg ldquoI have 15 snacks on the cart and 25 snacks in the cupboard how many snacks do I have all together)Ex Solve by adding (eg ldquoAdd the pencils in two boxes and tell how many pencils we haverdquo)
Level III Students willEE3OA8 Add to solve real world one-step story problems from 0-30 Represent the problem in pictures or with objectsEx Solve by adding (eg ldquoHere are 10 pencils We need 10 more for each person to get a pencil How many will we need in allrdquo)Ex Solve by adding (eg ldquoConnie had five marbles Juan gave her eight more marbles How many marbles does Connie have all togetherrdquo)Ex Solve by adding (eg ldquoAdd the crayons in these two boxes and show me how many we have in allrdquo)
Level II Students willEE3OA8 Add to solve word problems identified through symbol representationEx Complete word problems that have pictures rather than wordsEx Solve by adding (eg ldquoThere are three ducks in the pond two more joined How many ducks are in the pondrdquo [picture representation])
Level I Students willEE3OA8 Identify the object(s) that appear in a real world one-step story problemEx Given a simple word problem and asked ldquoWhat is the problem aboutrdquo point to an object from a choice of two that represents what the problem was about (eg box toy)Ex Indicate which object a word problem is about from an array of two choices
Version 3 2015-2016 24
solutions
Multiplication is putting together equal sized groups
Division is sharing into equal-sized shares or as sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models and representations
Solutions can be evaluated by using reasoning to compare the actual solution with estimated solutions
CCSS Math Pacing Guide
Version 3 2015-2016 25
Grade 3
Grade Level 3rdStandard with code 3OA9 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations For example observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addendsDomain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmeticQuarter 1
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 2
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 3
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 26
Students
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations (eg observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends)
Students know
Characteristics of numbers and properties of operations (eg odd even)
Properties from Table 3 etc
Students understand thatare able to
Identify arithmetic patterns in number sequences in the addition table or multiplication table
Use logical reasoning and properties of numbers and operations to explain arithmetic patterns
Characteristics of numbers and properties of operations justify patterns which can be used to reason about mathematical situations form conjectures and solve problems
EE3OA9 Identify arithmetic patterns
Level IV Students willEE3OA9 Complete a complex arithmetic patternEx Complete the pattern using more than two numbers (ie A B C A B C)Ex Using a 100s number chart complete the pattern identified
Level III Students willEE3OA9 Identify arithmetic patternsEx When provided arithmetic patterns on a 100s chart identify the next number in the patternEx When given two number stamps stamp an arithmetic pattern
Level II Students willEE3OA9 Identify a patternEx Make pattern jumps on a number lineEx Sing songs and identify the pattern in the song
Level I Students willEE3OA9 Follow patternsEx Sing ldquoHead Shoulders Knees and Toesrdquo and mimic the patternEx Using tactile objects (fur sand sand fur) in a pattern repeat the patternEx Using manipulatives mimic the teacher to create a pattern
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 27
Grade Level 3rdStandard with code 3NBT1 Use place value understanding to round whole numbers to the nearest 10 or 100Domain Number and Operations in Base Ten
Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 28
StudentsGiven any number less than 1000
Round it to the nearest 10 or 100 and justify the answer using place value vocabulary (eg Rounding 147 to the nearest 10 is 150 because 147 is between 140 and 150 and is more than half way to 150)
Students know
Place value (ones tens hundreds)
Rounding
Students understand thatare able to
Count by 10s and 100s
Determine what is halfway between two multiples of 10 or 100
Round to the nearest 10 or 100
Use place value vocabulary and logical reasoning to justify solutions to rounding problems
Rounding and place value can be used to estimate quantities by changing the original number to the closest multiple of a power of 10
EE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)
Level IV Students willEE3NBT1 Identify the two 10s a number comes in between and tell which is closest (numbers 0-50)Ex Use a color beaded number line to identify the number and round to the closest 10Ex Given a number line separated into tens (0-10 10-20 etc) stand on a number and identify the 10 that is closer
Level III Students willEE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)Ex Use a color beaded number line to identify the two 10s a number falls betweenEx Given the number 14 they would identify 10 and 20
Level II Students willEE3NBT1 Identify tens on a number lineEx Given a number line circle the tensEx Stand on a number chart on 10 20 30 etc
Level I Students willEE3NBT1 Identify a numberEx Point to any number from one to three on a number lineEx Participate in a cake walk When the music stops look to see if they are on the number that is called outEx Identify a number when point to or presented on a cardEx Given a number from one to three point to the number symbolRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 29
Grade Level 3rdStandard with code 3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtractionDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 30
Students
Fluently add and subtract within 1000 using strategies based on place values properties of operations andor the relationship between addition and subtraction
Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning
Students know
Tools for modeling addition and subtraction
Strategies for solving addition and subtraction problems
Methods for symbolically (numerically) recording strategies for solving addition and subtraction problems
Students understand thatare able to
Model addition and subtraction problems using appropriate tools
Record strategies for solving addition and subtraction problems
Communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems
Relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and solution strategies
EE3NBT2 Identify place value to tens
Level IV Students willEE3NBT2 Identify place value to 50Ex Build numbers with place value piecesEx Identify the number in the ones and tens place value (ie the price of an item)Ex Write the number in expanded form ndash 43 = 40 + 3
Level III Students willEE3NBT2 Identify place value to tensEx When given two-digit number cards identify the number in the tens place valueEx When given a group of 10 frame models arrange and count the value of the numberI saw three groups of 10 and five extras so three groups of 10 = 30 and 5 more makes 35
Level II Students willEE3NBT2 Count to 10 using one-to-one correspondenceEx Given a bag of Skittles pull 10 Skittles out of the bagEx Select a domino and tell what number the dots representEx Shown a set of 10 objects create a duplicate collectionEx Given a container of pennies count out 10 from the container
Level I Students willEE3NBT2 Identify more or lessEx Given two collections of objects (group of 10 group of 20) indicate ldquoWhich has morerdquoEx Given math manipulatives representing a single unit and multiple units point to the multiple unit representation when asked ldquowhich is morerdquoRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 31
Grade Level 3rdStandard with code 3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operationsDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 32
Students
Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers
Students know
Place value models for multiplying numbers (eg open arrays place value blocks)
Strategies for multiplying one-digit numbers
Strategies for mentally multiplying one-digit numbers by multiples of powers of 10
Students understand thatare able to
Use mental strategies based on an understanding of place value properties of operations and knowledge of one-digit multiplication to find products
Use a variety of place value models of multiplication problems to justify strategies and solutions
Patterns in the place value system and properties of operations can be used to efficiently compute products
EE3NBT3 Count by tens using money
Level IV Students willEE3NBT3 Compare the value of money based on place valueEx Use money (dimes and pennies) to represent place valueEx Given 15 pennies create a one group of 10 and a group of five ones
Level III Students willEE3NBT3 Count by tens using moneyEx Given three dimes count by 10 to determine totalEx Given five dimes count by 10 to determine total
Level II Students willEE3NBT3 Identify whole numbers to 10Ex Given sets of 10 pennies pair with numbersEx Given sets of 10 pennies pair with dimes
Level I Students willEE3NBT3 Count pennies to 10
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 33
Grade Level 3rdStandard with code 3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1bDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 34
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven any multiplication problem in the form a x b = c
Represent the problem physically or pictorially and describe the relationship between the factors and the product in the equation and the attributes of the representation (ie given 3 x 5 = 15 students make 3 piles of buttons with 5 buttons in each pile They explain that 15 represents the total number of buttons 3 is the number of piles and 5 is the number of buttons in each pile)
Write a corresponding word problem containing a multiplication context
Students know
Characteristics of multiplication contexts
Students understand thatare able to
Represent quantities and operations (multiplication) physically pictorially or symbolically
Use mathematical language to communicate the connections between multiplication equations and related representations
Write word problems containing multiplication contexts
Putting together equal sized groups may be represented by multiplication equations and totals found through multiplication
EE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sum
Level IV Students willEE3OA1-2 Use repeated addition to find the total number of objects arranged in a square or rectangular arrayEx Using tiles in a template identify the total number of tiles by adding the tiles in the templateEx Fill space of squares and rectangles with 1-inch tiles add tiles in rows or columns to determine total number of tiles it takes to fill the shape (squarerectangle)Ex Use an abacus to find the total
Level III Students willEE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sumEx Two birds + two Birds + two birds = six birdsEx Given a repeated addition number sentence use a number line to find the sum
Level II Students willEE3OA1-2 Use addition to find the total number of objectsEx Three apples + four apples = six applesEx Add to find the total number of starsEx Skip count by twos to tell how many
Level I Students willEE3OA1-2 Identify which group has more or less when objects are added or taken awayEx When an object is added to a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoEx When an object is taken from a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 9
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and divisionQuarter 1 Quarter 2
Know what the numbers in a division problem represent
Explain what division means and how it relates to equal shares
Interpret quotients as the number of shares or the number of groups when a set of objects is divided equally
Quarter 3
Know what the numbers in a division problem represent
Explain what division means and how it relates to equal shares
Interpret quotients as the number of shares or the number of groups when a set of objects is divided equally
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 10
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven any division problem in the form a divide b = c
Represent the problem physically or pictorially and describe the relationship between the dividend divisor and quotient in the equation and the attributes of the representation (eg given 15 divide 3 = 5 students make 3 piles of buttons with 5 buttons in each pile and explain that 15 represents the total number of buttons 3 is the number of piles the total was shared among and 5 is the number of buttons in each pile)
Write a corresponding word problem containing a division context
Students know
Characteristics of division contexts
Students understand thatare able to
Represent quantities and operations (division) physically pictorially or symbolically
Use mathematical language to communicate the connections between division equations and related representations
Write word problems containing division contexts
Both partitioning into equal-sized shares and partitioning equally among a given number of groups may be modeled by division equations and the desired results found through division
EE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sum
Level IV Students willEE3OA1-2 Use repeated addition to find the total number of objects arranged in a square or rectangular arrayEx Using tiles in a template identify the total number of tiles by adding the tiles in the templateEx Fill space of squares and rectangles with 1-inch tiles add tiles in rows or columns to determine total number of tiles it takes to fill the shape (squarerectangle)Ex Use an abacus to find the total
Level III Students willEE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sumEx Two birds + two Birds + two birds = six birdsEx Given a repeated addition number sentence use a number line to find the sum
Level II Students willEE3OA1-2 Use addition to find the total number of objectsEx Three apples + four apples = six applesEx Add to find the total number of starsEx Skip count by twos to tell how many
Level I Students willEE3OA1-2 Identify which group has more or less when objects are added or taken awayEx When an object is added to a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoEx When an object is taken from a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 11
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and division
Quarter 1 Quarter 2
Multiply and divide within 100
Solve word problems in situations involving equal groups arrays and measurement quantities
Represent a word problem using a picture an equation with a symbol for the unknown number or in other ways
Quarter 3
Multiply and divide within 100
Solve word problems in situations involving equal groups arrays and measurement quantities
Represent a word problem using a picture an equation with a symbol for the unknown number or in other ways
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 12
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a variety of multiplication and division word problems within 100
Explain and justify solutions and solution paths using connections among a variety of representations (eg place value blocks drawings open arrays and equations with a symbol for the unknown)
See glossary for problem types (Table 2)
Students know
Characteristics of multiplication and division contexts
Multiplication and division strategies
Students understand thatare able to
Represent quantities and operations (multiplication and division) physically pictorially or symbolically
Strategically use a variety of representations to solve multiplication and division word problems
Use informal and mathematical language to communicate the connections among multiplication and division contexts and related physical pictorial or symbolic representations
Accurately compute products and quotients
Use symbols to represent unknown quantities in equations
EE3OA3 See EE3OA1 for repeated addition a foundational skill for multiplication and division (Multiplication begins in grade 4 and division begins in grade 5)
EE3OA3 See EE3OA1 for repeated addition a foundational skill for multiplication and division (Multiplication begins in grade 4 and division begins in grade 5)
Version 3 2015-2016 13
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8times = 48 5 = 1048781 divide 3 6 times 6 = Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and division
Quarter 1 Quarter 2
Multiply and divide within 100
Determine which operation (multiplication or division) is needed to determine the unknown whole number
Solve to find the unknown whole number in a multiplication or division equation
Quarter 3
Multiply and divide within 100
Determine which operation (multiplication or division) is needed to determine the unknown whole number
Solve to find the unknown whole number in a multiplication or division equation
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 14
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 15
Students
Solve single operation multiplicationdivision equations containing a single unknown (eg 8x = 48 5= __ divide3 6x6 = ___)
Students know
Strategies for solving simple equations with one unknown
Students understand thatare able to
Efficiently apply strategies for solving simple equations with one unknown
Justify solutions for single unknown equations
Multiplication is putting together equal sized groups and division is sharing into equal-sized shares or is sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models representations
Variables represent unknown quantities when representing mathematical situations algebraically
EE3OA4 Solve addition and subtraction problems when result is unknown with number 0-30
Level IV Students willEE3OA4 Solve addition and subtraction problems when any number in the problem is unknown (result start change difference) with numbers to 50Ex Using base-10 pieces add and subtract two-digit numbers to find the sum and the differenceEx Use pictures of numbers to add and subtract two-digit numbers to find the sum and the difference
Level III Students willEE3OA4 Solve addition and subtraction problems when result is unknown with number 0-30Ex Using base-10 pieces or counters add and subtractEx Use a 100s chart to find the sum or difference of given problemsEx Use count on strategies to add (eg When asked what is 5 + 2 the student says 5 6 7)
Level II Students willEE3OA4 Solve addition and subtraction problems with numbers 0-10Ex Use counters to add and subtractEx Use number lines to add or subtractEx Match the symbol to more or less thanEx Add one to a number by indicating the next number when asked (eg when the teacher says 3 4 5 the student says 6)
Level I Students willEE3OA4 Identify numbers 1 to 9Ex Given a set of five match it to the numberEx Given a set of three identify the number of objects on number linesRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 16
Grade Level 3rdStandard with code 3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2Multiply and divide within 100
Explain how the properties of operations work
Apply properties of operations as strategies to multiply and divide
Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 17
StudentsGiven multiplication and division problems within 100
Use the properties of operations and descriptive language for the property to justify their products and quotients (eg If I know that 8 x 5 is 40 and two more groups of 8 would be 16 then 8 x 7 must be 40 + 16 or 56)
Commutative Property of Multiplication
Associative Property of Multiplication
Distributive Property
Students know
Commutative Associative Identity and Zero Properties of Multiplication and the Distributive Property
Strategies for finding products and quotients
Students understand thatare able to
Strategically and efficiently apply properties of multiplication and division in order to find products and quotients
The order in which factors are multiplied does not change the product
EE3OA5 NA (Multiplication begins at grade 4)
EE3OA5 NA (Multiplication begins at grade 4)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 18
Grade Level 3rdStandard with code 3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when multiplied by 8Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 3
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 19
StudentsGiven a division problem with an unknown quotient
Use a pictorial or physical model to explain the connection between the division problem and the related unknown factor equation
Factor Students know
Strategies for finding quotients and products
Students understand thatare able to
Use symbols to represent unknown quantities in equations
Use mathematical language to communicate the connections between an unknown quotient problem and the related unknown factor problem
Use the inverse relationship between multiplication and division to find quotients
The relationship between multiplication and division (that one undoes the other) can be used to solve problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA6 NA (Division begins at grade 5)
EE3OA6 NA (Division begins at grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 20
Grade Level 3rdStandard with code 3OA7 Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division (eg knowing that 8 times 5 = 40 one knows 40 divide 5 = 8) or properties of operations By the end of Grade 3 know from memory all products of two one-digit numbersDomain Operations and Algebraic Thinking Cluster Multiply and divide within 100
Quarter 1 Quarter 2
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 3
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Version 3 2015-2016 21
AttainmentStudentsGiven any single digit multiplication problem or a division problem with a single digit divisor and an unknown single digit quotient
Use an efficient strategy (eg recall inverse operations arrays derived facts properties of operations etc) to name the product or quotient
Students know
Strategies for finding products and quotients
Students understand thatare able to
Use multiplication and division strategies efficiently based on the numbers in the problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 22
Grade Level 3rdStandard with code 3OA8 Solve two-step word problems using the four operations Represent these problems using equations with a letter standing for the unknown quantity Assess the reasonableness of answers using mental computation and estimation strategies including rounding3
Domain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmetic
Quarter 1
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 2
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 3
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 23
StudentsGiven a variety of two-step word problems involving all four operations
Apply their understanding of operations to explain and justify solutions and solution paths using the connections among a variety of representations including equations with symbols for unknown quantities
Apply their understanding of operations and estimation strategies including rounding to evaluate the reasonableness of their solutions (eg The answer had to be around 125 because its a put together problem and 72 is close to 75 and 56 is close to 50 and 75 plus 50 is 125)
Students know
Characteristics of addition subtraction multiplication and division situations
Addition subtraction multiplication and division strategies
Strategies for mentally computing and estimating sums differences products and quotients
Students understand thatare able to
Strategically use a variety of representations to solve two-step word problems involving all four operations
Use symbols to represent unknown quantities in equations that relate to word problem contexts
Use mathematical language and contextual situations to communicate the connections among the four operations and related physical pictorial or symbolic representations and justify solutionssolution paths
Accurately compute sums differences products and quotients
Use logical reasoning mental computation strategies and estimation strategies to justify the reasonableness of
EE3OA8 Add to solve real world one-step story problems from 0-30
Level IV Students willEE3OA8 Add to solve real world one-step story problems with sums up to 50 using various problem-solving modelsEx Solve by adding (eg ldquoThere are 25 birds in a tree and 10 more joined them How many birds are in a treerdquo)Ex Solve by adding (eg ldquoI have 15 snacks on the cart and 25 snacks in the cupboard how many snacks do I have all together)Ex Solve by adding (eg ldquoAdd the pencils in two boxes and tell how many pencils we haverdquo)
Level III Students willEE3OA8 Add to solve real world one-step story problems from 0-30 Represent the problem in pictures or with objectsEx Solve by adding (eg ldquoHere are 10 pencils We need 10 more for each person to get a pencil How many will we need in allrdquo)Ex Solve by adding (eg ldquoConnie had five marbles Juan gave her eight more marbles How many marbles does Connie have all togetherrdquo)Ex Solve by adding (eg ldquoAdd the crayons in these two boxes and show me how many we have in allrdquo)
Level II Students willEE3OA8 Add to solve word problems identified through symbol representationEx Complete word problems that have pictures rather than wordsEx Solve by adding (eg ldquoThere are three ducks in the pond two more joined How many ducks are in the pondrdquo [picture representation])
Level I Students willEE3OA8 Identify the object(s) that appear in a real world one-step story problemEx Given a simple word problem and asked ldquoWhat is the problem aboutrdquo point to an object from a choice of two that represents what the problem was about (eg box toy)Ex Indicate which object a word problem is about from an array of two choices
Version 3 2015-2016 24
solutions
Multiplication is putting together equal sized groups
Division is sharing into equal-sized shares or as sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models and representations
Solutions can be evaluated by using reasoning to compare the actual solution with estimated solutions
CCSS Math Pacing Guide
Version 3 2015-2016 25
Grade 3
Grade Level 3rdStandard with code 3OA9 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations For example observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addendsDomain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmeticQuarter 1
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 2
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 3
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 26
Students
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations (eg observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends)
Students know
Characteristics of numbers and properties of operations (eg odd even)
Properties from Table 3 etc
Students understand thatare able to
Identify arithmetic patterns in number sequences in the addition table or multiplication table
Use logical reasoning and properties of numbers and operations to explain arithmetic patterns
Characteristics of numbers and properties of operations justify patterns which can be used to reason about mathematical situations form conjectures and solve problems
EE3OA9 Identify arithmetic patterns
Level IV Students willEE3OA9 Complete a complex arithmetic patternEx Complete the pattern using more than two numbers (ie A B C A B C)Ex Using a 100s number chart complete the pattern identified
Level III Students willEE3OA9 Identify arithmetic patternsEx When provided arithmetic patterns on a 100s chart identify the next number in the patternEx When given two number stamps stamp an arithmetic pattern
Level II Students willEE3OA9 Identify a patternEx Make pattern jumps on a number lineEx Sing songs and identify the pattern in the song
Level I Students willEE3OA9 Follow patternsEx Sing ldquoHead Shoulders Knees and Toesrdquo and mimic the patternEx Using tactile objects (fur sand sand fur) in a pattern repeat the patternEx Using manipulatives mimic the teacher to create a pattern
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 27
Grade Level 3rdStandard with code 3NBT1 Use place value understanding to round whole numbers to the nearest 10 or 100Domain Number and Operations in Base Ten
Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 28
StudentsGiven any number less than 1000
Round it to the nearest 10 or 100 and justify the answer using place value vocabulary (eg Rounding 147 to the nearest 10 is 150 because 147 is between 140 and 150 and is more than half way to 150)
Students know
Place value (ones tens hundreds)
Rounding
Students understand thatare able to
Count by 10s and 100s
Determine what is halfway between two multiples of 10 or 100
Round to the nearest 10 or 100
Use place value vocabulary and logical reasoning to justify solutions to rounding problems
Rounding and place value can be used to estimate quantities by changing the original number to the closest multiple of a power of 10
EE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)
Level IV Students willEE3NBT1 Identify the two 10s a number comes in between and tell which is closest (numbers 0-50)Ex Use a color beaded number line to identify the number and round to the closest 10Ex Given a number line separated into tens (0-10 10-20 etc) stand on a number and identify the 10 that is closer
Level III Students willEE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)Ex Use a color beaded number line to identify the two 10s a number falls betweenEx Given the number 14 they would identify 10 and 20
Level II Students willEE3NBT1 Identify tens on a number lineEx Given a number line circle the tensEx Stand on a number chart on 10 20 30 etc
Level I Students willEE3NBT1 Identify a numberEx Point to any number from one to three on a number lineEx Participate in a cake walk When the music stops look to see if they are on the number that is called outEx Identify a number when point to or presented on a cardEx Given a number from one to three point to the number symbolRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 29
Grade Level 3rdStandard with code 3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtractionDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 30
Students
Fluently add and subtract within 1000 using strategies based on place values properties of operations andor the relationship between addition and subtraction
Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning
Students know
Tools for modeling addition and subtraction
Strategies for solving addition and subtraction problems
Methods for symbolically (numerically) recording strategies for solving addition and subtraction problems
Students understand thatare able to
Model addition and subtraction problems using appropriate tools
Record strategies for solving addition and subtraction problems
Communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems
Relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and solution strategies
EE3NBT2 Identify place value to tens
Level IV Students willEE3NBT2 Identify place value to 50Ex Build numbers with place value piecesEx Identify the number in the ones and tens place value (ie the price of an item)Ex Write the number in expanded form ndash 43 = 40 + 3
Level III Students willEE3NBT2 Identify place value to tensEx When given two-digit number cards identify the number in the tens place valueEx When given a group of 10 frame models arrange and count the value of the numberI saw three groups of 10 and five extras so three groups of 10 = 30 and 5 more makes 35
Level II Students willEE3NBT2 Count to 10 using one-to-one correspondenceEx Given a bag of Skittles pull 10 Skittles out of the bagEx Select a domino and tell what number the dots representEx Shown a set of 10 objects create a duplicate collectionEx Given a container of pennies count out 10 from the container
Level I Students willEE3NBT2 Identify more or lessEx Given two collections of objects (group of 10 group of 20) indicate ldquoWhich has morerdquoEx Given math manipulatives representing a single unit and multiple units point to the multiple unit representation when asked ldquowhich is morerdquoRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 31
Grade Level 3rdStandard with code 3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operationsDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 32
Students
Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers
Students know
Place value models for multiplying numbers (eg open arrays place value blocks)
Strategies for multiplying one-digit numbers
Strategies for mentally multiplying one-digit numbers by multiples of powers of 10
Students understand thatare able to
Use mental strategies based on an understanding of place value properties of operations and knowledge of one-digit multiplication to find products
Use a variety of place value models of multiplication problems to justify strategies and solutions
Patterns in the place value system and properties of operations can be used to efficiently compute products
EE3NBT3 Count by tens using money
Level IV Students willEE3NBT3 Compare the value of money based on place valueEx Use money (dimes and pennies) to represent place valueEx Given 15 pennies create a one group of 10 and a group of five ones
Level III Students willEE3NBT3 Count by tens using moneyEx Given three dimes count by 10 to determine totalEx Given five dimes count by 10 to determine total
Level II Students willEE3NBT3 Identify whole numbers to 10Ex Given sets of 10 pennies pair with numbersEx Given sets of 10 pennies pair with dimes
Level I Students willEE3NBT3 Count pennies to 10
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 33
Grade Level 3rdStandard with code 3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1bDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 34
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and divisionQuarter 1 Quarter 2
Know what the numbers in a division problem represent
Explain what division means and how it relates to equal shares
Interpret quotients as the number of shares or the number of groups when a set of objects is divided equally
Quarter 3
Know what the numbers in a division problem represent
Explain what division means and how it relates to equal shares
Interpret quotients as the number of shares or the number of groups when a set of objects is divided equally
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 10
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven any division problem in the form a divide b = c
Represent the problem physically or pictorially and describe the relationship between the dividend divisor and quotient in the equation and the attributes of the representation (eg given 15 divide 3 = 5 students make 3 piles of buttons with 5 buttons in each pile and explain that 15 represents the total number of buttons 3 is the number of piles the total was shared among and 5 is the number of buttons in each pile)
Write a corresponding word problem containing a division context
Students know
Characteristics of division contexts
Students understand thatare able to
Represent quantities and operations (division) physically pictorially or symbolically
Use mathematical language to communicate the connections between division equations and related representations
Write word problems containing division contexts
Both partitioning into equal-sized shares and partitioning equally among a given number of groups may be modeled by division equations and the desired results found through division
EE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sum
Level IV Students willEE3OA1-2 Use repeated addition to find the total number of objects arranged in a square or rectangular arrayEx Using tiles in a template identify the total number of tiles by adding the tiles in the templateEx Fill space of squares and rectangles with 1-inch tiles add tiles in rows or columns to determine total number of tiles it takes to fill the shape (squarerectangle)Ex Use an abacus to find the total
Level III Students willEE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sumEx Two birds + two Birds + two birds = six birdsEx Given a repeated addition number sentence use a number line to find the sum
Level II Students willEE3OA1-2 Use addition to find the total number of objectsEx Three apples + four apples = six applesEx Add to find the total number of starsEx Skip count by twos to tell how many
Level I Students willEE3OA1-2 Identify which group has more or less when objects are added or taken awayEx When an object is added to a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoEx When an object is taken from a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 11
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and division
Quarter 1 Quarter 2
Multiply and divide within 100
Solve word problems in situations involving equal groups arrays and measurement quantities
Represent a word problem using a picture an equation with a symbol for the unknown number or in other ways
Quarter 3
Multiply and divide within 100
Solve word problems in situations involving equal groups arrays and measurement quantities
Represent a word problem using a picture an equation with a symbol for the unknown number or in other ways
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 12
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a variety of multiplication and division word problems within 100
Explain and justify solutions and solution paths using connections among a variety of representations (eg place value blocks drawings open arrays and equations with a symbol for the unknown)
See glossary for problem types (Table 2)
Students know
Characteristics of multiplication and division contexts
Multiplication and division strategies
Students understand thatare able to
Represent quantities and operations (multiplication and division) physically pictorially or symbolically
Strategically use a variety of representations to solve multiplication and division word problems
Use informal and mathematical language to communicate the connections among multiplication and division contexts and related physical pictorial or symbolic representations
Accurately compute products and quotients
Use symbols to represent unknown quantities in equations
EE3OA3 See EE3OA1 for repeated addition a foundational skill for multiplication and division (Multiplication begins in grade 4 and division begins in grade 5)
EE3OA3 See EE3OA1 for repeated addition a foundational skill for multiplication and division (Multiplication begins in grade 4 and division begins in grade 5)
Version 3 2015-2016 13
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8times = 48 5 = 1048781 divide 3 6 times 6 = Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and division
Quarter 1 Quarter 2
Multiply and divide within 100
Determine which operation (multiplication or division) is needed to determine the unknown whole number
Solve to find the unknown whole number in a multiplication or division equation
Quarter 3
Multiply and divide within 100
Determine which operation (multiplication or division) is needed to determine the unknown whole number
Solve to find the unknown whole number in a multiplication or division equation
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 14
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 15
Students
Solve single operation multiplicationdivision equations containing a single unknown (eg 8x = 48 5= __ divide3 6x6 = ___)
Students know
Strategies for solving simple equations with one unknown
Students understand thatare able to
Efficiently apply strategies for solving simple equations with one unknown
Justify solutions for single unknown equations
Multiplication is putting together equal sized groups and division is sharing into equal-sized shares or is sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models representations
Variables represent unknown quantities when representing mathematical situations algebraically
EE3OA4 Solve addition and subtraction problems when result is unknown with number 0-30
Level IV Students willEE3OA4 Solve addition and subtraction problems when any number in the problem is unknown (result start change difference) with numbers to 50Ex Using base-10 pieces add and subtract two-digit numbers to find the sum and the differenceEx Use pictures of numbers to add and subtract two-digit numbers to find the sum and the difference
Level III Students willEE3OA4 Solve addition and subtraction problems when result is unknown with number 0-30Ex Using base-10 pieces or counters add and subtractEx Use a 100s chart to find the sum or difference of given problemsEx Use count on strategies to add (eg When asked what is 5 + 2 the student says 5 6 7)
Level II Students willEE3OA4 Solve addition and subtraction problems with numbers 0-10Ex Use counters to add and subtractEx Use number lines to add or subtractEx Match the symbol to more or less thanEx Add one to a number by indicating the next number when asked (eg when the teacher says 3 4 5 the student says 6)
Level I Students willEE3OA4 Identify numbers 1 to 9Ex Given a set of five match it to the numberEx Given a set of three identify the number of objects on number linesRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 16
Grade Level 3rdStandard with code 3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2Multiply and divide within 100
Explain how the properties of operations work
Apply properties of operations as strategies to multiply and divide
Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 17
StudentsGiven multiplication and division problems within 100
Use the properties of operations and descriptive language for the property to justify their products and quotients (eg If I know that 8 x 5 is 40 and two more groups of 8 would be 16 then 8 x 7 must be 40 + 16 or 56)
Commutative Property of Multiplication
Associative Property of Multiplication
Distributive Property
Students know
Commutative Associative Identity and Zero Properties of Multiplication and the Distributive Property
Strategies for finding products and quotients
Students understand thatare able to
Strategically and efficiently apply properties of multiplication and division in order to find products and quotients
The order in which factors are multiplied does not change the product
EE3OA5 NA (Multiplication begins at grade 4)
EE3OA5 NA (Multiplication begins at grade 4)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 18
Grade Level 3rdStandard with code 3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when multiplied by 8Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 3
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 19
StudentsGiven a division problem with an unknown quotient
Use a pictorial or physical model to explain the connection between the division problem and the related unknown factor equation
Factor Students know
Strategies for finding quotients and products
Students understand thatare able to
Use symbols to represent unknown quantities in equations
Use mathematical language to communicate the connections between an unknown quotient problem and the related unknown factor problem
Use the inverse relationship between multiplication and division to find quotients
The relationship between multiplication and division (that one undoes the other) can be used to solve problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA6 NA (Division begins at grade 5)
EE3OA6 NA (Division begins at grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 20
Grade Level 3rdStandard with code 3OA7 Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division (eg knowing that 8 times 5 = 40 one knows 40 divide 5 = 8) or properties of operations By the end of Grade 3 know from memory all products of two one-digit numbersDomain Operations and Algebraic Thinking Cluster Multiply and divide within 100
Quarter 1 Quarter 2
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 3
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Version 3 2015-2016 21
AttainmentStudentsGiven any single digit multiplication problem or a division problem with a single digit divisor and an unknown single digit quotient
Use an efficient strategy (eg recall inverse operations arrays derived facts properties of operations etc) to name the product or quotient
Students know
Strategies for finding products and quotients
Students understand thatare able to
Use multiplication and division strategies efficiently based on the numbers in the problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 22
Grade Level 3rdStandard with code 3OA8 Solve two-step word problems using the four operations Represent these problems using equations with a letter standing for the unknown quantity Assess the reasonableness of answers using mental computation and estimation strategies including rounding3
Domain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmetic
Quarter 1
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 2
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 3
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 23
StudentsGiven a variety of two-step word problems involving all four operations
Apply their understanding of operations to explain and justify solutions and solution paths using the connections among a variety of representations including equations with symbols for unknown quantities
Apply their understanding of operations and estimation strategies including rounding to evaluate the reasonableness of their solutions (eg The answer had to be around 125 because its a put together problem and 72 is close to 75 and 56 is close to 50 and 75 plus 50 is 125)
Students know
Characteristics of addition subtraction multiplication and division situations
Addition subtraction multiplication and division strategies
Strategies for mentally computing and estimating sums differences products and quotients
Students understand thatare able to
Strategically use a variety of representations to solve two-step word problems involving all four operations
Use symbols to represent unknown quantities in equations that relate to word problem contexts
Use mathematical language and contextual situations to communicate the connections among the four operations and related physical pictorial or symbolic representations and justify solutionssolution paths
Accurately compute sums differences products and quotients
Use logical reasoning mental computation strategies and estimation strategies to justify the reasonableness of
EE3OA8 Add to solve real world one-step story problems from 0-30
Level IV Students willEE3OA8 Add to solve real world one-step story problems with sums up to 50 using various problem-solving modelsEx Solve by adding (eg ldquoThere are 25 birds in a tree and 10 more joined them How many birds are in a treerdquo)Ex Solve by adding (eg ldquoI have 15 snacks on the cart and 25 snacks in the cupboard how many snacks do I have all together)Ex Solve by adding (eg ldquoAdd the pencils in two boxes and tell how many pencils we haverdquo)
Level III Students willEE3OA8 Add to solve real world one-step story problems from 0-30 Represent the problem in pictures or with objectsEx Solve by adding (eg ldquoHere are 10 pencils We need 10 more for each person to get a pencil How many will we need in allrdquo)Ex Solve by adding (eg ldquoConnie had five marbles Juan gave her eight more marbles How many marbles does Connie have all togetherrdquo)Ex Solve by adding (eg ldquoAdd the crayons in these two boxes and show me how many we have in allrdquo)
Level II Students willEE3OA8 Add to solve word problems identified through symbol representationEx Complete word problems that have pictures rather than wordsEx Solve by adding (eg ldquoThere are three ducks in the pond two more joined How many ducks are in the pondrdquo [picture representation])
Level I Students willEE3OA8 Identify the object(s) that appear in a real world one-step story problemEx Given a simple word problem and asked ldquoWhat is the problem aboutrdquo point to an object from a choice of two that represents what the problem was about (eg box toy)Ex Indicate which object a word problem is about from an array of two choices
Version 3 2015-2016 24
solutions
Multiplication is putting together equal sized groups
Division is sharing into equal-sized shares or as sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models and representations
Solutions can be evaluated by using reasoning to compare the actual solution with estimated solutions
CCSS Math Pacing Guide
Version 3 2015-2016 25
Grade 3
Grade Level 3rdStandard with code 3OA9 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations For example observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addendsDomain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmeticQuarter 1
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 2
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 3
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 26
Students
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations (eg observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends)
Students know
Characteristics of numbers and properties of operations (eg odd even)
Properties from Table 3 etc
Students understand thatare able to
Identify arithmetic patterns in number sequences in the addition table or multiplication table
Use logical reasoning and properties of numbers and operations to explain arithmetic patterns
Characteristics of numbers and properties of operations justify patterns which can be used to reason about mathematical situations form conjectures and solve problems
EE3OA9 Identify arithmetic patterns
Level IV Students willEE3OA9 Complete a complex arithmetic patternEx Complete the pattern using more than two numbers (ie A B C A B C)Ex Using a 100s number chart complete the pattern identified
Level III Students willEE3OA9 Identify arithmetic patternsEx When provided arithmetic patterns on a 100s chart identify the next number in the patternEx When given two number stamps stamp an arithmetic pattern
Level II Students willEE3OA9 Identify a patternEx Make pattern jumps on a number lineEx Sing songs and identify the pattern in the song
Level I Students willEE3OA9 Follow patternsEx Sing ldquoHead Shoulders Knees and Toesrdquo and mimic the patternEx Using tactile objects (fur sand sand fur) in a pattern repeat the patternEx Using manipulatives mimic the teacher to create a pattern
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 27
Grade Level 3rdStandard with code 3NBT1 Use place value understanding to round whole numbers to the nearest 10 or 100Domain Number and Operations in Base Ten
Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 28
StudentsGiven any number less than 1000
Round it to the nearest 10 or 100 and justify the answer using place value vocabulary (eg Rounding 147 to the nearest 10 is 150 because 147 is between 140 and 150 and is more than half way to 150)
Students know
Place value (ones tens hundreds)
Rounding
Students understand thatare able to
Count by 10s and 100s
Determine what is halfway between two multiples of 10 or 100
Round to the nearest 10 or 100
Use place value vocabulary and logical reasoning to justify solutions to rounding problems
Rounding and place value can be used to estimate quantities by changing the original number to the closest multiple of a power of 10
EE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)
Level IV Students willEE3NBT1 Identify the two 10s a number comes in between and tell which is closest (numbers 0-50)Ex Use a color beaded number line to identify the number and round to the closest 10Ex Given a number line separated into tens (0-10 10-20 etc) stand on a number and identify the 10 that is closer
Level III Students willEE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)Ex Use a color beaded number line to identify the two 10s a number falls betweenEx Given the number 14 they would identify 10 and 20
Level II Students willEE3NBT1 Identify tens on a number lineEx Given a number line circle the tensEx Stand on a number chart on 10 20 30 etc
Level I Students willEE3NBT1 Identify a numberEx Point to any number from one to three on a number lineEx Participate in a cake walk When the music stops look to see if they are on the number that is called outEx Identify a number when point to or presented on a cardEx Given a number from one to three point to the number symbolRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 29
Grade Level 3rdStandard with code 3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtractionDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 30
Students
Fluently add and subtract within 1000 using strategies based on place values properties of operations andor the relationship between addition and subtraction
Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning
Students know
Tools for modeling addition and subtraction
Strategies for solving addition and subtraction problems
Methods for symbolically (numerically) recording strategies for solving addition and subtraction problems
Students understand thatare able to
Model addition and subtraction problems using appropriate tools
Record strategies for solving addition and subtraction problems
Communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems
Relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and solution strategies
EE3NBT2 Identify place value to tens
Level IV Students willEE3NBT2 Identify place value to 50Ex Build numbers with place value piecesEx Identify the number in the ones and tens place value (ie the price of an item)Ex Write the number in expanded form ndash 43 = 40 + 3
Level III Students willEE3NBT2 Identify place value to tensEx When given two-digit number cards identify the number in the tens place valueEx When given a group of 10 frame models arrange and count the value of the numberI saw three groups of 10 and five extras so three groups of 10 = 30 and 5 more makes 35
Level II Students willEE3NBT2 Count to 10 using one-to-one correspondenceEx Given a bag of Skittles pull 10 Skittles out of the bagEx Select a domino and tell what number the dots representEx Shown a set of 10 objects create a duplicate collectionEx Given a container of pennies count out 10 from the container
Level I Students willEE3NBT2 Identify more or lessEx Given two collections of objects (group of 10 group of 20) indicate ldquoWhich has morerdquoEx Given math manipulatives representing a single unit and multiple units point to the multiple unit representation when asked ldquowhich is morerdquoRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 31
Grade Level 3rdStandard with code 3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operationsDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 32
Students
Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers
Students know
Place value models for multiplying numbers (eg open arrays place value blocks)
Strategies for multiplying one-digit numbers
Strategies for mentally multiplying one-digit numbers by multiples of powers of 10
Students understand thatare able to
Use mental strategies based on an understanding of place value properties of operations and knowledge of one-digit multiplication to find products
Use a variety of place value models of multiplication problems to justify strategies and solutions
Patterns in the place value system and properties of operations can be used to efficiently compute products
EE3NBT3 Count by tens using money
Level IV Students willEE3NBT3 Compare the value of money based on place valueEx Use money (dimes and pennies) to represent place valueEx Given 15 pennies create a one group of 10 and a group of five ones
Level III Students willEE3NBT3 Count by tens using moneyEx Given three dimes count by 10 to determine totalEx Given five dimes count by 10 to determine total
Level II Students willEE3NBT3 Identify whole numbers to 10Ex Given sets of 10 pennies pair with numbersEx Given sets of 10 pennies pair with dimes
Level I Students willEE3NBT3 Count pennies to 10
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 33
Grade Level 3rdStandard with code 3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1bDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 34
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven any division problem in the form a divide b = c
Represent the problem physically or pictorially and describe the relationship between the dividend divisor and quotient in the equation and the attributes of the representation (eg given 15 divide 3 = 5 students make 3 piles of buttons with 5 buttons in each pile and explain that 15 represents the total number of buttons 3 is the number of piles the total was shared among and 5 is the number of buttons in each pile)
Write a corresponding word problem containing a division context
Students know
Characteristics of division contexts
Students understand thatare able to
Represent quantities and operations (division) physically pictorially or symbolically
Use mathematical language to communicate the connections between division equations and related representations
Write word problems containing division contexts
Both partitioning into equal-sized shares and partitioning equally among a given number of groups may be modeled by division equations and the desired results found through division
EE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sum
Level IV Students willEE3OA1-2 Use repeated addition to find the total number of objects arranged in a square or rectangular arrayEx Using tiles in a template identify the total number of tiles by adding the tiles in the templateEx Fill space of squares and rectangles with 1-inch tiles add tiles in rows or columns to determine total number of tiles it takes to fill the shape (squarerectangle)Ex Use an abacus to find the total
Level III Students willEE3OA1-2 Use repeated addition and equal groups to find the total number of objects to find the sumEx Two birds + two Birds + two birds = six birdsEx Given a repeated addition number sentence use a number line to find the sum
Level II Students willEE3OA1-2 Use addition to find the total number of objectsEx Three apples + four apples = six applesEx Add to find the total number of starsEx Skip count by twos to tell how many
Level I Students willEE3OA1-2 Identify which group has more or less when objects are added or taken awayEx When an object is added to a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoEx When an object is taken from a group of three ldquoIs this morerdquo and ldquoIs this lessrdquoRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 11
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and division
Quarter 1 Quarter 2
Multiply and divide within 100
Solve word problems in situations involving equal groups arrays and measurement quantities
Represent a word problem using a picture an equation with a symbol for the unknown number or in other ways
Quarter 3
Multiply and divide within 100
Solve word problems in situations involving equal groups arrays and measurement quantities
Represent a word problem using a picture an equation with a symbol for the unknown number or in other ways
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 12
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a variety of multiplication and division word problems within 100
Explain and justify solutions and solution paths using connections among a variety of representations (eg place value blocks drawings open arrays and equations with a symbol for the unknown)
See glossary for problem types (Table 2)
Students know
Characteristics of multiplication and division contexts
Multiplication and division strategies
Students understand thatare able to
Represent quantities and operations (multiplication and division) physically pictorially or symbolically
Strategically use a variety of representations to solve multiplication and division word problems
Use informal and mathematical language to communicate the connections among multiplication and division contexts and related physical pictorial or symbolic representations
Accurately compute products and quotients
Use symbols to represent unknown quantities in equations
EE3OA3 See EE3OA1 for repeated addition a foundational skill for multiplication and division (Multiplication begins in grade 4 and division begins in grade 5)
EE3OA3 See EE3OA1 for repeated addition a foundational skill for multiplication and division (Multiplication begins in grade 4 and division begins in grade 5)
Version 3 2015-2016 13
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8times = 48 5 = 1048781 divide 3 6 times 6 = Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and division
Quarter 1 Quarter 2
Multiply and divide within 100
Determine which operation (multiplication or division) is needed to determine the unknown whole number
Solve to find the unknown whole number in a multiplication or division equation
Quarter 3
Multiply and divide within 100
Determine which operation (multiplication or division) is needed to determine the unknown whole number
Solve to find the unknown whole number in a multiplication or division equation
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 14
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 15
Students
Solve single operation multiplicationdivision equations containing a single unknown (eg 8x = 48 5= __ divide3 6x6 = ___)
Students know
Strategies for solving simple equations with one unknown
Students understand thatare able to
Efficiently apply strategies for solving simple equations with one unknown
Justify solutions for single unknown equations
Multiplication is putting together equal sized groups and division is sharing into equal-sized shares or is sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models representations
Variables represent unknown quantities when representing mathematical situations algebraically
EE3OA4 Solve addition and subtraction problems when result is unknown with number 0-30
Level IV Students willEE3OA4 Solve addition and subtraction problems when any number in the problem is unknown (result start change difference) with numbers to 50Ex Using base-10 pieces add and subtract two-digit numbers to find the sum and the differenceEx Use pictures of numbers to add and subtract two-digit numbers to find the sum and the difference
Level III Students willEE3OA4 Solve addition and subtraction problems when result is unknown with number 0-30Ex Using base-10 pieces or counters add and subtractEx Use a 100s chart to find the sum or difference of given problemsEx Use count on strategies to add (eg When asked what is 5 + 2 the student says 5 6 7)
Level II Students willEE3OA4 Solve addition and subtraction problems with numbers 0-10Ex Use counters to add and subtractEx Use number lines to add or subtractEx Match the symbol to more or less thanEx Add one to a number by indicating the next number when asked (eg when the teacher says 3 4 5 the student says 6)
Level I Students willEE3OA4 Identify numbers 1 to 9Ex Given a set of five match it to the numberEx Given a set of three identify the number of objects on number linesRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 16
Grade Level 3rdStandard with code 3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2Multiply and divide within 100
Explain how the properties of operations work
Apply properties of operations as strategies to multiply and divide
Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 17
StudentsGiven multiplication and division problems within 100
Use the properties of operations and descriptive language for the property to justify their products and quotients (eg If I know that 8 x 5 is 40 and two more groups of 8 would be 16 then 8 x 7 must be 40 + 16 or 56)
Commutative Property of Multiplication
Associative Property of Multiplication
Distributive Property
Students know
Commutative Associative Identity and Zero Properties of Multiplication and the Distributive Property
Strategies for finding products and quotients
Students understand thatare able to
Strategically and efficiently apply properties of multiplication and division in order to find products and quotients
The order in which factors are multiplied does not change the product
EE3OA5 NA (Multiplication begins at grade 4)
EE3OA5 NA (Multiplication begins at grade 4)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 18
Grade Level 3rdStandard with code 3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when multiplied by 8Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 3
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 19
StudentsGiven a division problem with an unknown quotient
Use a pictorial or physical model to explain the connection between the division problem and the related unknown factor equation
Factor Students know
Strategies for finding quotients and products
Students understand thatare able to
Use symbols to represent unknown quantities in equations
Use mathematical language to communicate the connections between an unknown quotient problem and the related unknown factor problem
Use the inverse relationship between multiplication and division to find quotients
The relationship between multiplication and division (that one undoes the other) can be used to solve problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA6 NA (Division begins at grade 5)
EE3OA6 NA (Division begins at grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 20
Grade Level 3rdStandard with code 3OA7 Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division (eg knowing that 8 times 5 = 40 one knows 40 divide 5 = 8) or properties of operations By the end of Grade 3 know from memory all products of two one-digit numbersDomain Operations and Algebraic Thinking Cluster Multiply and divide within 100
Quarter 1 Quarter 2
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 3
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Version 3 2015-2016 21
AttainmentStudentsGiven any single digit multiplication problem or a division problem with a single digit divisor and an unknown single digit quotient
Use an efficient strategy (eg recall inverse operations arrays derived facts properties of operations etc) to name the product or quotient
Students know
Strategies for finding products and quotients
Students understand thatare able to
Use multiplication and division strategies efficiently based on the numbers in the problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 22
Grade Level 3rdStandard with code 3OA8 Solve two-step word problems using the four operations Represent these problems using equations with a letter standing for the unknown quantity Assess the reasonableness of answers using mental computation and estimation strategies including rounding3
Domain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmetic
Quarter 1
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 2
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 3
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 23
StudentsGiven a variety of two-step word problems involving all four operations
Apply their understanding of operations to explain and justify solutions and solution paths using the connections among a variety of representations including equations with symbols for unknown quantities
Apply their understanding of operations and estimation strategies including rounding to evaluate the reasonableness of their solutions (eg The answer had to be around 125 because its a put together problem and 72 is close to 75 and 56 is close to 50 and 75 plus 50 is 125)
Students know
Characteristics of addition subtraction multiplication and division situations
Addition subtraction multiplication and division strategies
Strategies for mentally computing and estimating sums differences products and quotients
Students understand thatare able to
Strategically use a variety of representations to solve two-step word problems involving all four operations
Use symbols to represent unknown quantities in equations that relate to word problem contexts
Use mathematical language and contextual situations to communicate the connections among the four operations and related physical pictorial or symbolic representations and justify solutionssolution paths
Accurately compute sums differences products and quotients
Use logical reasoning mental computation strategies and estimation strategies to justify the reasonableness of
EE3OA8 Add to solve real world one-step story problems from 0-30
Level IV Students willEE3OA8 Add to solve real world one-step story problems with sums up to 50 using various problem-solving modelsEx Solve by adding (eg ldquoThere are 25 birds in a tree and 10 more joined them How many birds are in a treerdquo)Ex Solve by adding (eg ldquoI have 15 snacks on the cart and 25 snacks in the cupboard how many snacks do I have all together)Ex Solve by adding (eg ldquoAdd the pencils in two boxes and tell how many pencils we haverdquo)
Level III Students willEE3OA8 Add to solve real world one-step story problems from 0-30 Represent the problem in pictures or with objectsEx Solve by adding (eg ldquoHere are 10 pencils We need 10 more for each person to get a pencil How many will we need in allrdquo)Ex Solve by adding (eg ldquoConnie had five marbles Juan gave her eight more marbles How many marbles does Connie have all togetherrdquo)Ex Solve by adding (eg ldquoAdd the crayons in these two boxes and show me how many we have in allrdquo)
Level II Students willEE3OA8 Add to solve word problems identified through symbol representationEx Complete word problems that have pictures rather than wordsEx Solve by adding (eg ldquoThere are three ducks in the pond two more joined How many ducks are in the pondrdquo [picture representation])
Level I Students willEE3OA8 Identify the object(s) that appear in a real world one-step story problemEx Given a simple word problem and asked ldquoWhat is the problem aboutrdquo point to an object from a choice of two that represents what the problem was about (eg box toy)Ex Indicate which object a word problem is about from an array of two choices
Version 3 2015-2016 24
solutions
Multiplication is putting together equal sized groups
Division is sharing into equal-sized shares or as sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models and representations
Solutions can be evaluated by using reasoning to compare the actual solution with estimated solutions
CCSS Math Pacing Guide
Version 3 2015-2016 25
Grade 3
Grade Level 3rdStandard with code 3OA9 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations For example observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addendsDomain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmeticQuarter 1
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 2
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 3
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 26
Students
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations (eg observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends)
Students know
Characteristics of numbers and properties of operations (eg odd even)
Properties from Table 3 etc
Students understand thatare able to
Identify arithmetic patterns in number sequences in the addition table or multiplication table
Use logical reasoning and properties of numbers and operations to explain arithmetic patterns
Characteristics of numbers and properties of operations justify patterns which can be used to reason about mathematical situations form conjectures and solve problems
EE3OA9 Identify arithmetic patterns
Level IV Students willEE3OA9 Complete a complex arithmetic patternEx Complete the pattern using more than two numbers (ie A B C A B C)Ex Using a 100s number chart complete the pattern identified
Level III Students willEE3OA9 Identify arithmetic patternsEx When provided arithmetic patterns on a 100s chart identify the next number in the patternEx When given two number stamps stamp an arithmetic pattern
Level II Students willEE3OA9 Identify a patternEx Make pattern jumps on a number lineEx Sing songs and identify the pattern in the song
Level I Students willEE3OA9 Follow patternsEx Sing ldquoHead Shoulders Knees and Toesrdquo and mimic the patternEx Using tactile objects (fur sand sand fur) in a pattern repeat the patternEx Using manipulatives mimic the teacher to create a pattern
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 27
Grade Level 3rdStandard with code 3NBT1 Use place value understanding to round whole numbers to the nearest 10 or 100Domain Number and Operations in Base Ten
Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 28
StudentsGiven any number less than 1000
Round it to the nearest 10 or 100 and justify the answer using place value vocabulary (eg Rounding 147 to the nearest 10 is 150 because 147 is between 140 and 150 and is more than half way to 150)
Students know
Place value (ones tens hundreds)
Rounding
Students understand thatare able to
Count by 10s and 100s
Determine what is halfway between two multiples of 10 or 100
Round to the nearest 10 or 100
Use place value vocabulary and logical reasoning to justify solutions to rounding problems
Rounding and place value can be used to estimate quantities by changing the original number to the closest multiple of a power of 10
EE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)
Level IV Students willEE3NBT1 Identify the two 10s a number comes in between and tell which is closest (numbers 0-50)Ex Use a color beaded number line to identify the number and round to the closest 10Ex Given a number line separated into tens (0-10 10-20 etc) stand on a number and identify the 10 that is closer
Level III Students willEE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)Ex Use a color beaded number line to identify the two 10s a number falls betweenEx Given the number 14 they would identify 10 and 20
Level II Students willEE3NBT1 Identify tens on a number lineEx Given a number line circle the tensEx Stand on a number chart on 10 20 30 etc
Level I Students willEE3NBT1 Identify a numberEx Point to any number from one to three on a number lineEx Participate in a cake walk When the music stops look to see if they are on the number that is called outEx Identify a number when point to or presented on a cardEx Given a number from one to three point to the number symbolRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 29
Grade Level 3rdStandard with code 3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtractionDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 30
Students
Fluently add and subtract within 1000 using strategies based on place values properties of operations andor the relationship between addition and subtraction
Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning
Students know
Tools for modeling addition and subtraction
Strategies for solving addition and subtraction problems
Methods for symbolically (numerically) recording strategies for solving addition and subtraction problems
Students understand thatare able to
Model addition and subtraction problems using appropriate tools
Record strategies for solving addition and subtraction problems
Communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems
Relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and solution strategies
EE3NBT2 Identify place value to tens
Level IV Students willEE3NBT2 Identify place value to 50Ex Build numbers with place value piecesEx Identify the number in the ones and tens place value (ie the price of an item)Ex Write the number in expanded form ndash 43 = 40 + 3
Level III Students willEE3NBT2 Identify place value to tensEx When given two-digit number cards identify the number in the tens place valueEx When given a group of 10 frame models arrange and count the value of the numberI saw three groups of 10 and five extras so three groups of 10 = 30 and 5 more makes 35
Level II Students willEE3NBT2 Count to 10 using one-to-one correspondenceEx Given a bag of Skittles pull 10 Skittles out of the bagEx Select a domino and tell what number the dots representEx Shown a set of 10 objects create a duplicate collectionEx Given a container of pennies count out 10 from the container
Level I Students willEE3NBT2 Identify more or lessEx Given two collections of objects (group of 10 group of 20) indicate ldquoWhich has morerdquoEx Given math manipulatives representing a single unit and multiple units point to the multiple unit representation when asked ldquowhich is morerdquoRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 31
Grade Level 3rdStandard with code 3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operationsDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 32
Students
Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers
Students know
Place value models for multiplying numbers (eg open arrays place value blocks)
Strategies for multiplying one-digit numbers
Strategies for mentally multiplying one-digit numbers by multiples of powers of 10
Students understand thatare able to
Use mental strategies based on an understanding of place value properties of operations and knowledge of one-digit multiplication to find products
Use a variety of place value models of multiplication problems to justify strategies and solutions
Patterns in the place value system and properties of operations can be used to efficiently compute products
EE3NBT3 Count by tens using money
Level IV Students willEE3NBT3 Compare the value of money based on place valueEx Use money (dimes and pennies) to represent place valueEx Given 15 pennies create a one group of 10 and a group of five ones
Level III Students willEE3NBT3 Count by tens using moneyEx Given three dimes count by 10 to determine totalEx Given five dimes count by 10 to determine total
Level II Students willEE3NBT3 Identify whole numbers to 10Ex Given sets of 10 pennies pair with numbersEx Given sets of 10 pennies pair with dimes
Level I Students willEE3NBT3 Count pennies to 10
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 33
Grade Level 3rdStandard with code 3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1bDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 34
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1
Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and division
Quarter 1 Quarter 2
Multiply and divide within 100
Solve word problems in situations involving equal groups arrays and measurement quantities
Represent a word problem using a picture an equation with a symbol for the unknown number or in other ways
Quarter 3
Multiply and divide within 100
Solve word problems in situations involving equal groups arrays and measurement quantities
Represent a word problem using a picture an equation with a symbol for the unknown number or in other ways
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 12
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a variety of multiplication and division word problems within 100
Explain and justify solutions and solution paths using connections among a variety of representations (eg place value blocks drawings open arrays and equations with a symbol for the unknown)
See glossary for problem types (Table 2)
Students know
Characteristics of multiplication and division contexts
Multiplication and division strategies
Students understand thatare able to
Represent quantities and operations (multiplication and division) physically pictorially or symbolically
Strategically use a variety of representations to solve multiplication and division word problems
Use informal and mathematical language to communicate the connections among multiplication and division contexts and related physical pictorial or symbolic representations
Accurately compute products and quotients
Use symbols to represent unknown quantities in equations
EE3OA3 See EE3OA1 for repeated addition a foundational skill for multiplication and division (Multiplication begins in grade 4 and division begins in grade 5)
EE3OA3 See EE3OA1 for repeated addition a foundational skill for multiplication and division (Multiplication begins in grade 4 and division begins in grade 5)
Version 3 2015-2016 13
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8times = 48 5 = 1048781 divide 3 6 times 6 = Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and division
Quarter 1 Quarter 2
Multiply and divide within 100
Determine which operation (multiplication or division) is needed to determine the unknown whole number
Solve to find the unknown whole number in a multiplication or division equation
Quarter 3
Multiply and divide within 100
Determine which operation (multiplication or division) is needed to determine the unknown whole number
Solve to find the unknown whole number in a multiplication or division equation
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 14
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 15
Students
Solve single operation multiplicationdivision equations containing a single unknown (eg 8x = 48 5= __ divide3 6x6 = ___)
Students know
Strategies for solving simple equations with one unknown
Students understand thatare able to
Efficiently apply strategies for solving simple equations with one unknown
Justify solutions for single unknown equations
Multiplication is putting together equal sized groups and division is sharing into equal-sized shares or is sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models representations
Variables represent unknown quantities when representing mathematical situations algebraically
EE3OA4 Solve addition and subtraction problems when result is unknown with number 0-30
Level IV Students willEE3OA4 Solve addition and subtraction problems when any number in the problem is unknown (result start change difference) with numbers to 50Ex Using base-10 pieces add and subtract two-digit numbers to find the sum and the differenceEx Use pictures of numbers to add and subtract two-digit numbers to find the sum and the difference
Level III Students willEE3OA4 Solve addition and subtraction problems when result is unknown with number 0-30Ex Using base-10 pieces or counters add and subtractEx Use a 100s chart to find the sum or difference of given problemsEx Use count on strategies to add (eg When asked what is 5 + 2 the student says 5 6 7)
Level II Students willEE3OA4 Solve addition and subtraction problems with numbers 0-10Ex Use counters to add and subtractEx Use number lines to add or subtractEx Match the symbol to more or less thanEx Add one to a number by indicating the next number when asked (eg when the teacher says 3 4 5 the student says 6)
Level I Students willEE3OA4 Identify numbers 1 to 9Ex Given a set of five match it to the numberEx Given a set of three identify the number of objects on number linesRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 16
Grade Level 3rdStandard with code 3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2Multiply and divide within 100
Explain how the properties of operations work
Apply properties of operations as strategies to multiply and divide
Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 17
StudentsGiven multiplication and division problems within 100
Use the properties of operations and descriptive language for the property to justify their products and quotients (eg If I know that 8 x 5 is 40 and two more groups of 8 would be 16 then 8 x 7 must be 40 + 16 or 56)
Commutative Property of Multiplication
Associative Property of Multiplication
Distributive Property
Students know
Commutative Associative Identity and Zero Properties of Multiplication and the Distributive Property
Strategies for finding products and quotients
Students understand thatare able to
Strategically and efficiently apply properties of multiplication and division in order to find products and quotients
The order in which factors are multiplied does not change the product
EE3OA5 NA (Multiplication begins at grade 4)
EE3OA5 NA (Multiplication begins at grade 4)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 18
Grade Level 3rdStandard with code 3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when multiplied by 8Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 3
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 19
StudentsGiven a division problem with an unknown quotient
Use a pictorial or physical model to explain the connection between the division problem and the related unknown factor equation
Factor Students know
Strategies for finding quotients and products
Students understand thatare able to
Use symbols to represent unknown quantities in equations
Use mathematical language to communicate the connections between an unknown quotient problem and the related unknown factor problem
Use the inverse relationship between multiplication and division to find quotients
The relationship between multiplication and division (that one undoes the other) can be used to solve problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA6 NA (Division begins at grade 5)
EE3OA6 NA (Division begins at grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 20
Grade Level 3rdStandard with code 3OA7 Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division (eg knowing that 8 times 5 = 40 one knows 40 divide 5 = 8) or properties of operations By the end of Grade 3 know from memory all products of two one-digit numbersDomain Operations and Algebraic Thinking Cluster Multiply and divide within 100
Quarter 1 Quarter 2
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 3
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Version 3 2015-2016 21
AttainmentStudentsGiven any single digit multiplication problem or a division problem with a single digit divisor and an unknown single digit quotient
Use an efficient strategy (eg recall inverse operations arrays derived facts properties of operations etc) to name the product or quotient
Students know
Strategies for finding products and quotients
Students understand thatare able to
Use multiplication and division strategies efficiently based on the numbers in the problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 22
Grade Level 3rdStandard with code 3OA8 Solve two-step word problems using the four operations Represent these problems using equations with a letter standing for the unknown quantity Assess the reasonableness of answers using mental computation and estimation strategies including rounding3
Domain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmetic
Quarter 1
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 2
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 3
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 23
StudentsGiven a variety of two-step word problems involving all four operations
Apply their understanding of operations to explain and justify solutions and solution paths using the connections among a variety of representations including equations with symbols for unknown quantities
Apply their understanding of operations and estimation strategies including rounding to evaluate the reasonableness of their solutions (eg The answer had to be around 125 because its a put together problem and 72 is close to 75 and 56 is close to 50 and 75 plus 50 is 125)
Students know
Characteristics of addition subtraction multiplication and division situations
Addition subtraction multiplication and division strategies
Strategies for mentally computing and estimating sums differences products and quotients
Students understand thatare able to
Strategically use a variety of representations to solve two-step word problems involving all four operations
Use symbols to represent unknown quantities in equations that relate to word problem contexts
Use mathematical language and contextual situations to communicate the connections among the four operations and related physical pictorial or symbolic representations and justify solutionssolution paths
Accurately compute sums differences products and quotients
Use logical reasoning mental computation strategies and estimation strategies to justify the reasonableness of
EE3OA8 Add to solve real world one-step story problems from 0-30
Level IV Students willEE3OA8 Add to solve real world one-step story problems with sums up to 50 using various problem-solving modelsEx Solve by adding (eg ldquoThere are 25 birds in a tree and 10 more joined them How many birds are in a treerdquo)Ex Solve by adding (eg ldquoI have 15 snacks on the cart and 25 snacks in the cupboard how many snacks do I have all together)Ex Solve by adding (eg ldquoAdd the pencils in two boxes and tell how many pencils we haverdquo)
Level III Students willEE3OA8 Add to solve real world one-step story problems from 0-30 Represent the problem in pictures or with objectsEx Solve by adding (eg ldquoHere are 10 pencils We need 10 more for each person to get a pencil How many will we need in allrdquo)Ex Solve by adding (eg ldquoConnie had five marbles Juan gave her eight more marbles How many marbles does Connie have all togetherrdquo)Ex Solve by adding (eg ldquoAdd the crayons in these two boxes and show me how many we have in allrdquo)
Level II Students willEE3OA8 Add to solve word problems identified through symbol representationEx Complete word problems that have pictures rather than wordsEx Solve by adding (eg ldquoThere are three ducks in the pond two more joined How many ducks are in the pondrdquo [picture representation])
Level I Students willEE3OA8 Identify the object(s) that appear in a real world one-step story problemEx Given a simple word problem and asked ldquoWhat is the problem aboutrdquo point to an object from a choice of two that represents what the problem was about (eg box toy)Ex Indicate which object a word problem is about from an array of two choices
Version 3 2015-2016 24
solutions
Multiplication is putting together equal sized groups
Division is sharing into equal-sized shares or as sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models and representations
Solutions can be evaluated by using reasoning to compare the actual solution with estimated solutions
CCSS Math Pacing Guide
Version 3 2015-2016 25
Grade 3
Grade Level 3rdStandard with code 3OA9 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations For example observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addendsDomain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmeticQuarter 1
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 2
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 3
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 26
Students
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations (eg observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends)
Students know
Characteristics of numbers and properties of operations (eg odd even)
Properties from Table 3 etc
Students understand thatare able to
Identify arithmetic patterns in number sequences in the addition table or multiplication table
Use logical reasoning and properties of numbers and operations to explain arithmetic patterns
Characteristics of numbers and properties of operations justify patterns which can be used to reason about mathematical situations form conjectures and solve problems
EE3OA9 Identify arithmetic patterns
Level IV Students willEE3OA9 Complete a complex arithmetic patternEx Complete the pattern using more than two numbers (ie A B C A B C)Ex Using a 100s number chart complete the pattern identified
Level III Students willEE3OA9 Identify arithmetic patternsEx When provided arithmetic patterns on a 100s chart identify the next number in the patternEx When given two number stamps stamp an arithmetic pattern
Level II Students willEE3OA9 Identify a patternEx Make pattern jumps on a number lineEx Sing songs and identify the pattern in the song
Level I Students willEE3OA9 Follow patternsEx Sing ldquoHead Shoulders Knees and Toesrdquo and mimic the patternEx Using tactile objects (fur sand sand fur) in a pattern repeat the patternEx Using manipulatives mimic the teacher to create a pattern
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 27
Grade Level 3rdStandard with code 3NBT1 Use place value understanding to round whole numbers to the nearest 10 or 100Domain Number and Operations in Base Ten
Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 28
StudentsGiven any number less than 1000
Round it to the nearest 10 or 100 and justify the answer using place value vocabulary (eg Rounding 147 to the nearest 10 is 150 because 147 is between 140 and 150 and is more than half way to 150)
Students know
Place value (ones tens hundreds)
Rounding
Students understand thatare able to
Count by 10s and 100s
Determine what is halfway between two multiples of 10 or 100
Round to the nearest 10 or 100
Use place value vocabulary and logical reasoning to justify solutions to rounding problems
Rounding and place value can be used to estimate quantities by changing the original number to the closest multiple of a power of 10
EE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)
Level IV Students willEE3NBT1 Identify the two 10s a number comes in between and tell which is closest (numbers 0-50)Ex Use a color beaded number line to identify the number and round to the closest 10Ex Given a number line separated into tens (0-10 10-20 etc) stand on a number and identify the 10 that is closer
Level III Students willEE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)Ex Use a color beaded number line to identify the two 10s a number falls betweenEx Given the number 14 they would identify 10 and 20
Level II Students willEE3NBT1 Identify tens on a number lineEx Given a number line circle the tensEx Stand on a number chart on 10 20 30 etc
Level I Students willEE3NBT1 Identify a numberEx Point to any number from one to three on a number lineEx Participate in a cake walk When the music stops look to see if they are on the number that is called outEx Identify a number when point to or presented on a cardEx Given a number from one to three point to the number symbolRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 29
Grade Level 3rdStandard with code 3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtractionDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 30
Students
Fluently add and subtract within 1000 using strategies based on place values properties of operations andor the relationship between addition and subtraction
Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning
Students know
Tools for modeling addition and subtraction
Strategies for solving addition and subtraction problems
Methods for symbolically (numerically) recording strategies for solving addition and subtraction problems
Students understand thatare able to
Model addition and subtraction problems using appropriate tools
Record strategies for solving addition and subtraction problems
Communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems
Relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and solution strategies
EE3NBT2 Identify place value to tens
Level IV Students willEE3NBT2 Identify place value to 50Ex Build numbers with place value piecesEx Identify the number in the ones and tens place value (ie the price of an item)Ex Write the number in expanded form ndash 43 = 40 + 3
Level III Students willEE3NBT2 Identify place value to tensEx When given two-digit number cards identify the number in the tens place valueEx When given a group of 10 frame models arrange and count the value of the numberI saw three groups of 10 and five extras so three groups of 10 = 30 and 5 more makes 35
Level II Students willEE3NBT2 Count to 10 using one-to-one correspondenceEx Given a bag of Skittles pull 10 Skittles out of the bagEx Select a domino and tell what number the dots representEx Shown a set of 10 objects create a duplicate collectionEx Given a container of pennies count out 10 from the container
Level I Students willEE3NBT2 Identify more or lessEx Given two collections of objects (group of 10 group of 20) indicate ldquoWhich has morerdquoEx Given math manipulatives representing a single unit and multiple units point to the multiple unit representation when asked ldquowhich is morerdquoRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 31
Grade Level 3rdStandard with code 3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operationsDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 32
Students
Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers
Students know
Place value models for multiplying numbers (eg open arrays place value blocks)
Strategies for multiplying one-digit numbers
Strategies for mentally multiplying one-digit numbers by multiples of powers of 10
Students understand thatare able to
Use mental strategies based on an understanding of place value properties of operations and knowledge of one-digit multiplication to find products
Use a variety of place value models of multiplication problems to justify strategies and solutions
Patterns in the place value system and properties of operations can be used to efficiently compute products
EE3NBT3 Count by tens using money
Level IV Students willEE3NBT3 Compare the value of money based on place valueEx Use money (dimes and pennies) to represent place valueEx Given 15 pennies create a one group of 10 and a group of five ones
Level III Students willEE3NBT3 Count by tens using moneyEx Given three dimes count by 10 to determine totalEx Given five dimes count by 10 to determine total
Level II Students willEE3NBT3 Identify whole numbers to 10Ex Given sets of 10 pennies pair with numbersEx Given sets of 10 pennies pair with dimes
Level I Students willEE3NBT3 Count pennies to 10
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 33
Grade Level 3rdStandard with code 3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1bDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 34
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a variety of multiplication and division word problems within 100
Explain and justify solutions and solution paths using connections among a variety of representations (eg place value blocks drawings open arrays and equations with a symbol for the unknown)
See glossary for problem types (Table 2)
Students know
Characteristics of multiplication and division contexts
Multiplication and division strategies
Students understand thatare able to
Represent quantities and operations (multiplication and division) physically pictorially or symbolically
Strategically use a variety of representations to solve multiplication and division word problems
Use informal and mathematical language to communicate the connections among multiplication and division contexts and related physical pictorial or symbolic representations
Accurately compute products and quotients
Use symbols to represent unknown quantities in equations
EE3OA3 See EE3OA1 for repeated addition a foundational skill for multiplication and division (Multiplication begins in grade 4 and division begins in grade 5)
EE3OA3 See EE3OA1 for repeated addition a foundational skill for multiplication and division (Multiplication begins in grade 4 and division begins in grade 5)
Version 3 2015-2016 13
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8times = 48 5 = 1048781 divide 3 6 times 6 = Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and division
Quarter 1 Quarter 2
Multiply and divide within 100
Determine which operation (multiplication or division) is needed to determine the unknown whole number
Solve to find the unknown whole number in a multiplication or division equation
Quarter 3
Multiply and divide within 100
Determine which operation (multiplication or division) is needed to determine the unknown whole number
Solve to find the unknown whole number in a multiplication or division equation
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 14
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 15
Students
Solve single operation multiplicationdivision equations containing a single unknown (eg 8x = 48 5= __ divide3 6x6 = ___)
Students know
Strategies for solving simple equations with one unknown
Students understand thatare able to
Efficiently apply strategies for solving simple equations with one unknown
Justify solutions for single unknown equations
Multiplication is putting together equal sized groups and division is sharing into equal-sized shares or is sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models representations
Variables represent unknown quantities when representing mathematical situations algebraically
EE3OA4 Solve addition and subtraction problems when result is unknown with number 0-30
Level IV Students willEE3OA4 Solve addition and subtraction problems when any number in the problem is unknown (result start change difference) with numbers to 50Ex Using base-10 pieces add and subtract two-digit numbers to find the sum and the differenceEx Use pictures of numbers to add and subtract two-digit numbers to find the sum and the difference
Level III Students willEE3OA4 Solve addition and subtraction problems when result is unknown with number 0-30Ex Using base-10 pieces or counters add and subtractEx Use a 100s chart to find the sum or difference of given problemsEx Use count on strategies to add (eg When asked what is 5 + 2 the student says 5 6 7)
Level II Students willEE3OA4 Solve addition and subtraction problems with numbers 0-10Ex Use counters to add and subtractEx Use number lines to add or subtractEx Match the symbol to more or less thanEx Add one to a number by indicating the next number when asked (eg when the teacher says 3 4 5 the student says 6)
Level I Students willEE3OA4 Identify numbers 1 to 9Ex Given a set of five match it to the numberEx Given a set of three identify the number of objects on number linesRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 16
Grade Level 3rdStandard with code 3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2Multiply and divide within 100
Explain how the properties of operations work
Apply properties of operations as strategies to multiply and divide
Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 17
StudentsGiven multiplication and division problems within 100
Use the properties of operations and descriptive language for the property to justify their products and quotients (eg If I know that 8 x 5 is 40 and two more groups of 8 would be 16 then 8 x 7 must be 40 + 16 or 56)
Commutative Property of Multiplication
Associative Property of Multiplication
Distributive Property
Students know
Commutative Associative Identity and Zero Properties of Multiplication and the Distributive Property
Strategies for finding products and quotients
Students understand thatare able to
Strategically and efficiently apply properties of multiplication and division in order to find products and quotients
The order in which factors are multiplied does not change the product
EE3OA5 NA (Multiplication begins at grade 4)
EE3OA5 NA (Multiplication begins at grade 4)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 18
Grade Level 3rdStandard with code 3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when multiplied by 8Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 3
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 19
StudentsGiven a division problem with an unknown quotient
Use a pictorial or physical model to explain the connection between the division problem and the related unknown factor equation
Factor Students know
Strategies for finding quotients and products
Students understand thatare able to
Use symbols to represent unknown quantities in equations
Use mathematical language to communicate the connections between an unknown quotient problem and the related unknown factor problem
Use the inverse relationship between multiplication and division to find quotients
The relationship between multiplication and division (that one undoes the other) can be used to solve problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA6 NA (Division begins at grade 5)
EE3OA6 NA (Division begins at grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 20
Grade Level 3rdStandard with code 3OA7 Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division (eg knowing that 8 times 5 = 40 one knows 40 divide 5 = 8) or properties of operations By the end of Grade 3 know from memory all products of two one-digit numbersDomain Operations and Algebraic Thinking Cluster Multiply and divide within 100
Quarter 1 Quarter 2
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 3
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Version 3 2015-2016 21
AttainmentStudentsGiven any single digit multiplication problem or a division problem with a single digit divisor and an unknown single digit quotient
Use an efficient strategy (eg recall inverse operations arrays derived facts properties of operations etc) to name the product or quotient
Students know
Strategies for finding products and quotients
Students understand thatare able to
Use multiplication and division strategies efficiently based on the numbers in the problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 22
Grade Level 3rdStandard with code 3OA8 Solve two-step word problems using the four operations Represent these problems using equations with a letter standing for the unknown quantity Assess the reasonableness of answers using mental computation and estimation strategies including rounding3
Domain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmetic
Quarter 1
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 2
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 3
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 23
StudentsGiven a variety of two-step word problems involving all four operations
Apply their understanding of operations to explain and justify solutions and solution paths using the connections among a variety of representations including equations with symbols for unknown quantities
Apply their understanding of operations and estimation strategies including rounding to evaluate the reasonableness of their solutions (eg The answer had to be around 125 because its a put together problem and 72 is close to 75 and 56 is close to 50 and 75 plus 50 is 125)
Students know
Characteristics of addition subtraction multiplication and division situations
Addition subtraction multiplication and division strategies
Strategies for mentally computing and estimating sums differences products and quotients
Students understand thatare able to
Strategically use a variety of representations to solve two-step word problems involving all four operations
Use symbols to represent unknown quantities in equations that relate to word problem contexts
Use mathematical language and contextual situations to communicate the connections among the four operations and related physical pictorial or symbolic representations and justify solutionssolution paths
Accurately compute sums differences products and quotients
Use logical reasoning mental computation strategies and estimation strategies to justify the reasonableness of
EE3OA8 Add to solve real world one-step story problems from 0-30
Level IV Students willEE3OA8 Add to solve real world one-step story problems with sums up to 50 using various problem-solving modelsEx Solve by adding (eg ldquoThere are 25 birds in a tree and 10 more joined them How many birds are in a treerdquo)Ex Solve by adding (eg ldquoI have 15 snacks on the cart and 25 snacks in the cupboard how many snacks do I have all together)Ex Solve by adding (eg ldquoAdd the pencils in two boxes and tell how many pencils we haverdquo)
Level III Students willEE3OA8 Add to solve real world one-step story problems from 0-30 Represent the problem in pictures or with objectsEx Solve by adding (eg ldquoHere are 10 pencils We need 10 more for each person to get a pencil How many will we need in allrdquo)Ex Solve by adding (eg ldquoConnie had five marbles Juan gave her eight more marbles How many marbles does Connie have all togetherrdquo)Ex Solve by adding (eg ldquoAdd the crayons in these two boxes and show me how many we have in allrdquo)
Level II Students willEE3OA8 Add to solve word problems identified through symbol representationEx Complete word problems that have pictures rather than wordsEx Solve by adding (eg ldquoThere are three ducks in the pond two more joined How many ducks are in the pondrdquo [picture representation])
Level I Students willEE3OA8 Identify the object(s) that appear in a real world one-step story problemEx Given a simple word problem and asked ldquoWhat is the problem aboutrdquo point to an object from a choice of two that represents what the problem was about (eg box toy)Ex Indicate which object a word problem is about from an array of two choices
Version 3 2015-2016 24
solutions
Multiplication is putting together equal sized groups
Division is sharing into equal-sized shares or as sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models and representations
Solutions can be evaluated by using reasoning to compare the actual solution with estimated solutions
CCSS Math Pacing Guide
Version 3 2015-2016 25
Grade 3
Grade Level 3rdStandard with code 3OA9 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations For example observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addendsDomain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmeticQuarter 1
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 2
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 3
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 26
Students
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations (eg observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends)
Students know
Characteristics of numbers and properties of operations (eg odd even)
Properties from Table 3 etc
Students understand thatare able to
Identify arithmetic patterns in number sequences in the addition table or multiplication table
Use logical reasoning and properties of numbers and operations to explain arithmetic patterns
Characteristics of numbers and properties of operations justify patterns which can be used to reason about mathematical situations form conjectures and solve problems
EE3OA9 Identify arithmetic patterns
Level IV Students willEE3OA9 Complete a complex arithmetic patternEx Complete the pattern using more than two numbers (ie A B C A B C)Ex Using a 100s number chart complete the pattern identified
Level III Students willEE3OA9 Identify arithmetic patternsEx When provided arithmetic patterns on a 100s chart identify the next number in the patternEx When given two number stamps stamp an arithmetic pattern
Level II Students willEE3OA9 Identify a patternEx Make pattern jumps on a number lineEx Sing songs and identify the pattern in the song
Level I Students willEE3OA9 Follow patternsEx Sing ldquoHead Shoulders Knees and Toesrdquo and mimic the patternEx Using tactile objects (fur sand sand fur) in a pattern repeat the patternEx Using manipulatives mimic the teacher to create a pattern
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 27
Grade Level 3rdStandard with code 3NBT1 Use place value understanding to round whole numbers to the nearest 10 or 100Domain Number and Operations in Base Ten
Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 28
StudentsGiven any number less than 1000
Round it to the nearest 10 or 100 and justify the answer using place value vocabulary (eg Rounding 147 to the nearest 10 is 150 because 147 is between 140 and 150 and is more than half way to 150)
Students know
Place value (ones tens hundreds)
Rounding
Students understand thatare able to
Count by 10s and 100s
Determine what is halfway between two multiples of 10 or 100
Round to the nearest 10 or 100
Use place value vocabulary and logical reasoning to justify solutions to rounding problems
Rounding and place value can be used to estimate quantities by changing the original number to the closest multiple of a power of 10
EE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)
Level IV Students willEE3NBT1 Identify the two 10s a number comes in between and tell which is closest (numbers 0-50)Ex Use a color beaded number line to identify the number and round to the closest 10Ex Given a number line separated into tens (0-10 10-20 etc) stand on a number and identify the 10 that is closer
Level III Students willEE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)Ex Use a color beaded number line to identify the two 10s a number falls betweenEx Given the number 14 they would identify 10 and 20
Level II Students willEE3NBT1 Identify tens on a number lineEx Given a number line circle the tensEx Stand on a number chart on 10 20 30 etc
Level I Students willEE3NBT1 Identify a numberEx Point to any number from one to three on a number lineEx Participate in a cake walk When the music stops look to see if they are on the number that is called outEx Identify a number when point to or presented on a cardEx Given a number from one to three point to the number symbolRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 29
Grade Level 3rdStandard with code 3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtractionDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 30
Students
Fluently add and subtract within 1000 using strategies based on place values properties of operations andor the relationship between addition and subtraction
Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning
Students know
Tools for modeling addition and subtraction
Strategies for solving addition and subtraction problems
Methods for symbolically (numerically) recording strategies for solving addition and subtraction problems
Students understand thatare able to
Model addition and subtraction problems using appropriate tools
Record strategies for solving addition and subtraction problems
Communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems
Relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and solution strategies
EE3NBT2 Identify place value to tens
Level IV Students willEE3NBT2 Identify place value to 50Ex Build numbers with place value piecesEx Identify the number in the ones and tens place value (ie the price of an item)Ex Write the number in expanded form ndash 43 = 40 + 3
Level III Students willEE3NBT2 Identify place value to tensEx When given two-digit number cards identify the number in the tens place valueEx When given a group of 10 frame models arrange and count the value of the numberI saw three groups of 10 and five extras so three groups of 10 = 30 and 5 more makes 35
Level II Students willEE3NBT2 Count to 10 using one-to-one correspondenceEx Given a bag of Skittles pull 10 Skittles out of the bagEx Select a domino and tell what number the dots representEx Shown a set of 10 objects create a duplicate collectionEx Given a container of pennies count out 10 from the container
Level I Students willEE3NBT2 Identify more or lessEx Given two collections of objects (group of 10 group of 20) indicate ldquoWhich has morerdquoEx Given math manipulatives representing a single unit and multiple units point to the multiple unit representation when asked ldquowhich is morerdquoRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 31
Grade Level 3rdStandard with code 3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operationsDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 32
Students
Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers
Students know
Place value models for multiplying numbers (eg open arrays place value blocks)
Strategies for multiplying one-digit numbers
Strategies for mentally multiplying one-digit numbers by multiples of powers of 10
Students understand thatare able to
Use mental strategies based on an understanding of place value properties of operations and knowledge of one-digit multiplication to find products
Use a variety of place value models of multiplication problems to justify strategies and solutions
Patterns in the place value system and properties of operations can be used to efficiently compute products
EE3NBT3 Count by tens using money
Level IV Students willEE3NBT3 Compare the value of money based on place valueEx Use money (dimes and pennies) to represent place valueEx Given 15 pennies create a one group of 10 and a group of five ones
Level III Students willEE3NBT3 Count by tens using moneyEx Given three dimes count by 10 to determine totalEx Given five dimes count by 10 to determine total
Level II Students willEE3NBT3 Identify whole numbers to 10Ex Given sets of 10 pennies pair with numbersEx Given sets of 10 pennies pair with dimes
Level I Students willEE3NBT3 Count pennies to 10
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 33
Grade Level 3rdStandard with code 3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1bDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 34
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8times = 48 5 = 1048781 divide 3 6 times 6 = Domain Operations and Algebraic Thinking Cluster Represent and solve problems involving multiplication and division
Quarter 1 Quarter 2
Multiply and divide within 100
Determine which operation (multiplication or division) is needed to determine the unknown whole number
Solve to find the unknown whole number in a multiplication or division equation
Quarter 3
Multiply and divide within 100
Determine which operation (multiplication or division) is needed to determine the unknown whole number
Solve to find the unknown whole number in a multiplication or division equation
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Version 3 2015-2016 14
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 15
Students
Solve single operation multiplicationdivision equations containing a single unknown (eg 8x = 48 5= __ divide3 6x6 = ___)
Students know
Strategies for solving simple equations with one unknown
Students understand thatare able to
Efficiently apply strategies for solving simple equations with one unknown
Justify solutions for single unknown equations
Multiplication is putting together equal sized groups and division is sharing into equal-sized shares or is sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models representations
Variables represent unknown quantities when representing mathematical situations algebraically
EE3OA4 Solve addition and subtraction problems when result is unknown with number 0-30
Level IV Students willEE3OA4 Solve addition and subtraction problems when any number in the problem is unknown (result start change difference) with numbers to 50Ex Using base-10 pieces add and subtract two-digit numbers to find the sum and the differenceEx Use pictures of numbers to add and subtract two-digit numbers to find the sum and the difference
Level III Students willEE3OA4 Solve addition and subtraction problems when result is unknown with number 0-30Ex Using base-10 pieces or counters add and subtractEx Use a 100s chart to find the sum or difference of given problemsEx Use count on strategies to add (eg When asked what is 5 + 2 the student says 5 6 7)
Level II Students willEE3OA4 Solve addition and subtraction problems with numbers 0-10Ex Use counters to add and subtractEx Use number lines to add or subtractEx Match the symbol to more or less thanEx Add one to a number by indicating the next number when asked (eg when the teacher says 3 4 5 the student says 6)
Level I Students willEE3OA4 Identify numbers 1 to 9Ex Given a set of five match it to the numberEx Given a set of three identify the number of objects on number linesRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 16
Grade Level 3rdStandard with code 3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2Multiply and divide within 100
Explain how the properties of operations work
Apply properties of operations as strategies to multiply and divide
Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 17
StudentsGiven multiplication and division problems within 100
Use the properties of operations and descriptive language for the property to justify their products and quotients (eg If I know that 8 x 5 is 40 and two more groups of 8 would be 16 then 8 x 7 must be 40 + 16 or 56)
Commutative Property of Multiplication
Associative Property of Multiplication
Distributive Property
Students know
Commutative Associative Identity and Zero Properties of Multiplication and the Distributive Property
Strategies for finding products and quotients
Students understand thatare able to
Strategically and efficiently apply properties of multiplication and division in order to find products and quotients
The order in which factors are multiplied does not change the product
EE3OA5 NA (Multiplication begins at grade 4)
EE3OA5 NA (Multiplication begins at grade 4)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 18
Grade Level 3rdStandard with code 3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when multiplied by 8Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 3
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 19
StudentsGiven a division problem with an unknown quotient
Use a pictorial or physical model to explain the connection between the division problem and the related unknown factor equation
Factor Students know
Strategies for finding quotients and products
Students understand thatare able to
Use symbols to represent unknown quantities in equations
Use mathematical language to communicate the connections between an unknown quotient problem and the related unknown factor problem
Use the inverse relationship between multiplication and division to find quotients
The relationship between multiplication and division (that one undoes the other) can be used to solve problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA6 NA (Division begins at grade 5)
EE3OA6 NA (Division begins at grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 20
Grade Level 3rdStandard with code 3OA7 Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division (eg knowing that 8 times 5 = 40 one knows 40 divide 5 = 8) or properties of operations By the end of Grade 3 know from memory all products of two one-digit numbersDomain Operations and Algebraic Thinking Cluster Multiply and divide within 100
Quarter 1 Quarter 2
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 3
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Version 3 2015-2016 21
AttainmentStudentsGiven any single digit multiplication problem or a division problem with a single digit divisor and an unknown single digit quotient
Use an efficient strategy (eg recall inverse operations arrays derived facts properties of operations etc) to name the product or quotient
Students know
Strategies for finding products and quotients
Students understand thatare able to
Use multiplication and division strategies efficiently based on the numbers in the problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 22
Grade Level 3rdStandard with code 3OA8 Solve two-step word problems using the four operations Represent these problems using equations with a letter standing for the unknown quantity Assess the reasonableness of answers using mental computation and estimation strategies including rounding3
Domain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmetic
Quarter 1
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 2
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 3
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 23
StudentsGiven a variety of two-step word problems involving all four operations
Apply their understanding of operations to explain and justify solutions and solution paths using the connections among a variety of representations including equations with symbols for unknown quantities
Apply their understanding of operations and estimation strategies including rounding to evaluate the reasonableness of their solutions (eg The answer had to be around 125 because its a put together problem and 72 is close to 75 and 56 is close to 50 and 75 plus 50 is 125)
Students know
Characteristics of addition subtraction multiplication and division situations
Addition subtraction multiplication and division strategies
Strategies for mentally computing and estimating sums differences products and quotients
Students understand thatare able to
Strategically use a variety of representations to solve two-step word problems involving all four operations
Use symbols to represent unknown quantities in equations that relate to word problem contexts
Use mathematical language and contextual situations to communicate the connections among the four operations and related physical pictorial or symbolic representations and justify solutionssolution paths
Accurately compute sums differences products and quotients
Use logical reasoning mental computation strategies and estimation strategies to justify the reasonableness of
EE3OA8 Add to solve real world one-step story problems from 0-30
Level IV Students willEE3OA8 Add to solve real world one-step story problems with sums up to 50 using various problem-solving modelsEx Solve by adding (eg ldquoThere are 25 birds in a tree and 10 more joined them How many birds are in a treerdquo)Ex Solve by adding (eg ldquoI have 15 snacks on the cart and 25 snacks in the cupboard how many snacks do I have all together)Ex Solve by adding (eg ldquoAdd the pencils in two boxes and tell how many pencils we haverdquo)
Level III Students willEE3OA8 Add to solve real world one-step story problems from 0-30 Represent the problem in pictures or with objectsEx Solve by adding (eg ldquoHere are 10 pencils We need 10 more for each person to get a pencil How many will we need in allrdquo)Ex Solve by adding (eg ldquoConnie had five marbles Juan gave her eight more marbles How many marbles does Connie have all togetherrdquo)Ex Solve by adding (eg ldquoAdd the crayons in these two boxes and show me how many we have in allrdquo)
Level II Students willEE3OA8 Add to solve word problems identified through symbol representationEx Complete word problems that have pictures rather than wordsEx Solve by adding (eg ldquoThere are three ducks in the pond two more joined How many ducks are in the pondrdquo [picture representation])
Level I Students willEE3OA8 Identify the object(s) that appear in a real world one-step story problemEx Given a simple word problem and asked ldquoWhat is the problem aboutrdquo point to an object from a choice of two that represents what the problem was about (eg box toy)Ex Indicate which object a word problem is about from an array of two choices
Version 3 2015-2016 24
solutions
Multiplication is putting together equal sized groups
Division is sharing into equal-sized shares or as sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models and representations
Solutions can be evaluated by using reasoning to compare the actual solution with estimated solutions
CCSS Math Pacing Guide
Version 3 2015-2016 25
Grade 3
Grade Level 3rdStandard with code 3OA9 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations For example observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addendsDomain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmeticQuarter 1
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 2
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 3
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 26
Students
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations (eg observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends)
Students know
Characteristics of numbers and properties of operations (eg odd even)
Properties from Table 3 etc
Students understand thatare able to
Identify arithmetic patterns in number sequences in the addition table or multiplication table
Use logical reasoning and properties of numbers and operations to explain arithmetic patterns
Characteristics of numbers and properties of operations justify patterns which can be used to reason about mathematical situations form conjectures and solve problems
EE3OA9 Identify arithmetic patterns
Level IV Students willEE3OA9 Complete a complex arithmetic patternEx Complete the pattern using more than two numbers (ie A B C A B C)Ex Using a 100s number chart complete the pattern identified
Level III Students willEE3OA9 Identify arithmetic patternsEx When provided arithmetic patterns on a 100s chart identify the next number in the patternEx When given two number stamps stamp an arithmetic pattern
Level II Students willEE3OA9 Identify a patternEx Make pattern jumps on a number lineEx Sing songs and identify the pattern in the song
Level I Students willEE3OA9 Follow patternsEx Sing ldquoHead Shoulders Knees and Toesrdquo and mimic the patternEx Using tactile objects (fur sand sand fur) in a pattern repeat the patternEx Using manipulatives mimic the teacher to create a pattern
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 27
Grade Level 3rdStandard with code 3NBT1 Use place value understanding to round whole numbers to the nearest 10 or 100Domain Number and Operations in Base Ten
Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 28
StudentsGiven any number less than 1000
Round it to the nearest 10 or 100 and justify the answer using place value vocabulary (eg Rounding 147 to the nearest 10 is 150 because 147 is between 140 and 150 and is more than half way to 150)
Students know
Place value (ones tens hundreds)
Rounding
Students understand thatare able to
Count by 10s and 100s
Determine what is halfway between two multiples of 10 or 100
Round to the nearest 10 or 100
Use place value vocabulary and logical reasoning to justify solutions to rounding problems
Rounding and place value can be used to estimate quantities by changing the original number to the closest multiple of a power of 10
EE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)
Level IV Students willEE3NBT1 Identify the two 10s a number comes in between and tell which is closest (numbers 0-50)Ex Use a color beaded number line to identify the number and round to the closest 10Ex Given a number line separated into tens (0-10 10-20 etc) stand on a number and identify the 10 that is closer
Level III Students willEE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)Ex Use a color beaded number line to identify the two 10s a number falls betweenEx Given the number 14 they would identify 10 and 20
Level II Students willEE3NBT1 Identify tens on a number lineEx Given a number line circle the tensEx Stand on a number chart on 10 20 30 etc
Level I Students willEE3NBT1 Identify a numberEx Point to any number from one to three on a number lineEx Participate in a cake walk When the music stops look to see if they are on the number that is called outEx Identify a number when point to or presented on a cardEx Given a number from one to three point to the number symbolRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 29
Grade Level 3rdStandard with code 3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtractionDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 30
Students
Fluently add and subtract within 1000 using strategies based on place values properties of operations andor the relationship between addition and subtraction
Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning
Students know
Tools for modeling addition and subtraction
Strategies for solving addition and subtraction problems
Methods for symbolically (numerically) recording strategies for solving addition and subtraction problems
Students understand thatare able to
Model addition and subtraction problems using appropriate tools
Record strategies for solving addition and subtraction problems
Communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems
Relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and solution strategies
EE3NBT2 Identify place value to tens
Level IV Students willEE3NBT2 Identify place value to 50Ex Build numbers with place value piecesEx Identify the number in the ones and tens place value (ie the price of an item)Ex Write the number in expanded form ndash 43 = 40 + 3
Level III Students willEE3NBT2 Identify place value to tensEx When given two-digit number cards identify the number in the tens place valueEx When given a group of 10 frame models arrange and count the value of the numberI saw three groups of 10 and five extras so three groups of 10 = 30 and 5 more makes 35
Level II Students willEE3NBT2 Count to 10 using one-to-one correspondenceEx Given a bag of Skittles pull 10 Skittles out of the bagEx Select a domino and tell what number the dots representEx Shown a set of 10 objects create a duplicate collectionEx Given a container of pennies count out 10 from the container
Level I Students willEE3NBT2 Identify more or lessEx Given two collections of objects (group of 10 group of 20) indicate ldquoWhich has morerdquoEx Given math manipulatives representing a single unit and multiple units point to the multiple unit representation when asked ldquowhich is morerdquoRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 31
Grade Level 3rdStandard with code 3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operationsDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 32
Students
Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers
Students know
Place value models for multiplying numbers (eg open arrays place value blocks)
Strategies for multiplying one-digit numbers
Strategies for mentally multiplying one-digit numbers by multiples of powers of 10
Students understand thatare able to
Use mental strategies based on an understanding of place value properties of operations and knowledge of one-digit multiplication to find products
Use a variety of place value models of multiplication problems to justify strategies and solutions
Patterns in the place value system and properties of operations can be used to efficiently compute products
EE3NBT3 Count by tens using money
Level IV Students willEE3NBT3 Compare the value of money based on place valueEx Use money (dimes and pennies) to represent place valueEx Given 15 pennies create a one group of 10 and a group of five ones
Level III Students willEE3NBT3 Count by tens using moneyEx Given three dimes count by 10 to determine totalEx Given five dimes count by 10 to determine total
Level II Students willEE3NBT3 Identify whole numbers to 10Ex Given sets of 10 pennies pair with numbersEx Given sets of 10 pennies pair with dimes
Level I Students willEE3NBT3 Count pennies to 10
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 33
Grade Level 3rdStandard with code 3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1bDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 34
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 15
Students
Solve single operation multiplicationdivision equations containing a single unknown (eg 8x = 48 5= __ divide3 6x6 = ___)
Students know
Strategies for solving simple equations with one unknown
Students understand thatare able to
Efficiently apply strategies for solving simple equations with one unknown
Justify solutions for single unknown equations
Multiplication is putting together equal sized groups and division is sharing into equal-sized shares or is sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models representations
Variables represent unknown quantities when representing mathematical situations algebraically
EE3OA4 Solve addition and subtraction problems when result is unknown with number 0-30
Level IV Students willEE3OA4 Solve addition and subtraction problems when any number in the problem is unknown (result start change difference) with numbers to 50Ex Using base-10 pieces add and subtract two-digit numbers to find the sum and the differenceEx Use pictures of numbers to add and subtract two-digit numbers to find the sum and the difference
Level III Students willEE3OA4 Solve addition and subtraction problems when result is unknown with number 0-30Ex Using base-10 pieces or counters add and subtractEx Use a 100s chart to find the sum or difference of given problemsEx Use count on strategies to add (eg When asked what is 5 + 2 the student says 5 6 7)
Level II Students willEE3OA4 Solve addition and subtraction problems with numbers 0-10Ex Use counters to add and subtractEx Use number lines to add or subtractEx Match the symbol to more or less thanEx Add one to a number by indicating the next number when asked (eg when the teacher says 3 4 5 the student says 6)
Level I Students willEE3OA4 Identify numbers 1 to 9Ex Given a set of five match it to the numberEx Given a set of three identify the number of objects on number linesRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 16
Grade Level 3rdStandard with code 3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2Multiply and divide within 100
Explain how the properties of operations work
Apply properties of operations as strategies to multiply and divide
Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 17
StudentsGiven multiplication and division problems within 100
Use the properties of operations and descriptive language for the property to justify their products and quotients (eg If I know that 8 x 5 is 40 and two more groups of 8 would be 16 then 8 x 7 must be 40 + 16 or 56)
Commutative Property of Multiplication
Associative Property of Multiplication
Distributive Property
Students know
Commutative Associative Identity and Zero Properties of Multiplication and the Distributive Property
Strategies for finding products and quotients
Students understand thatare able to
Strategically and efficiently apply properties of multiplication and division in order to find products and quotients
The order in which factors are multiplied does not change the product
EE3OA5 NA (Multiplication begins at grade 4)
EE3OA5 NA (Multiplication begins at grade 4)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 18
Grade Level 3rdStandard with code 3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when multiplied by 8Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 3
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 19
StudentsGiven a division problem with an unknown quotient
Use a pictorial or physical model to explain the connection between the division problem and the related unknown factor equation
Factor Students know
Strategies for finding quotients and products
Students understand thatare able to
Use symbols to represent unknown quantities in equations
Use mathematical language to communicate the connections between an unknown quotient problem and the related unknown factor problem
Use the inverse relationship between multiplication and division to find quotients
The relationship between multiplication and division (that one undoes the other) can be used to solve problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA6 NA (Division begins at grade 5)
EE3OA6 NA (Division begins at grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 20
Grade Level 3rdStandard with code 3OA7 Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division (eg knowing that 8 times 5 = 40 one knows 40 divide 5 = 8) or properties of operations By the end of Grade 3 know from memory all products of two one-digit numbersDomain Operations and Algebraic Thinking Cluster Multiply and divide within 100
Quarter 1 Quarter 2
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 3
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Version 3 2015-2016 21
AttainmentStudentsGiven any single digit multiplication problem or a division problem with a single digit divisor and an unknown single digit quotient
Use an efficient strategy (eg recall inverse operations arrays derived facts properties of operations etc) to name the product or quotient
Students know
Strategies for finding products and quotients
Students understand thatare able to
Use multiplication and division strategies efficiently based on the numbers in the problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 22
Grade Level 3rdStandard with code 3OA8 Solve two-step word problems using the four operations Represent these problems using equations with a letter standing for the unknown quantity Assess the reasonableness of answers using mental computation and estimation strategies including rounding3
Domain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmetic
Quarter 1
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 2
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 3
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 23
StudentsGiven a variety of two-step word problems involving all four operations
Apply their understanding of operations to explain and justify solutions and solution paths using the connections among a variety of representations including equations with symbols for unknown quantities
Apply their understanding of operations and estimation strategies including rounding to evaluate the reasonableness of their solutions (eg The answer had to be around 125 because its a put together problem and 72 is close to 75 and 56 is close to 50 and 75 plus 50 is 125)
Students know
Characteristics of addition subtraction multiplication and division situations
Addition subtraction multiplication and division strategies
Strategies for mentally computing and estimating sums differences products and quotients
Students understand thatare able to
Strategically use a variety of representations to solve two-step word problems involving all four operations
Use symbols to represent unknown quantities in equations that relate to word problem contexts
Use mathematical language and contextual situations to communicate the connections among the four operations and related physical pictorial or symbolic representations and justify solutionssolution paths
Accurately compute sums differences products and quotients
Use logical reasoning mental computation strategies and estimation strategies to justify the reasonableness of
EE3OA8 Add to solve real world one-step story problems from 0-30
Level IV Students willEE3OA8 Add to solve real world one-step story problems with sums up to 50 using various problem-solving modelsEx Solve by adding (eg ldquoThere are 25 birds in a tree and 10 more joined them How many birds are in a treerdquo)Ex Solve by adding (eg ldquoI have 15 snacks on the cart and 25 snacks in the cupboard how many snacks do I have all together)Ex Solve by adding (eg ldquoAdd the pencils in two boxes and tell how many pencils we haverdquo)
Level III Students willEE3OA8 Add to solve real world one-step story problems from 0-30 Represent the problem in pictures or with objectsEx Solve by adding (eg ldquoHere are 10 pencils We need 10 more for each person to get a pencil How many will we need in allrdquo)Ex Solve by adding (eg ldquoConnie had five marbles Juan gave her eight more marbles How many marbles does Connie have all togetherrdquo)Ex Solve by adding (eg ldquoAdd the crayons in these two boxes and show me how many we have in allrdquo)
Level II Students willEE3OA8 Add to solve word problems identified through symbol representationEx Complete word problems that have pictures rather than wordsEx Solve by adding (eg ldquoThere are three ducks in the pond two more joined How many ducks are in the pondrdquo [picture representation])
Level I Students willEE3OA8 Identify the object(s) that appear in a real world one-step story problemEx Given a simple word problem and asked ldquoWhat is the problem aboutrdquo point to an object from a choice of two that represents what the problem was about (eg box toy)Ex Indicate which object a word problem is about from an array of two choices
Version 3 2015-2016 24
solutions
Multiplication is putting together equal sized groups
Division is sharing into equal-sized shares or as sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models and representations
Solutions can be evaluated by using reasoning to compare the actual solution with estimated solutions
CCSS Math Pacing Guide
Version 3 2015-2016 25
Grade 3
Grade Level 3rdStandard with code 3OA9 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations For example observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addendsDomain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmeticQuarter 1
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 2
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 3
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 26
Students
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations (eg observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends)
Students know
Characteristics of numbers and properties of operations (eg odd even)
Properties from Table 3 etc
Students understand thatare able to
Identify arithmetic patterns in number sequences in the addition table or multiplication table
Use logical reasoning and properties of numbers and operations to explain arithmetic patterns
Characteristics of numbers and properties of operations justify patterns which can be used to reason about mathematical situations form conjectures and solve problems
EE3OA9 Identify arithmetic patterns
Level IV Students willEE3OA9 Complete a complex arithmetic patternEx Complete the pattern using more than two numbers (ie A B C A B C)Ex Using a 100s number chart complete the pattern identified
Level III Students willEE3OA9 Identify arithmetic patternsEx When provided arithmetic patterns on a 100s chart identify the next number in the patternEx When given two number stamps stamp an arithmetic pattern
Level II Students willEE3OA9 Identify a patternEx Make pattern jumps on a number lineEx Sing songs and identify the pattern in the song
Level I Students willEE3OA9 Follow patternsEx Sing ldquoHead Shoulders Knees and Toesrdquo and mimic the patternEx Using tactile objects (fur sand sand fur) in a pattern repeat the patternEx Using manipulatives mimic the teacher to create a pattern
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 27
Grade Level 3rdStandard with code 3NBT1 Use place value understanding to round whole numbers to the nearest 10 or 100Domain Number and Operations in Base Ten
Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 28
StudentsGiven any number less than 1000
Round it to the nearest 10 or 100 and justify the answer using place value vocabulary (eg Rounding 147 to the nearest 10 is 150 because 147 is between 140 and 150 and is more than half way to 150)
Students know
Place value (ones tens hundreds)
Rounding
Students understand thatare able to
Count by 10s and 100s
Determine what is halfway between two multiples of 10 or 100
Round to the nearest 10 or 100
Use place value vocabulary and logical reasoning to justify solutions to rounding problems
Rounding and place value can be used to estimate quantities by changing the original number to the closest multiple of a power of 10
EE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)
Level IV Students willEE3NBT1 Identify the two 10s a number comes in between and tell which is closest (numbers 0-50)Ex Use a color beaded number line to identify the number and round to the closest 10Ex Given a number line separated into tens (0-10 10-20 etc) stand on a number and identify the 10 that is closer
Level III Students willEE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)Ex Use a color beaded number line to identify the two 10s a number falls betweenEx Given the number 14 they would identify 10 and 20
Level II Students willEE3NBT1 Identify tens on a number lineEx Given a number line circle the tensEx Stand on a number chart on 10 20 30 etc
Level I Students willEE3NBT1 Identify a numberEx Point to any number from one to three on a number lineEx Participate in a cake walk When the music stops look to see if they are on the number that is called outEx Identify a number when point to or presented on a cardEx Given a number from one to three point to the number symbolRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 29
Grade Level 3rdStandard with code 3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtractionDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 30
Students
Fluently add and subtract within 1000 using strategies based on place values properties of operations andor the relationship between addition and subtraction
Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning
Students know
Tools for modeling addition and subtraction
Strategies for solving addition and subtraction problems
Methods for symbolically (numerically) recording strategies for solving addition and subtraction problems
Students understand thatare able to
Model addition and subtraction problems using appropriate tools
Record strategies for solving addition and subtraction problems
Communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems
Relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and solution strategies
EE3NBT2 Identify place value to tens
Level IV Students willEE3NBT2 Identify place value to 50Ex Build numbers with place value piecesEx Identify the number in the ones and tens place value (ie the price of an item)Ex Write the number in expanded form ndash 43 = 40 + 3
Level III Students willEE3NBT2 Identify place value to tensEx When given two-digit number cards identify the number in the tens place valueEx When given a group of 10 frame models arrange and count the value of the numberI saw three groups of 10 and five extras so three groups of 10 = 30 and 5 more makes 35
Level II Students willEE3NBT2 Count to 10 using one-to-one correspondenceEx Given a bag of Skittles pull 10 Skittles out of the bagEx Select a domino and tell what number the dots representEx Shown a set of 10 objects create a duplicate collectionEx Given a container of pennies count out 10 from the container
Level I Students willEE3NBT2 Identify more or lessEx Given two collections of objects (group of 10 group of 20) indicate ldquoWhich has morerdquoEx Given math manipulatives representing a single unit and multiple units point to the multiple unit representation when asked ldquowhich is morerdquoRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 31
Grade Level 3rdStandard with code 3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operationsDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 32
Students
Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers
Students know
Place value models for multiplying numbers (eg open arrays place value blocks)
Strategies for multiplying one-digit numbers
Strategies for mentally multiplying one-digit numbers by multiples of powers of 10
Students understand thatare able to
Use mental strategies based on an understanding of place value properties of operations and knowledge of one-digit multiplication to find products
Use a variety of place value models of multiplication problems to justify strategies and solutions
Patterns in the place value system and properties of operations can be used to efficiently compute products
EE3NBT3 Count by tens using money
Level IV Students willEE3NBT3 Compare the value of money based on place valueEx Use money (dimes and pennies) to represent place valueEx Given 15 pennies create a one group of 10 and a group of five ones
Level III Students willEE3NBT3 Count by tens using moneyEx Given three dimes count by 10 to determine totalEx Given five dimes count by 10 to determine total
Level II Students willEE3NBT3 Identify whole numbers to 10Ex Given sets of 10 pennies pair with numbersEx Given sets of 10 pennies pair with dimes
Level I Students willEE3NBT3 Count pennies to 10
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 33
Grade Level 3rdStandard with code 3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1bDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 34
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Students
Solve single operation multiplicationdivision equations containing a single unknown (eg 8x = 48 5= __ divide3 6x6 = ___)
Students know
Strategies for solving simple equations with one unknown
Students understand thatare able to
Efficiently apply strategies for solving simple equations with one unknown
Justify solutions for single unknown equations
Multiplication is putting together equal sized groups and division is sharing into equal-sized shares or is sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models representations
Variables represent unknown quantities when representing mathematical situations algebraically
EE3OA4 Solve addition and subtraction problems when result is unknown with number 0-30
Level IV Students willEE3OA4 Solve addition and subtraction problems when any number in the problem is unknown (result start change difference) with numbers to 50Ex Using base-10 pieces add and subtract two-digit numbers to find the sum and the differenceEx Use pictures of numbers to add and subtract two-digit numbers to find the sum and the difference
Level III Students willEE3OA4 Solve addition and subtraction problems when result is unknown with number 0-30Ex Using base-10 pieces or counters add and subtractEx Use a 100s chart to find the sum or difference of given problemsEx Use count on strategies to add (eg When asked what is 5 + 2 the student says 5 6 7)
Level II Students willEE3OA4 Solve addition and subtraction problems with numbers 0-10Ex Use counters to add and subtractEx Use number lines to add or subtractEx Match the symbol to more or less thanEx Add one to a number by indicating the next number when asked (eg when the teacher says 3 4 5 the student says 6)
Level I Students willEE3OA4 Identify numbers 1 to 9Ex Given a set of five match it to the numberEx Given a set of three identify the number of objects on number linesRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 16
Grade Level 3rdStandard with code 3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2Multiply and divide within 100
Explain how the properties of operations work
Apply properties of operations as strategies to multiply and divide
Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 17
StudentsGiven multiplication and division problems within 100
Use the properties of operations and descriptive language for the property to justify their products and quotients (eg If I know that 8 x 5 is 40 and two more groups of 8 would be 16 then 8 x 7 must be 40 + 16 or 56)
Commutative Property of Multiplication
Associative Property of Multiplication
Distributive Property
Students know
Commutative Associative Identity and Zero Properties of Multiplication and the Distributive Property
Strategies for finding products and quotients
Students understand thatare able to
Strategically and efficiently apply properties of multiplication and division in order to find products and quotients
The order in which factors are multiplied does not change the product
EE3OA5 NA (Multiplication begins at grade 4)
EE3OA5 NA (Multiplication begins at grade 4)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 18
Grade Level 3rdStandard with code 3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when multiplied by 8Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 3
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 19
StudentsGiven a division problem with an unknown quotient
Use a pictorial or physical model to explain the connection between the division problem and the related unknown factor equation
Factor Students know
Strategies for finding quotients and products
Students understand thatare able to
Use symbols to represent unknown quantities in equations
Use mathematical language to communicate the connections between an unknown quotient problem and the related unknown factor problem
Use the inverse relationship between multiplication and division to find quotients
The relationship between multiplication and division (that one undoes the other) can be used to solve problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA6 NA (Division begins at grade 5)
EE3OA6 NA (Division begins at grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 20
Grade Level 3rdStandard with code 3OA7 Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division (eg knowing that 8 times 5 = 40 one knows 40 divide 5 = 8) or properties of operations By the end of Grade 3 know from memory all products of two one-digit numbersDomain Operations and Algebraic Thinking Cluster Multiply and divide within 100
Quarter 1 Quarter 2
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 3
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Version 3 2015-2016 21
AttainmentStudentsGiven any single digit multiplication problem or a division problem with a single digit divisor and an unknown single digit quotient
Use an efficient strategy (eg recall inverse operations arrays derived facts properties of operations etc) to name the product or quotient
Students know
Strategies for finding products and quotients
Students understand thatare able to
Use multiplication and division strategies efficiently based on the numbers in the problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 22
Grade Level 3rdStandard with code 3OA8 Solve two-step word problems using the four operations Represent these problems using equations with a letter standing for the unknown quantity Assess the reasonableness of answers using mental computation and estimation strategies including rounding3
Domain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmetic
Quarter 1
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 2
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 3
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 23
StudentsGiven a variety of two-step word problems involving all four operations
Apply their understanding of operations to explain and justify solutions and solution paths using the connections among a variety of representations including equations with symbols for unknown quantities
Apply their understanding of operations and estimation strategies including rounding to evaluate the reasonableness of their solutions (eg The answer had to be around 125 because its a put together problem and 72 is close to 75 and 56 is close to 50 and 75 plus 50 is 125)
Students know
Characteristics of addition subtraction multiplication and division situations
Addition subtraction multiplication and division strategies
Strategies for mentally computing and estimating sums differences products and quotients
Students understand thatare able to
Strategically use a variety of representations to solve two-step word problems involving all four operations
Use symbols to represent unknown quantities in equations that relate to word problem contexts
Use mathematical language and contextual situations to communicate the connections among the four operations and related physical pictorial or symbolic representations and justify solutionssolution paths
Accurately compute sums differences products and quotients
Use logical reasoning mental computation strategies and estimation strategies to justify the reasonableness of
EE3OA8 Add to solve real world one-step story problems from 0-30
Level IV Students willEE3OA8 Add to solve real world one-step story problems with sums up to 50 using various problem-solving modelsEx Solve by adding (eg ldquoThere are 25 birds in a tree and 10 more joined them How many birds are in a treerdquo)Ex Solve by adding (eg ldquoI have 15 snacks on the cart and 25 snacks in the cupboard how many snacks do I have all together)Ex Solve by adding (eg ldquoAdd the pencils in two boxes and tell how many pencils we haverdquo)
Level III Students willEE3OA8 Add to solve real world one-step story problems from 0-30 Represent the problem in pictures or with objectsEx Solve by adding (eg ldquoHere are 10 pencils We need 10 more for each person to get a pencil How many will we need in allrdquo)Ex Solve by adding (eg ldquoConnie had five marbles Juan gave her eight more marbles How many marbles does Connie have all togetherrdquo)Ex Solve by adding (eg ldquoAdd the crayons in these two boxes and show me how many we have in allrdquo)
Level II Students willEE3OA8 Add to solve word problems identified through symbol representationEx Complete word problems that have pictures rather than wordsEx Solve by adding (eg ldquoThere are three ducks in the pond two more joined How many ducks are in the pondrdquo [picture representation])
Level I Students willEE3OA8 Identify the object(s) that appear in a real world one-step story problemEx Given a simple word problem and asked ldquoWhat is the problem aboutrdquo point to an object from a choice of two that represents what the problem was about (eg box toy)Ex Indicate which object a word problem is about from an array of two choices
Version 3 2015-2016 24
solutions
Multiplication is putting together equal sized groups
Division is sharing into equal-sized shares or as sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models and representations
Solutions can be evaluated by using reasoning to compare the actual solution with estimated solutions
CCSS Math Pacing Guide
Version 3 2015-2016 25
Grade 3
Grade Level 3rdStandard with code 3OA9 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations For example observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addendsDomain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmeticQuarter 1
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 2
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 3
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 26
Students
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations (eg observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends)
Students know
Characteristics of numbers and properties of operations (eg odd even)
Properties from Table 3 etc
Students understand thatare able to
Identify arithmetic patterns in number sequences in the addition table or multiplication table
Use logical reasoning and properties of numbers and operations to explain arithmetic patterns
Characteristics of numbers and properties of operations justify patterns which can be used to reason about mathematical situations form conjectures and solve problems
EE3OA9 Identify arithmetic patterns
Level IV Students willEE3OA9 Complete a complex arithmetic patternEx Complete the pattern using more than two numbers (ie A B C A B C)Ex Using a 100s number chart complete the pattern identified
Level III Students willEE3OA9 Identify arithmetic patternsEx When provided arithmetic patterns on a 100s chart identify the next number in the patternEx When given two number stamps stamp an arithmetic pattern
Level II Students willEE3OA9 Identify a patternEx Make pattern jumps on a number lineEx Sing songs and identify the pattern in the song
Level I Students willEE3OA9 Follow patternsEx Sing ldquoHead Shoulders Knees and Toesrdquo and mimic the patternEx Using tactile objects (fur sand sand fur) in a pattern repeat the patternEx Using manipulatives mimic the teacher to create a pattern
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 27
Grade Level 3rdStandard with code 3NBT1 Use place value understanding to round whole numbers to the nearest 10 or 100Domain Number and Operations in Base Ten
Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 28
StudentsGiven any number less than 1000
Round it to the nearest 10 or 100 and justify the answer using place value vocabulary (eg Rounding 147 to the nearest 10 is 150 because 147 is between 140 and 150 and is more than half way to 150)
Students know
Place value (ones tens hundreds)
Rounding
Students understand thatare able to
Count by 10s and 100s
Determine what is halfway between two multiples of 10 or 100
Round to the nearest 10 or 100
Use place value vocabulary and logical reasoning to justify solutions to rounding problems
Rounding and place value can be used to estimate quantities by changing the original number to the closest multiple of a power of 10
EE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)
Level IV Students willEE3NBT1 Identify the two 10s a number comes in between and tell which is closest (numbers 0-50)Ex Use a color beaded number line to identify the number and round to the closest 10Ex Given a number line separated into tens (0-10 10-20 etc) stand on a number and identify the 10 that is closer
Level III Students willEE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)Ex Use a color beaded number line to identify the two 10s a number falls betweenEx Given the number 14 they would identify 10 and 20
Level II Students willEE3NBT1 Identify tens on a number lineEx Given a number line circle the tensEx Stand on a number chart on 10 20 30 etc
Level I Students willEE3NBT1 Identify a numberEx Point to any number from one to three on a number lineEx Participate in a cake walk When the music stops look to see if they are on the number that is called outEx Identify a number when point to or presented on a cardEx Given a number from one to three point to the number symbolRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 29
Grade Level 3rdStandard with code 3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtractionDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 30
Students
Fluently add and subtract within 1000 using strategies based on place values properties of operations andor the relationship between addition and subtraction
Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning
Students know
Tools for modeling addition and subtraction
Strategies for solving addition and subtraction problems
Methods for symbolically (numerically) recording strategies for solving addition and subtraction problems
Students understand thatare able to
Model addition and subtraction problems using appropriate tools
Record strategies for solving addition and subtraction problems
Communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems
Relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and solution strategies
EE3NBT2 Identify place value to tens
Level IV Students willEE3NBT2 Identify place value to 50Ex Build numbers with place value piecesEx Identify the number in the ones and tens place value (ie the price of an item)Ex Write the number in expanded form ndash 43 = 40 + 3
Level III Students willEE3NBT2 Identify place value to tensEx When given two-digit number cards identify the number in the tens place valueEx When given a group of 10 frame models arrange and count the value of the numberI saw three groups of 10 and five extras so three groups of 10 = 30 and 5 more makes 35
Level II Students willEE3NBT2 Count to 10 using one-to-one correspondenceEx Given a bag of Skittles pull 10 Skittles out of the bagEx Select a domino and tell what number the dots representEx Shown a set of 10 objects create a duplicate collectionEx Given a container of pennies count out 10 from the container
Level I Students willEE3NBT2 Identify more or lessEx Given two collections of objects (group of 10 group of 20) indicate ldquoWhich has morerdquoEx Given math manipulatives representing a single unit and multiple units point to the multiple unit representation when asked ldquowhich is morerdquoRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 31
Grade Level 3rdStandard with code 3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operationsDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 32
Students
Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers
Students know
Place value models for multiplying numbers (eg open arrays place value blocks)
Strategies for multiplying one-digit numbers
Strategies for mentally multiplying one-digit numbers by multiples of powers of 10
Students understand thatare able to
Use mental strategies based on an understanding of place value properties of operations and knowledge of one-digit multiplication to find products
Use a variety of place value models of multiplication problems to justify strategies and solutions
Patterns in the place value system and properties of operations can be used to efficiently compute products
EE3NBT3 Count by tens using money
Level IV Students willEE3NBT3 Compare the value of money based on place valueEx Use money (dimes and pennies) to represent place valueEx Given 15 pennies create a one group of 10 and a group of five ones
Level III Students willEE3NBT3 Count by tens using moneyEx Given three dimes count by 10 to determine totalEx Given five dimes count by 10 to determine total
Level II Students willEE3NBT3 Identify whole numbers to 10Ex Given sets of 10 pennies pair with numbersEx Given sets of 10 pennies pair with dimes
Level I Students willEE3NBT3 Count pennies to 10
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 33
Grade Level 3rdStandard with code 3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1bDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 34
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Grade Level 3rdStandard with code 3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2Multiply and divide within 100
Explain how the properties of operations work
Apply properties of operations as strategies to multiply and divide
Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 17
StudentsGiven multiplication and division problems within 100
Use the properties of operations and descriptive language for the property to justify their products and quotients (eg If I know that 8 x 5 is 40 and two more groups of 8 would be 16 then 8 x 7 must be 40 + 16 or 56)
Commutative Property of Multiplication
Associative Property of Multiplication
Distributive Property
Students know
Commutative Associative Identity and Zero Properties of Multiplication and the Distributive Property
Strategies for finding products and quotients
Students understand thatare able to
Strategically and efficiently apply properties of multiplication and division in order to find products and quotients
The order in which factors are multiplied does not change the product
EE3OA5 NA (Multiplication begins at grade 4)
EE3OA5 NA (Multiplication begins at grade 4)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 18
Grade Level 3rdStandard with code 3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when multiplied by 8Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 3
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 19
StudentsGiven a division problem with an unknown quotient
Use a pictorial or physical model to explain the connection between the division problem and the related unknown factor equation
Factor Students know
Strategies for finding quotients and products
Students understand thatare able to
Use symbols to represent unknown quantities in equations
Use mathematical language to communicate the connections between an unknown quotient problem and the related unknown factor problem
Use the inverse relationship between multiplication and division to find quotients
The relationship between multiplication and division (that one undoes the other) can be used to solve problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA6 NA (Division begins at grade 5)
EE3OA6 NA (Division begins at grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 20
Grade Level 3rdStandard with code 3OA7 Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division (eg knowing that 8 times 5 = 40 one knows 40 divide 5 = 8) or properties of operations By the end of Grade 3 know from memory all products of two one-digit numbersDomain Operations and Algebraic Thinking Cluster Multiply and divide within 100
Quarter 1 Quarter 2
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 3
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Version 3 2015-2016 21
AttainmentStudentsGiven any single digit multiplication problem or a division problem with a single digit divisor and an unknown single digit quotient
Use an efficient strategy (eg recall inverse operations arrays derived facts properties of operations etc) to name the product or quotient
Students know
Strategies for finding products and quotients
Students understand thatare able to
Use multiplication and division strategies efficiently based on the numbers in the problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 22
Grade Level 3rdStandard with code 3OA8 Solve two-step word problems using the four operations Represent these problems using equations with a letter standing for the unknown quantity Assess the reasonableness of answers using mental computation and estimation strategies including rounding3
Domain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmetic
Quarter 1
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 2
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 3
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 23
StudentsGiven a variety of two-step word problems involving all four operations
Apply their understanding of operations to explain and justify solutions and solution paths using the connections among a variety of representations including equations with symbols for unknown quantities
Apply their understanding of operations and estimation strategies including rounding to evaluate the reasonableness of their solutions (eg The answer had to be around 125 because its a put together problem and 72 is close to 75 and 56 is close to 50 and 75 plus 50 is 125)
Students know
Characteristics of addition subtraction multiplication and division situations
Addition subtraction multiplication and division strategies
Strategies for mentally computing and estimating sums differences products and quotients
Students understand thatare able to
Strategically use a variety of representations to solve two-step word problems involving all four operations
Use symbols to represent unknown quantities in equations that relate to word problem contexts
Use mathematical language and contextual situations to communicate the connections among the four operations and related physical pictorial or symbolic representations and justify solutionssolution paths
Accurately compute sums differences products and quotients
Use logical reasoning mental computation strategies and estimation strategies to justify the reasonableness of
EE3OA8 Add to solve real world one-step story problems from 0-30
Level IV Students willEE3OA8 Add to solve real world one-step story problems with sums up to 50 using various problem-solving modelsEx Solve by adding (eg ldquoThere are 25 birds in a tree and 10 more joined them How many birds are in a treerdquo)Ex Solve by adding (eg ldquoI have 15 snacks on the cart and 25 snacks in the cupboard how many snacks do I have all together)Ex Solve by adding (eg ldquoAdd the pencils in two boxes and tell how many pencils we haverdquo)
Level III Students willEE3OA8 Add to solve real world one-step story problems from 0-30 Represent the problem in pictures or with objectsEx Solve by adding (eg ldquoHere are 10 pencils We need 10 more for each person to get a pencil How many will we need in allrdquo)Ex Solve by adding (eg ldquoConnie had five marbles Juan gave her eight more marbles How many marbles does Connie have all togetherrdquo)Ex Solve by adding (eg ldquoAdd the crayons in these two boxes and show me how many we have in allrdquo)
Level II Students willEE3OA8 Add to solve word problems identified through symbol representationEx Complete word problems that have pictures rather than wordsEx Solve by adding (eg ldquoThere are three ducks in the pond two more joined How many ducks are in the pondrdquo [picture representation])
Level I Students willEE3OA8 Identify the object(s) that appear in a real world one-step story problemEx Given a simple word problem and asked ldquoWhat is the problem aboutrdquo point to an object from a choice of two that represents what the problem was about (eg box toy)Ex Indicate which object a word problem is about from an array of two choices
Version 3 2015-2016 24
solutions
Multiplication is putting together equal sized groups
Division is sharing into equal-sized shares or as sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models and representations
Solutions can be evaluated by using reasoning to compare the actual solution with estimated solutions
CCSS Math Pacing Guide
Version 3 2015-2016 25
Grade 3
Grade Level 3rdStandard with code 3OA9 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations For example observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addendsDomain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmeticQuarter 1
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 2
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 3
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 26
Students
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations (eg observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends)
Students know
Characteristics of numbers and properties of operations (eg odd even)
Properties from Table 3 etc
Students understand thatare able to
Identify arithmetic patterns in number sequences in the addition table or multiplication table
Use logical reasoning and properties of numbers and operations to explain arithmetic patterns
Characteristics of numbers and properties of operations justify patterns which can be used to reason about mathematical situations form conjectures and solve problems
EE3OA9 Identify arithmetic patterns
Level IV Students willEE3OA9 Complete a complex arithmetic patternEx Complete the pattern using more than two numbers (ie A B C A B C)Ex Using a 100s number chart complete the pattern identified
Level III Students willEE3OA9 Identify arithmetic patternsEx When provided arithmetic patterns on a 100s chart identify the next number in the patternEx When given two number stamps stamp an arithmetic pattern
Level II Students willEE3OA9 Identify a patternEx Make pattern jumps on a number lineEx Sing songs and identify the pattern in the song
Level I Students willEE3OA9 Follow patternsEx Sing ldquoHead Shoulders Knees and Toesrdquo and mimic the patternEx Using tactile objects (fur sand sand fur) in a pattern repeat the patternEx Using manipulatives mimic the teacher to create a pattern
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 27
Grade Level 3rdStandard with code 3NBT1 Use place value understanding to round whole numbers to the nearest 10 or 100Domain Number and Operations in Base Ten
Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 28
StudentsGiven any number less than 1000
Round it to the nearest 10 or 100 and justify the answer using place value vocabulary (eg Rounding 147 to the nearest 10 is 150 because 147 is between 140 and 150 and is more than half way to 150)
Students know
Place value (ones tens hundreds)
Rounding
Students understand thatare able to
Count by 10s and 100s
Determine what is halfway between two multiples of 10 or 100
Round to the nearest 10 or 100
Use place value vocabulary and logical reasoning to justify solutions to rounding problems
Rounding and place value can be used to estimate quantities by changing the original number to the closest multiple of a power of 10
EE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)
Level IV Students willEE3NBT1 Identify the two 10s a number comes in between and tell which is closest (numbers 0-50)Ex Use a color beaded number line to identify the number and round to the closest 10Ex Given a number line separated into tens (0-10 10-20 etc) stand on a number and identify the 10 that is closer
Level III Students willEE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)Ex Use a color beaded number line to identify the two 10s a number falls betweenEx Given the number 14 they would identify 10 and 20
Level II Students willEE3NBT1 Identify tens on a number lineEx Given a number line circle the tensEx Stand on a number chart on 10 20 30 etc
Level I Students willEE3NBT1 Identify a numberEx Point to any number from one to three on a number lineEx Participate in a cake walk When the music stops look to see if they are on the number that is called outEx Identify a number when point to or presented on a cardEx Given a number from one to three point to the number symbolRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 29
Grade Level 3rdStandard with code 3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtractionDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 30
Students
Fluently add and subtract within 1000 using strategies based on place values properties of operations andor the relationship between addition and subtraction
Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning
Students know
Tools for modeling addition and subtraction
Strategies for solving addition and subtraction problems
Methods for symbolically (numerically) recording strategies for solving addition and subtraction problems
Students understand thatare able to
Model addition and subtraction problems using appropriate tools
Record strategies for solving addition and subtraction problems
Communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems
Relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and solution strategies
EE3NBT2 Identify place value to tens
Level IV Students willEE3NBT2 Identify place value to 50Ex Build numbers with place value piecesEx Identify the number in the ones and tens place value (ie the price of an item)Ex Write the number in expanded form ndash 43 = 40 + 3
Level III Students willEE3NBT2 Identify place value to tensEx When given two-digit number cards identify the number in the tens place valueEx When given a group of 10 frame models arrange and count the value of the numberI saw three groups of 10 and five extras so three groups of 10 = 30 and 5 more makes 35
Level II Students willEE3NBT2 Count to 10 using one-to-one correspondenceEx Given a bag of Skittles pull 10 Skittles out of the bagEx Select a domino and tell what number the dots representEx Shown a set of 10 objects create a duplicate collectionEx Given a container of pennies count out 10 from the container
Level I Students willEE3NBT2 Identify more or lessEx Given two collections of objects (group of 10 group of 20) indicate ldquoWhich has morerdquoEx Given math manipulatives representing a single unit and multiple units point to the multiple unit representation when asked ldquowhich is morerdquoRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 31
Grade Level 3rdStandard with code 3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operationsDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 32
Students
Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers
Students know
Place value models for multiplying numbers (eg open arrays place value blocks)
Strategies for multiplying one-digit numbers
Strategies for mentally multiplying one-digit numbers by multiples of powers of 10
Students understand thatare able to
Use mental strategies based on an understanding of place value properties of operations and knowledge of one-digit multiplication to find products
Use a variety of place value models of multiplication problems to justify strategies and solutions
Patterns in the place value system and properties of operations can be used to efficiently compute products
EE3NBT3 Count by tens using money
Level IV Students willEE3NBT3 Compare the value of money based on place valueEx Use money (dimes and pennies) to represent place valueEx Given 15 pennies create a one group of 10 and a group of five ones
Level III Students willEE3NBT3 Count by tens using moneyEx Given three dimes count by 10 to determine totalEx Given five dimes count by 10 to determine total
Level II Students willEE3NBT3 Identify whole numbers to 10Ex Given sets of 10 pennies pair with numbersEx Given sets of 10 pennies pair with dimes
Level I Students willEE3NBT3 Count pennies to 10
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 33
Grade Level 3rdStandard with code 3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1bDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 34
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
StudentsGiven multiplication and division problems within 100
Use the properties of operations and descriptive language for the property to justify their products and quotients (eg If I know that 8 x 5 is 40 and two more groups of 8 would be 16 then 8 x 7 must be 40 + 16 or 56)
Commutative Property of Multiplication
Associative Property of Multiplication
Distributive Property
Students know
Commutative Associative Identity and Zero Properties of Multiplication and the Distributive Property
Strategies for finding products and quotients
Students understand thatare able to
Strategically and efficiently apply properties of multiplication and division in order to find products and quotients
The order in which factors are multiplied does not change the product
EE3OA5 NA (Multiplication begins at grade 4)
EE3OA5 NA (Multiplication begins at grade 4)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 18
Grade Level 3rdStandard with code 3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when multiplied by 8Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 3
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 19
StudentsGiven a division problem with an unknown quotient
Use a pictorial or physical model to explain the connection between the division problem and the related unknown factor equation
Factor Students know
Strategies for finding quotients and products
Students understand thatare able to
Use symbols to represent unknown quantities in equations
Use mathematical language to communicate the connections between an unknown quotient problem and the related unknown factor problem
Use the inverse relationship between multiplication and division to find quotients
The relationship between multiplication and division (that one undoes the other) can be used to solve problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA6 NA (Division begins at grade 5)
EE3OA6 NA (Division begins at grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 20
Grade Level 3rdStandard with code 3OA7 Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division (eg knowing that 8 times 5 = 40 one knows 40 divide 5 = 8) or properties of operations By the end of Grade 3 know from memory all products of two one-digit numbersDomain Operations and Algebraic Thinking Cluster Multiply and divide within 100
Quarter 1 Quarter 2
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 3
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Version 3 2015-2016 21
AttainmentStudentsGiven any single digit multiplication problem or a division problem with a single digit divisor and an unknown single digit quotient
Use an efficient strategy (eg recall inverse operations arrays derived facts properties of operations etc) to name the product or quotient
Students know
Strategies for finding products and quotients
Students understand thatare able to
Use multiplication and division strategies efficiently based on the numbers in the problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 22
Grade Level 3rdStandard with code 3OA8 Solve two-step word problems using the four operations Represent these problems using equations with a letter standing for the unknown quantity Assess the reasonableness of answers using mental computation and estimation strategies including rounding3
Domain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmetic
Quarter 1
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 2
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 3
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 23
StudentsGiven a variety of two-step word problems involving all four operations
Apply their understanding of operations to explain and justify solutions and solution paths using the connections among a variety of representations including equations with symbols for unknown quantities
Apply their understanding of operations and estimation strategies including rounding to evaluate the reasonableness of their solutions (eg The answer had to be around 125 because its a put together problem and 72 is close to 75 and 56 is close to 50 and 75 plus 50 is 125)
Students know
Characteristics of addition subtraction multiplication and division situations
Addition subtraction multiplication and division strategies
Strategies for mentally computing and estimating sums differences products and quotients
Students understand thatare able to
Strategically use a variety of representations to solve two-step word problems involving all four operations
Use symbols to represent unknown quantities in equations that relate to word problem contexts
Use mathematical language and contextual situations to communicate the connections among the four operations and related physical pictorial or symbolic representations and justify solutionssolution paths
Accurately compute sums differences products and quotients
Use logical reasoning mental computation strategies and estimation strategies to justify the reasonableness of
EE3OA8 Add to solve real world one-step story problems from 0-30
Level IV Students willEE3OA8 Add to solve real world one-step story problems with sums up to 50 using various problem-solving modelsEx Solve by adding (eg ldquoThere are 25 birds in a tree and 10 more joined them How many birds are in a treerdquo)Ex Solve by adding (eg ldquoI have 15 snacks on the cart and 25 snacks in the cupboard how many snacks do I have all together)Ex Solve by adding (eg ldquoAdd the pencils in two boxes and tell how many pencils we haverdquo)
Level III Students willEE3OA8 Add to solve real world one-step story problems from 0-30 Represent the problem in pictures or with objectsEx Solve by adding (eg ldquoHere are 10 pencils We need 10 more for each person to get a pencil How many will we need in allrdquo)Ex Solve by adding (eg ldquoConnie had five marbles Juan gave her eight more marbles How many marbles does Connie have all togetherrdquo)Ex Solve by adding (eg ldquoAdd the crayons in these two boxes and show me how many we have in allrdquo)
Level II Students willEE3OA8 Add to solve word problems identified through symbol representationEx Complete word problems that have pictures rather than wordsEx Solve by adding (eg ldquoThere are three ducks in the pond two more joined How many ducks are in the pondrdquo [picture representation])
Level I Students willEE3OA8 Identify the object(s) that appear in a real world one-step story problemEx Given a simple word problem and asked ldquoWhat is the problem aboutrdquo point to an object from a choice of two that represents what the problem was about (eg box toy)Ex Indicate which object a word problem is about from an array of two choices
Version 3 2015-2016 24
solutions
Multiplication is putting together equal sized groups
Division is sharing into equal-sized shares or as sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models and representations
Solutions can be evaluated by using reasoning to compare the actual solution with estimated solutions
CCSS Math Pacing Guide
Version 3 2015-2016 25
Grade 3
Grade Level 3rdStandard with code 3OA9 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations For example observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addendsDomain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmeticQuarter 1
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 2
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 3
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 26
Students
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations (eg observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends)
Students know
Characteristics of numbers and properties of operations (eg odd even)
Properties from Table 3 etc
Students understand thatare able to
Identify arithmetic patterns in number sequences in the addition table or multiplication table
Use logical reasoning and properties of numbers and operations to explain arithmetic patterns
Characteristics of numbers and properties of operations justify patterns which can be used to reason about mathematical situations form conjectures and solve problems
EE3OA9 Identify arithmetic patterns
Level IV Students willEE3OA9 Complete a complex arithmetic patternEx Complete the pattern using more than two numbers (ie A B C A B C)Ex Using a 100s number chart complete the pattern identified
Level III Students willEE3OA9 Identify arithmetic patternsEx When provided arithmetic patterns on a 100s chart identify the next number in the patternEx When given two number stamps stamp an arithmetic pattern
Level II Students willEE3OA9 Identify a patternEx Make pattern jumps on a number lineEx Sing songs and identify the pattern in the song
Level I Students willEE3OA9 Follow patternsEx Sing ldquoHead Shoulders Knees and Toesrdquo and mimic the patternEx Using tactile objects (fur sand sand fur) in a pattern repeat the patternEx Using manipulatives mimic the teacher to create a pattern
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 27
Grade Level 3rdStandard with code 3NBT1 Use place value understanding to round whole numbers to the nearest 10 or 100Domain Number and Operations in Base Ten
Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 28
StudentsGiven any number less than 1000
Round it to the nearest 10 or 100 and justify the answer using place value vocabulary (eg Rounding 147 to the nearest 10 is 150 because 147 is between 140 and 150 and is more than half way to 150)
Students know
Place value (ones tens hundreds)
Rounding
Students understand thatare able to
Count by 10s and 100s
Determine what is halfway between two multiples of 10 or 100
Round to the nearest 10 or 100
Use place value vocabulary and logical reasoning to justify solutions to rounding problems
Rounding and place value can be used to estimate quantities by changing the original number to the closest multiple of a power of 10
EE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)
Level IV Students willEE3NBT1 Identify the two 10s a number comes in between and tell which is closest (numbers 0-50)Ex Use a color beaded number line to identify the number and round to the closest 10Ex Given a number line separated into tens (0-10 10-20 etc) stand on a number and identify the 10 that is closer
Level III Students willEE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)Ex Use a color beaded number line to identify the two 10s a number falls betweenEx Given the number 14 they would identify 10 and 20
Level II Students willEE3NBT1 Identify tens on a number lineEx Given a number line circle the tensEx Stand on a number chart on 10 20 30 etc
Level I Students willEE3NBT1 Identify a numberEx Point to any number from one to three on a number lineEx Participate in a cake walk When the music stops look to see if they are on the number that is called outEx Identify a number when point to or presented on a cardEx Given a number from one to three point to the number symbolRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 29
Grade Level 3rdStandard with code 3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtractionDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 30
Students
Fluently add and subtract within 1000 using strategies based on place values properties of operations andor the relationship between addition and subtraction
Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning
Students know
Tools for modeling addition and subtraction
Strategies for solving addition and subtraction problems
Methods for symbolically (numerically) recording strategies for solving addition and subtraction problems
Students understand thatare able to
Model addition and subtraction problems using appropriate tools
Record strategies for solving addition and subtraction problems
Communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems
Relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and solution strategies
EE3NBT2 Identify place value to tens
Level IV Students willEE3NBT2 Identify place value to 50Ex Build numbers with place value piecesEx Identify the number in the ones and tens place value (ie the price of an item)Ex Write the number in expanded form ndash 43 = 40 + 3
Level III Students willEE3NBT2 Identify place value to tensEx When given two-digit number cards identify the number in the tens place valueEx When given a group of 10 frame models arrange and count the value of the numberI saw three groups of 10 and five extras so three groups of 10 = 30 and 5 more makes 35
Level II Students willEE3NBT2 Count to 10 using one-to-one correspondenceEx Given a bag of Skittles pull 10 Skittles out of the bagEx Select a domino and tell what number the dots representEx Shown a set of 10 objects create a duplicate collectionEx Given a container of pennies count out 10 from the container
Level I Students willEE3NBT2 Identify more or lessEx Given two collections of objects (group of 10 group of 20) indicate ldquoWhich has morerdquoEx Given math manipulatives representing a single unit and multiple units point to the multiple unit representation when asked ldquowhich is morerdquoRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 31
Grade Level 3rdStandard with code 3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operationsDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 32
Students
Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers
Students know
Place value models for multiplying numbers (eg open arrays place value blocks)
Strategies for multiplying one-digit numbers
Strategies for mentally multiplying one-digit numbers by multiples of powers of 10
Students understand thatare able to
Use mental strategies based on an understanding of place value properties of operations and knowledge of one-digit multiplication to find products
Use a variety of place value models of multiplication problems to justify strategies and solutions
Patterns in the place value system and properties of operations can be used to efficiently compute products
EE3NBT3 Count by tens using money
Level IV Students willEE3NBT3 Compare the value of money based on place valueEx Use money (dimes and pennies) to represent place valueEx Given 15 pennies create a one group of 10 and a group of five ones
Level III Students willEE3NBT3 Count by tens using moneyEx Given three dimes count by 10 to determine totalEx Given five dimes count by 10 to determine total
Level II Students willEE3NBT3 Identify whole numbers to 10Ex Given sets of 10 pennies pair with numbersEx Given sets of 10 pennies pair with dimes
Level I Students willEE3NBT3 Count pennies to 10
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 33
Grade Level 3rdStandard with code 3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1bDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 34
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Grade Level 3rdStandard with code 3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when multiplied by 8Domain Operations and Algebraic Thinking Cluster Understand properties of multiplication and the relationship between multiplication and division
Quarter 1 Quarter 2
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 3
Identify the multiplication problemrelated to the division problem
Identify the unknown factor in the related multiplication problem
Use multiplication to solve division problems
Recognize multiplication and division as related operations and explain how they are related
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 19
StudentsGiven a division problem with an unknown quotient
Use a pictorial or physical model to explain the connection between the division problem and the related unknown factor equation
Factor Students know
Strategies for finding quotients and products
Students understand thatare able to
Use symbols to represent unknown quantities in equations
Use mathematical language to communicate the connections between an unknown quotient problem and the related unknown factor problem
Use the inverse relationship between multiplication and division to find quotients
The relationship between multiplication and division (that one undoes the other) can be used to solve problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA6 NA (Division begins at grade 5)
EE3OA6 NA (Division begins at grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 20
Grade Level 3rdStandard with code 3OA7 Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division (eg knowing that 8 times 5 = 40 one knows 40 divide 5 = 8) or properties of operations By the end of Grade 3 know from memory all products of two one-digit numbersDomain Operations and Algebraic Thinking Cluster Multiply and divide within 100
Quarter 1 Quarter 2
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 3
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Version 3 2015-2016 21
AttainmentStudentsGiven any single digit multiplication problem or a division problem with a single digit divisor and an unknown single digit quotient
Use an efficient strategy (eg recall inverse operations arrays derived facts properties of operations etc) to name the product or quotient
Students know
Strategies for finding products and quotients
Students understand thatare able to
Use multiplication and division strategies efficiently based on the numbers in the problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 22
Grade Level 3rdStandard with code 3OA8 Solve two-step word problems using the four operations Represent these problems using equations with a letter standing for the unknown quantity Assess the reasonableness of answers using mental computation and estimation strategies including rounding3
Domain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmetic
Quarter 1
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 2
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 3
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 23
StudentsGiven a variety of two-step word problems involving all four operations
Apply their understanding of operations to explain and justify solutions and solution paths using the connections among a variety of representations including equations with symbols for unknown quantities
Apply their understanding of operations and estimation strategies including rounding to evaluate the reasonableness of their solutions (eg The answer had to be around 125 because its a put together problem and 72 is close to 75 and 56 is close to 50 and 75 plus 50 is 125)
Students know
Characteristics of addition subtraction multiplication and division situations
Addition subtraction multiplication and division strategies
Strategies for mentally computing and estimating sums differences products and quotients
Students understand thatare able to
Strategically use a variety of representations to solve two-step word problems involving all four operations
Use symbols to represent unknown quantities in equations that relate to word problem contexts
Use mathematical language and contextual situations to communicate the connections among the four operations and related physical pictorial or symbolic representations and justify solutionssolution paths
Accurately compute sums differences products and quotients
Use logical reasoning mental computation strategies and estimation strategies to justify the reasonableness of
EE3OA8 Add to solve real world one-step story problems from 0-30
Level IV Students willEE3OA8 Add to solve real world one-step story problems with sums up to 50 using various problem-solving modelsEx Solve by adding (eg ldquoThere are 25 birds in a tree and 10 more joined them How many birds are in a treerdquo)Ex Solve by adding (eg ldquoI have 15 snacks on the cart and 25 snacks in the cupboard how many snacks do I have all together)Ex Solve by adding (eg ldquoAdd the pencils in two boxes and tell how many pencils we haverdquo)
Level III Students willEE3OA8 Add to solve real world one-step story problems from 0-30 Represent the problem in pictures or with objectsEx Solve by adding (eg ldquoHere are 10 pencils We need 10 more for each person to get a pencil How many will we need in allrdquo)Ex Solve by adding (eg ldquoConnie had five marbles Juan gave her eight more marbles How many marbles does Connie have all togetherrdquo)Ex Solve by adding (eg ldquoAdd the crayons in these two boxes and show me how many we have in allrdquo)
Level II Students willEE3OA8 Add to solve word problems identified through symbol representationEx Complete word problems that have pictures rather than wordsEx Solve by adding (eg ldquoThere are three ducks in the pond two more joined How many ducks are in the pondrdquo [picture representation])
Level I Students willEE3OA8 Identify the object(s) that appear in a real world one-step story problemEx Given a simple word problem and asked ldquoWhat is the problem aboutrdquo point to an object from a choice of two that represents what the problem was about (eg box toy)Ex Indicate which object a word problem is about from an array of two choices
Version 3 2015-2016 24
solutions
Multiplication is putting together equal sized groups
Division is sharing into equal-sized shares or as sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models and representations
Solutions can be evaluated by using reasoning to compare the actual solution with estimated solutions
CCSS Math Pacing Guide
Version 3 2015-2016 25
Grade 3
Grade Level 3rdStandard with code 3OA9 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations For example observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addendsDomain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmeticQuarter 1
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 2
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 3
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 26
Students
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations (eg observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends)
Students know
Characteristics of numbers and properties of operations (eg odd even)
Properties from Table 3 etc
Students understand thatare able to
Identify arithmetic patterns in number sequences in the addition table or multiplication table
Use logical reasoning and properties of numbers and operations to explain arithmetic patterns
Characteristics of numbers and properties of operations justify patterns which can be used to reason about mathematical situations form conjectures and solve problems
EE3OA9 Identify arithmetic patterns
Level IV Students willEE3OA9 Complete a complex arithmetic patternEx Complete the pattern using more than two numbers (ie A B C A B C)Ex Using a 100s number chart complete the pattern identified
Level III Students willEE3OA9 Identify arithmetic patternsEx When provided arithmetic patterns on a 100s chart identify the next number in the patternEx When given two number stamps stamp an arithmetic pattern
Level II Students willEE3OA9 Identify a patternEx Make pattern jumps on a number lineEx Sing songs and identify the pattern in the song
Level I Students willEE3OA9 Follow patternsEx Sing ldquoHead Shoulders Knees and Toesrdquo and mimic the patternEx Using tactile objects (fur sand sand fur) in a pattern repeat the patternEx Using manipulatives mimic the teacher to create a pattern
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 27
Grade Level 3rdStandard with code 3NBT1 Use place value understanding to round whole numbers to the nearest 10 or 100Domain Number and Operations in Base Ten
Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 28
StudentsGiven any number less than 1000
Round it to the nearest 10 or 100 and justify the answer using place value vocabulary (eg Rounding 147 to the nearest 10 is 150 because 147 is between 140 and 150 and is more than half way to 150)
Students know
Place value (ones tens hundreds)
Rounding
Students understand thatare able to
Count by 10s and 100s
Determine what is halfway between two multiples of 10 or 100
Round to the nearest 10 or 100
Use place value vocabulary and logical reasoning to justify solutions to rounding problems
Rounding and place value can be used to estimate quantities by changing the original number to the closest multiple of a power of 10
EE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)
Level IV Students willEE3NBT1 Identify the two 10s a number comes in between and tell which is closest (numbers 0-50)Ex Use a color beaded number line to identify the number and round to the closest 10Ex Given a number line separated into tens (0-10 10-20 etc) stand on a number and identify the 10 that is closer
Level III Students willEE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)Ex Use a color beaded number line to identify the two 10s a number falls betweenEx Given the number 14 they would identify 10 and 20
Level II Students willEE3NBT1 Identify tens on a number lineEx Given a number line circle the tensEx Stand on a number chart on 10 20 30 etc
Level I Students willEE3NBT1 Identify a numberEx Point to any number from one to three on a number lineEx Participate in a cake walk When the music stops look to see if they are on the number that is called outEx Identify a number when point to or presented on a cardEx Given a number from one to three point to the number symbolRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 29
Grade Level 3rdStandard with code 3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtractionDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 30
Students
Fluently add and subtract within 1000 using strategies based on place values properties of operations andor the relationship between addition and subtraction
Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning
Students know
Tools for modeling addition and subtraction
Strategies for solving addition and subtraction problems
Methods for symbolically (numerically) recording strategies for solving addition and subtraction problems
Students understand thatare able to
Model addition and subtraction problems using appropriate tools
Record strategies for solving addition and subtraction problems
Communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems
Relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and solution strategies
EE3NBT2 Identify place value to tens
Level IV Students willEE3NBT2 Identify place value to 50Ex Build numbers with place value piecesEx Identify the number in the ones and tens place value (ie the price of an item)Ex Write the number in expanded form ndash 43 = 40 + 3
Level III Students willEE3NBT2 Identify place value to tensEx When given two-digit number cards identify the number in the tens place valueEx When given a group of 10 frame models arrange and count the value of the numberI saw three groups of 10 and five extras so three groups of 10 = 30 and 5 more makes 35
Level II Students willEE3NBT2 Count to 10 using one-to-one correspondenceEx Given a bag of Skittles pull 10 Skittles out of the bagEx Select a domino and tell what number the dots representEx Shown a set of 10 objects create a duplicate collectionEx Given a container of pennies count out 10 from the container
Level I Students willEE3NBT2 Identify more or lessEx Given two collections of objects (group of 10 group of 20) indicate ldquoWhich has morerdquoEx Given math manipulatives representing a single unit and multiple units point to the multiple unit representation when asked ldquowhich is morerdquoRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 31
Grade Level 3rdStandard with code 3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operationsDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 32
Students
Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers
Students know
Place value models for multiplying numbers (eg open arrays place value blocks)
Strategies for multiplying one-digit numbers
Strategies for mentally multiplying one-digit numbers by multiples of powers of 10
Students understand thatare able to
Use mental strategies based on an understanding of place value properties of operations and knowledge of one-digit multiplication to find products
Use a variety of place value models of multiplication problems to justify strategies and solutions
Patterns in the place value system and properties of operations can be used to efficiently compute products
EE3NBT3 Count by tens using money
Level IV Students willEE3NBT3 Compare the value of money based on place valueEx Use money (dimes and pennies) to represent place valueEx Given 15 pennies create a one group of 10 and a group of five ones
Level III Students willEE3NBT3 Count by tens using moneyEx Given three dimes count by 10 to determine totalEx Given five dimes count by 10 to determine total
Level II Students willEE3NBT3 Identify whole numbers to 10Ex Given sets of 10 pennies pair with numbersEx Given sets of 10 pennies pair with dimes
Level I Students willEE3NBT3 Count pennies to 10
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 33
Grade Level 3rdStandard with code 3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1bDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 34
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
StudentsGiven a division problem with an unknown quotient
Use a pictorial or physical model to explain the connection between the division problem and the related unknown factor equation
Factor Students know
Strategies for finding quotients and products
Students understand thatare able to
Use symbols to represent unknown quantities in equations
Use mathematical language to communicate the connections between an unknown quotient problem and the related unknown factor problem
Use the inverse relationship between multiplication and division to find quotients
The relationship between multiplication and division (that one undoes the other) can be used to solve problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA6 NA (Division begins at grade 5)
EE3OA6 NA (Division begins at grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 20
Grade Level 3rdStandard with code 3OA7 Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division (eg knowing that 8 times 5 = 40 one knows 40 divide 5 = 8) or properties of operations By the end of Grade 3 know from memory all products of two one-digit numbersDomain Operations and Algebraic Thinking Cluster Multiply and divide within 100
Quarter 1 Quarter 2
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 3
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Version 3 2015-2016 21
AttainmentStudentsGiven any single digit multiplication problem or a division problem with a single digit divisor and an unknown single digit quotient
Use an efficient strategy (eg recall inverse operations arrays derived facts properties of operations etc) to name the product or quotient
Students know
Strategies for finding products and quotients
Students understand thatare able to
Use multiplication and division strategies efficiently based on the numbers in the problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 22
Grade Level 3rdStandard with code 3OA8 Solve two-step word problems using the four operations Represent these problems using equations with a letter standing for the unknown quantity Assess the reasonableness of answers using mental computation and estimation strategies including rounding3
Domain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmetic
Quarter 1
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 2
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 3
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 23
StudentsGiven a variety of two-step word problems involving all four operations
Apply their understanding of operations to explain and justify solutions and solution paths using the connections among a variety of representations including equations with symbols for unknown quantities
Apply their understanding of operations and estimation strategies including rounding to evaluate the reasonableness of their solutions (eg The answer had to be around 125 because its a put together problem and 72 is close to 75 and 56 is close to 50 and 75 plus 50 is 125)
Students know
Characteristics of addition subtraction multiplication and division situations
Addition subtraction multiplication and division strategies
Strategies for mentally computing and estimating sums differences products and quotients
Students understand thatare able to
Strategically use a variety of representations to solve two-step word problems involving all four operations
Use symbols to represent unknown quantities in equations that relate to word problem contexts
Use mathematical language and contextual situations to communicate the connections among the four operations and related physical pictorial or symbolic representations and justify solutionssolution paths
Accurately compute sums differences products and quotients
Use logical reasoning mental computation strategies and estimation strategies to justify the reasonableness of
EE3OA8 Add to solve real world one-step story problems from 0-30
Level IV Students willEE3OA8 Add to solve real world one-step story problems with sums up to 50 using various problem-solving modelsEx Solve by adding (eg ldquoThere are 25 birds in a tree and 10 more joined them How many birds are in a treerdquo)Ex Solve by adding (eg ldquoI have 15 snacks on the cart and 25 snacks in the cupboard how many snacks do I have all together)Ex Solve by adding (eg ldquoAdd the pencils in two boxes and tell how many pencils we haverdquo)
Level III Students willEE3OA8 Add to solve real world one-step story problems from 0-30 Represent the problem in pictures or with objectsEx Solve by adding (eg ldquoHere are 10 pencils We need 10 more for each person to get a pencil How many will we need in allrdquo)Ex Solve by adding (eg ldquoConnie had five marbles Juan gave her eight more marbles How many marbles does Connie have all togetherrdquo)Ex Solve by adding (eg ldquoAdd the crayons in these two boxes and show me how many we have in allrdquo)
Level II Students willEE3OA8 Add to solve word problems identified through symbol representationEx Complete word problems that have pictures rather than wordsEx Solve by adding (eg ldquoThere are three ducks in the pond two more joined How many ducks are in the pondrdquo [picture representation])
Level I Students willEE3OA8 Identify the object(s) that appear in a real world one-step story problemEx Given a simple word problem and asked ldquoWhat is the problem aboutrdquo point to an object from a choice of two that represents what the problem was about (eg box toy)Ex Indicate which object a word problem is about from an array of two choices
Version 3 2015-2016 24
solutions
Multiplication is putting together equal sized groups
Division is sharing into equal-sized shares or as sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models and representations
Solutions can be evaluated by using reasoning to compare the actual solution with estimated solutions
CCSS Math Pacing Guide
Version 3 2015-2016 25
Grade 3
Grade Level 3rdStandard with code 3OA9 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations For example observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addendsDomain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmeticQuarter 1
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 2
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 3
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 26
Students
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations (eg observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends)
Students know
Characteristics of numbers and properties of operations (eg odd even)
Properties from Table 3 etc
Students understand thatare able to
Identify arithmetic patterns in number sequences in the addition table or multiplication table
Use logical reasoning and properties of numbers and operations to explain arithmetic patterns
Characteristics of numbers and properties of operations justify patterns which can be used to reason about mathematical situations form conjectures and solve problems
EE3OA9 Identify arithmetic patterns
Level IV Students willEE3OA9 Complete a complex arithmetic patternEx Complete the pattern using more than two numbers (ie A B C A B C)Ex Using a 100s number chart complete the pattern identified
Level III Students willEE3OA9 Identify arithmetic patternsEx When provided arithmetic patterns on a 100s chart identify the next number in the patternEx When given two number stamps stamp an arithmetic pattern
Level II Students willEE3OA9 Identify a patternEx Make pattern jumps on a number lineEx Sing songs and identify the pattern in the song
Level I Students willEE3OA9 Follow patternsEx Sing ldquoHead Shoulders Knees and Toesrdquo and mimic the patternEx Using tactile objects (fur sand sand fur) in a pattern repeat the patternEx Using manipulatives mimic the teacher to create a pattern
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 27
Grade Level 3rdStandard with code 3NBT1 Use place value understanding to round whole numbers to the nearest 10 or 100Domain Number and Operations in Base Ten
Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 28
StudentsGiven any number less than 1000
Round it to the nearest 10 or 100 and justify the answer using place value vocabulary (eg Rounding 147 to the nearest 10 is 150 because 147 is between 140 and 150 and is more than half way to 150)
Students know
Place value (ones tens hundreds)
Rounding
Students understand thatare able to
Count by 10s and 100s
Determine what is halfway between two multiples of 10 or 100
Round to the nearest 10 or 100
Use place value vocabulary and logical reasoning to justify solutions to rounding problems
Rounding and place value can be used to estimate quantities by changing the original number to the closest multiple of a power of 10
EE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)
Level IV Students willEE3NBT1 Identify the two 10s a number comes in between and tell which is closest (numbers 0-50)Ex Use a color beaded number line to identify the number and round to the closest 10Ex Given a number line separated into tens (0-10 10-20 etc) stand on a number and identify the 10 that is closer
Level III Students willEE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)Ex Use a color beaded number line to identify the two 10s a number falls betweenEx Given the number 14 they would identify 10 and 20
Level II Students willEE3NBT1 Identify tens on a number lineEx Given a number line circle the tensEx Stand on a number chart on 10 20 30 etc
Level I Students willEE3NBT1 Identify a numberEx Point to any number from one to three on a number lineEx Participate in a cake walk When the music stops look to see if they are on the number that is called outEx Identify a number when point to or presented on a cardEx Given a number from one to three point to the number symbolRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 29
Grade Level 3rdStandard with code 3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtractionDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 30
Students
Fluently add and subtract within 1000 using strategies based on place values properties of operations andor the relationship between addition and subtraction
Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning
Students know
Tools for modeling addition and subtraction
Strategies for solving addition and subtraction problems
Methods for symbolically (numerically) recording strategies for solving addition and subtraction problems
Students understand thatare able to
Model addition and subtraction problems using appropriate tools
Record strategies for solving addition and subtraction problems
Communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems
Relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and solution strategies
EE3NBT2 Identify place value to tens
Level IV Students willEE3NBT2 Identify place value to 50Ex Build numbers with place value piecesEx Identify the number in the ones and tens place value (ie the price of an item)Ex Write the number in expanded form ndash 43 = 40 + 3
Level III Students willEE3NBT2 Identify place value to tensEx When given two-digit number cards identify the number in the tens place valueEx When given a group of 10 frame models arrange and count the value of the numberI saw three groups of 10 and five extras so three groups of 10 = 30 and 5 more makes 35
Level II Students willEE3NBT2 Count to 10 using one-to-one correspondenceEx Given a bag of Skittles pull 10 Skittles out of the bagEx Select a domino and tell what number the dots representEx Shown a set of 10 objects create a duplicate collectionEx Given a container of pennies count out 10 from the container
Level I Students willEE3NBT2 Identify more or lessEx Given two collections of objects (group of 10 group of 20) indicate ldquoWhich has morerdquoEx Given math manipulatives representing a single unit and multiple units point to the multiple unit representation when asked ldquowhich is morerdquoRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 31
Grade Level 3rdStandard with code 3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operationsDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 32
Students
Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers
Students know
Place value models for multiplying numbers (eg open arrays place value blocks)
Strategies for multiplying one-digit numbers
Strategies for mentally multiplying one-digit numbers by multiples of powers of 10
Students understand thatare able to
Use mental strategies based on an understanding of place value properties of operations and knowledge of one-digit multiplication to find products
Use a variety of place value models of multiplication problems to justify strategies and solutions
Patterns in the place value system and properties of operations can be used to efficiently compute products
EE3NBT3 Count by tens using money
Level IV Students willEE3NBT3 Compare the value of money based on place valueEx Use money (dimes and pennies) to represent place valueEx Given 15 pennies create a one group of 10 and a group of five ones
Level III Students willEE3NBT3 Count by tens using moneyEx Given three dimes count by 10 to determine totalEx Given five dimes count by 10 to determine total
Level II Students willEE3NBT3 Identify whole numbers to 10Ex Given sets of 10 pennies pair with numbersEx Given sets of 10 pennies pair with dimes
Level I Students willEE3NBT3 Count pennies to 10
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 33
Grade Level 3rdStandard with code 3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1bDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 34
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Grade Level 3rdStandard with code 3OA7 Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division (eg knowing that 8 times 5 = 40 one knows 40 divide 5 = 8) or properties of operations By the end of Grade 3 know from memory all products of two one-digit numbersDomain Operations and Algebraic Thinking Cluster Multiply and divide within 100
Quarter 1 Quarter 2
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 3
Know from memory all products of two one-digit numbers
Analyze a multiplication or division problem in order to choose an appropriate strategy to fluently multiply or divide within 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Version 3 2015-2016 21
AttainmentStudentsGiven any single digit multiplication problem or a division problem with a single digit divisor and an unknown single digit quotient
Use an efficient strategy (eg recall inverse operations arrays derived facts properties of operations etc) to name the product or quotient
Students know
Strategies for finding products and quotients
Students understand thatare able to
Use multiplication and division strategies efficiently based on the numbers in the problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 22
Grade Level 3rdStandard with code 3OA8 Solve two-step word problems using the four operations Represent these problems using equations with a letter standing for the unknown quantity Assess the reasonableness of answers using mental computation and estimation strategies including rounding3
Domain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmetic
Quarter 1
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 2
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 3
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 23
StudentsGiven a variety of two-step word problems involving all four operations
Apply their understanding of operations to explain and justify solutions and solution paths using the connections among a variety of representations including equations with symbols for unknown quantities
Apply their understanding of operations and estimation strategies including rounding to evaluate the reasonableness of their solutions (eg The answer had to be around 125 because its a put together problem and 72 is close to 75 and 56 is close to 50 and 75 plus 50 is 125)
Students know
Characteristics of addition subtraction multiplication and division situations
Addition subtraction multiplication and division strategies
Strategies for mentally computing and estimating sums differences products and quotients
Students understand thatare able to
Strategically use a variety of representations to solve two-step word problems involving all four operations
Use symbols to represent unknown quantities in equations that relate to word problem contexts
Use mathematical language and contextual situations to communicate the connections among the four operations and related physical pictorial or symbolic representations and justify solutionssolution paths
Accurately compute sums differences products and quotients
Use logical reasoning mental computation strategies and estimation strategies to justify the reasonableness of
EE3OA8 Add to solve real world one-step story problems from 0-30
Level IV Students willEE3OA8 Add to solve real world one-step story problems with sums up to 50 using various problem-solving modelsEx Solve by adding (eg ldquoThere are 25 birds in a tree and 10 more joined them How many birds are in a treerdquo)Ex Solve by adding (eg ldquoI have 15 snacks on the cart and 25 snacks in the cupboard how many snacks do I have all together)Ex Solve by adding (eg ldquoAdd the pencils in two boxes and tell how many pencils we haverdquo)
Level III Students willEE3OA8 Add to solve real world one-step story problems from 0-30 Represent the problem in pictures or with objectsEx Solve by adding (eg ldquoHere are 10 pencils We need 10 more for each person to get a pencil How many will we need in allrdquo)Ex Solve by adding (eg ldquoConnie had five marbles Juan gave her eight more marbles How many marbles does Connie have all togetherrdquo)Ex Solve by adding (eg ldquoAdd the crayons in these two boxes and show me how many we have in allrdquo)
Level II Students willEE3OA8 Add to solve word problems identified through symbol representationEx Complete word problems that have pictures rather than wordsEx Solve by adding (eg ldquoThere are three ducks in the pond two more joined How many ducks are in the pondrdquo [picture representation])
Level I Students willEE3OA8 Identify the object(s) that appear in a real world one-step story problemEx Given a simple word problem and asked ldquoWhat is the problem aboutrdquo point to an object from a choice of two that represents what the problem was about (eg box toy)Ex Indicate which object a word problem is about from an array of two choices
Version 3 2015-2016 24
solutions
Multiplication is putting together equal sized groups
Division is sharing into equal-sized shares or as sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models and representations
Solutions can be evaluated by using reasoning to compare the actual solution with estimated solutions
CCSS Math Pacing Guide
Version 3 2015-2016 25
Grade 3
Grade Level 3rdStandard with code 3OA9 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations For example observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addendsDomain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmeticQuarter 1
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 2
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 3
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 26
Students
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations (eg observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends)
Students know
Characteristics of numbers and properties of operations (eg odd even)
Properties from Table 3 etc
Students understand thatare able to
Identify arithmetic patterns in number sequences in the addition table or multiplication table
Use logical reasoning and properties of numbers and operations to explain arithmetic patterns
Characteristics of numbers and properties of operations justify patterns which can be used to reason about mathematical situations form conjectures and solve problems
EE3OA9 Identify arithmetic patterns
Level IV Students willEE3OA9 Complete a complex arithmetic patternEx Complete the pattern using more than two numbers (ie A B C A B C)Ex Using a 100s number chart complete the pattern identified
Level III Students willEE3OA9 Identify arithmetic patternsEx When provided arithmetic patterns on a 100s chart identify the next number in the patternEx When given two number stamps stamp an arithmetic pattern
Level II Students willEE3OA9 Identify a patternEx Make pattern jumps on a number lineEx Sing songs and identify the pattern in the song
Level I Students willEE3OA9 Follow patternsEx Sing ldquoHead Shoulders Knees and Toesrdquo and mimic the patternEx Using tactile objects (fur sand sand fur) in a pattern repeat the patternEx Using manipulatives mimic the teacher to create a pattern
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 27
Grade Level 3rdStandard with code 3NBT1 Use place value understanding to round whole numbers to the nearest 10 or 100Domain Number and Operations in Base Ten
Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 28
StudentsGiven any number less than 1000
Round it to the nearest 10 or 100 and justify the answer using place value vocabulary (eg Rounding 147 to the nearest 10 is 150 because 147 is between 140 and 150 and is more than half way to 150)
Students know
Place value (ones tens hundreds)
Rounding
Students understand thatare able to
Count by 10s and 100s
Determine what is halfway between two multiples of 10 or 100
Round to the nearest 10 or 100
Use place value vocabulary and logical reasoning to justify solutions to rounding problems
Rounding and place value can be used to estimate quantities by changing the original number to the closest multiple of a power of 10
EE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)
Level IV Students willEE3NBT1 Identify the two 10s a number comes in between and tell which is closest (numbers 0-50)Ex Use a color beaded number line to identify the number and round to the closest 10Ex Given a number line separated into tens (0-10 10-20 etc) stand on a number and identify the 10 that is closer
Level III Students willEE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)Ex Use a color beaded number line to identify the two 10s a number falls betweenEx Given the number 14 they would identify 10 and 20
Level II Students willEE3NBT1 Identify tens on a number lineEx Given a number line circle the tensEx Stand on a number chart on 10 20 30 etc
Level I Students willEE3NBT1 Identify a numberEx Point to any number from one to three on a number lineEx Participate in a cake walk When the music stops look to see if they are on the number that is called outEx Identify a number when point to or presented on a cardEx Given a number from one to three point to the number symbolRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 29
Grade Level 3rdStandard with code 3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtractionDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 30
Students
Fluently add and subtract within 1000 using strategies based on place values properties of operations andor the relationship between addition and subtraction
Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning
Students know
Tools for modeling addition and subtraction
Strategies for solving addition and subtraction problems
Methods for symbolically (numerically) recording strategies for solving addition and subtraction problems
Students understand thatare able to
Model addition and subtraction problems using appropriate tools
Record strategies for solving addition and subtraction problems
Communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems
Relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and solution strategies
EE3NBT2 Identify place value to tens
Level IV Students willEE3NBT2 Identify place value to 50Ex Build numbers with place value piecesEx Identify the number in the ones and tens place value (ie the price of an item)Ex Write the number in expanded form ndash 43 = 40 + 3
Level III Students willEE3NBT2 Identify place value to tensEx When given two-digit number cards identify the number in the tens place valueEx When given a group of 10 frame models arrange and count the value of the numberI saw three groups of 10 and five extras so three groups of 10 = 30 and 5 more makes 35
Level II Students willEE3NBT2 Count to 10 using one-to-one correspondenceEx Given a bag of Skittles pull 10 Skittles out of the bagEx Select a domino and tell what number the dots representEx Shown a set of 10 objects create a duplicate collectionEx Given a container of pennies count out 10 from the container
Level I Students willEE3NBT2 Identify more or lessEx Given two collections of objects (group of 10 group of 20) indicate ldquoWhich has morerdquoEx Given math manipulatives representing a single unit and multiple units point to the multiple unit representation when asked ldquowhich is morerdquoRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 31
Grade Level 3rdStandard with code 3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operationsDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 32
Students
Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers
Students know
Place value models for multiplying numbers (eg open arrays place value blocks)
Strategies for multiplying one-digit numbers
Strategies for mentally multiplying one-digit numbers by multiples of powers of 10
Students understand thatare able to
Use mental strategies based on an understanding of place value properties of operations and knowledge of one-digit multiplication to find products
Use a variety of place value models of multiplication problems to justify strategies and solutions
Patterns in the place value system and properties of operations can be used to efficiently compute products
EE3NBT3 Count by tens using money
Level IV Students willEE3NBT3 Compare the value of money based on place valueEx Use money (dimes and pennies) to represent place valueEx Given 15 pennies create a one group of 10 and a group of five ones
Level III Students willEE3NBT3 Count by tens using moneyEx Given three dimes count by 10 to determine totalEx Given five dimes count by 10 to determine total
Level II Students willEE3NBT3 Identify whole numbers to 10Ex Given sets of 10 pennies pair with numbersEx Given sets of 10 pennies pair with dimes
Level I Students willEE3NBT3 Count pennies to 10
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 33
Grade Level 3rdStandard with code 3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1bDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 34
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
AttainmentStudentsGiven any single digit multiplication problem or a division problem with a single digit divisor and an unknown single digit quotient
Use an efficient strategy (eg recall inverse operations arrays derived facts properties of operations etc) to name the product or quotient
Students know
Strategies for finding products and quotients
Students understand thatare able to
Use multiplication and division strategies efficiently based on the numbers in the problems
Efficient application of computation strategies are based on the numbers in the problems
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
EE3OA7 NA (Multiplication begins grade 4 and division begins in grade 5)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 22
Grade Level 3rdStandard with code 3OA8 Solve two-step word problems using the four operations Represent these problems using equations with a letter standing for the unknown quantity Assess the reasonableness of answers using mental computation and estimation strategies including rounding3
Domain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmetic
Quarter 1
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 2
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 3
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 23
StudentsGiven a variety of two-step word problems involving all four operations
Apply their understanding of operations to explain and justify solutions and solution paths using the connections among a variety of representations including equations with symbols for unknown quantities
Apply their understanding of operations and estimation strategies including rounding to evaluate the reasonableness of their solutions (eg The answer had to be around 125 because its a put together problem and 72 is close to 75 and 56 is close to 50 and 75 plus 50 is 125)
Students know
Characteristics of addition subtraction multiplication and division situations
Addition subtraction multiplication and division strategies
Strategies for mentally computing and estimating sums differences products and quotients
Students understand thatare able to
Strategically use a variety of representations to solve two-step word problems involving all four operations
Use symbols to represent unknown quantities in equations that relate to word problem contexts
Use mathematical language and contextual situations to communicate the connections among the four operations and related physical pictorial or symbolic representations and justify solutionssolution paths
Accurately compute sums differences products and quotients
Use logical reasoning mental computation strategies and estimation strategies to justify the reasonableness of
EE3OA8 Add to solve real world one-step story problems from 0-30
Level IV Students willEE3OA8 Add to solve real world one-step story problems with sums up to 50 using various problem-solving modelsEx Solve by adding (eg ldquoThere are 25 birds in a tree and 10 more joined them How many birds are in a treerdquo)Ex Solve by adding (eg ldquoI have 15 snacks on the cart and 25 snacks in the cupboard how many snacks do I have all together)Ex Solve by adding (eg ldquoAdd the pencils in two boxes and tell how many pencils we haverdquo)
Level III Students willEE3OA8 Add to solve real world one-step story problems from 0-30 Represent the problem in pictures or with objectsEx Solve by adding (eg ldquoHere are 10 pencils We need 10 more for each person to get a pencil How many will we need in allrdquo)Ex Solve by adding (eg ldquoConnie had five marbles Juan gave her eight more marbles How many marbles does Connie have all togetherrdquo)Ex Solve by adding (eg ldquoAdd the crayons in these two boxes and show me how many we have in allrdquo)
Level II Students willEE3OA8 Add to solve word problems identified through symbol representationEx Complete word problems that have pictures rather than wordsEx Solve by adding (eg ldquoThere are three ducks in the pond two more joined How many ducks are in the pondrdquo [picture representation])
Level I Students willEE3OA8 Identify the object(s) that appear in a real world one-step story problemEx Given a simple word problem and asked ldquoWhat is the problem aboutrdquo point to an object from a choice of two that represents what the problem was about (eg box toy)Ex Indicate which object a word problem is about from an array of two choices
Version 3 2015-2016 24
solutions
Multiplication is putting together equal sized groups
Division is sharing into equal-sized shares or as sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models and representations
Solutions can be evaluated by using reasoning to compare the actual solution with estimated solutions
CCSS Math Pacing Guide
Version 3 2015-2016 25
Grade 3
Grade Level 3rdStandard with code 3OA9 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations For example observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addendsDomain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmeticQuarter 1
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 2
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 3
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 26
Students
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations (eg observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends)
Students know
Characteristics of numbers and properties of operations (eg odd even)
Properties from Table 3 etc
Students understand thatare able to
Identify arithmetic patterns in number sequences in the addition table or multiplication table
Use logical reasoning and properties of numbers and operations to explain arithmetic patterns
Characteristics of numbers and properties of operations justify patterns which can be used to reason about mathematical situations form conjectures and solve problems
EE3OA9 Identify arithmetic patterns
Level IV Students willEE3OA9 Complete a complex arithmetic patternEx Complete the pattern using more than two numbers (ie A B C A B C)Ex Using a 100s number chart complete the pattern identified
Level III Students willEE3OA9 Identify arithmetic patternsEx When provided arithmetic patterns on a 100s chart identify the next number in the patternEx When given two number stamps stamp an arithmetic pattern
Level II Students willEE3OA9 Identify a patternEx Make pattern jumps on a number lineEx Sing songs and identify the pattern in the song
Level I Students willEE3OA9 Follow patternsEx Sing ldquoHead Shoulders Knees and Toesrdquo and mimic the patternEx Using tactile objects (fur sand sand fur) in a pattern repeat the patternEx Using manipulatives mimic the teacher to create a pattern
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 27
Grade Level 3rdStandard with code 3NBT1 Use place value understanding to round whole numbers to the nearest 10 or 100Domain Number and Operations in Base Ten
Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 28
StudentsGiven any number less than 1000
Round it to the nearest 10 or 100 and justify the answer using place value vocabulary (eg Rounding 147 to the nearest 10 is 150 because 147 is between 140 and 150 and is more than half way to 150)
Students know
Place value (ones tens hundreds)
Rounding
Students understand thatare able to
Count by 10s and 100s
Determine what is halfway between two multiples of 10 or 100
Round to the nearest 10 or 100
Use place value vocabulary and logical reasoning to justify solutions to rounding problems
Rounding and place value can be used to estimate quantities by changing the original number to the closest multiple of a power of 10
EE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)
Level IV Students willEE3NBT1 Identify the two 10s a number comes in between and tell which is closest (numbers 0-50)Ex Use a color beaded number line to identify the number and round to the closest 10Ex Given a number line separated into tens (0-10 10-20 etc) stand on a number and identify the 10 that is closer
Level III Students willEE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)Ex Use a color beaded number line to identify the two 10s a number falls betweenEx Given the number 14 they would identify 10 and 20
Level II Students willEE3NBT1 Identify tens on a number lineEx Given a number line circle the tensEx Stand on a number chart on 10 20 30 etc
Level I Students willEE3NBT1 Identify a numberEx Point to any number from one to three on a number lineEx Participate in a cake walk When the music stops look to see if they are on the number that is called outEx Identify a number when point to or presented on a cardEx Given a number from one to three point to the number symbolRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 29
Grade Level 3rdStandard with code 3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtractionDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 30
Students
Fluently add and subtract within 1000 using strategies based on place values properties of operations andor the relationship between addition and subtraction
Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning
Students know
Tools for modeling addition and subtraction
Strategies for solving addition and subtraction problems
Methods for symbolically (numerically) recording strategies for solving addition and subtraction problems
Students understand thatare able to
Model addition and subtraction problems using appropriate tools
Record strategies for solving addition and subtraction problems
Communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems
Relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and solution strategies
EE3NBT2 Identify place value to tens
Level IV Students willEE3NBT2 Identify place value to 50Ex Build numbers with place value piecesEx Identify the number in the ones and tens place value (ie the price of an item)Ex Write the number in expanded form ndash 43 = 40 + 3
Level III Students willEE3NBT2 Identify place value to tensEx When given two-digit number cards identify the number in the tens place valueEx When given a group of 10 frame models arrange and count the value of the numberI saw three groups of 10 and five extras so three groups of 10 = 30 and 5 more makes 35
Level II Students willEE3NBT2 Count to 10 using one-to-one correspondenceEx Given a bag of Skittles pull 10 Skittles out of the bagEx Select a domino and tell what number the dots representEx Shown a set of 10 objects create a duplicate collectionEx Given a container of pennies count out 10 from the container
Level I Students willEE3NBT2 Identify more or lessEx Given two collections of objects (group of 10 group of 20) indicate ldquoWhich has morerdquoEx Given math manipulatives representing a single unit and multiple units point to the multiple unit representation when asked ldquowhich is morerdquoRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 31
Grade Level 3rdStandard with code 3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operationsDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 32
Students
Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers
Students know
Place value models for multiplying numbers (eg open arrays place value blocks)
Strategies for multiplying one-digit numbers
Strategies for mentally multiplying one-digit numbers by multiples of powers of 10
Students understand thatare able to
Use mental strategies based on an understanding of place value properties of operations and knowledge of one-digit multiplication to find products
Use a variety of place value models of multiplication problems to justify strategies and solutions
Patterns in the place value system and properties of operations can be used to efficiently compute products
EE3NBT3 Count by tens using money
Level IV Students willEE3NBT3 Compare the value of money based on place valueEx Use money (dimes and pennies) to represent place valueEx Given 15 pennies create a one group of 10 and a group of five ones
Level III Students willEE3NBT3 Count by tens using moneyEx Given three dimes count by 10 to determine totalEx Given five dimes count by 10 to determine total
Level II Students willEE3NBT3 Identify whole numbers to 10Ex Given sets of 10 pennies pair with numbersEx Given sets of 10 pennies pair with dimes
Level I Students willEE3NBT3 Count pennies to 10
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 33
Grade Level 3rdStandard with code 3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1bDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 34
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Grade Level 3rdStandard with code 3OA8 Solve two-step word problems using the four operations Represent these problems using equations with a letter standing for the unknown quantity Assess the reasonableness of answers using mental computation and estimation strategies including rounding3
Domain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmetic
Quarter 1
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 2
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 3
Know the order of operations (without parentheses)
Know strategies for estimating
Construct an equation with a letter standing for the unknown quantity
Solve two-step word problems using the four operations
Justify your answer using various estimation strategies
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 23
StudentsGiven a variety of two-step word problems involving all four operations
Apply their understanding of operations to explain and justify solutions and solution paths using the connections among a variety of representations including equations with symbols for unknown quantities
Apply their understanding of operations and estimation strategies including rounding to evaluate the reasonableness of their solutions (eg The answer had to be around 125 because its a put together problem and 72 is close to 75 and 56 is close to 50 and 75 plus 50 is 125)
Students know
Characteristics of addition subtraction multiplication and division situations
Addition subtraction multiplication and division strategies
Strategies for mentally computing and estimating sums differences products and quotients
Students understand thatare able to
Strategically use a variety of representations to solve two-step word problems involving all four operations
Use symbols to represent unknown quantities in equations that relate to word problem contexts
Use mathematical language and contextual situations to communicate the connections among the four operations and related physical pictorial or symbolic representations and justify solutionssolution paths
Accurately compute sums differences products and quotients
Use logical reasoning mental computation strategies and estimation strategies to justify the reasonableness of
EE3OA8 Add to solve real world one-step story problems from 0-30
Level IV Students willEE3OA8 Add to solve real world one-step story problems with sums up to 50 using various problem-solving modelsEx Solve by adding (eg ldquoThere are 25 birds in a tree and 10 more joined them How many birds are in a treerdquo)Ex Solve by adding (eg ldquoI have 15 snacks on the cart and 25 snacks in the cupboard how many snacks do I have all together)Ex Solve by adding (eg ldquoAdd the pencils in two boxes and tell how many pencils we haverdquo)
Level III Students willEE3OA8 Add to solve real world one-step story problems from 0-30 Represent the problem in pictures or with objectsEx Solve by adding (eg ldquoHere are 10 pencils We need 10 more for each person to get a pencil How many will we need in allrdquo)Ex Solve by adding (eg ldquoConnie had five marbles Juan gave her eight more marbles How many marbles does Connie have all togetherrdquo)Ex Solve by adding (eg ldquoAdd the crayons in these two boxes and show me how many we have in allrdquo)
Level II Students willEE3OA8 Add to solve word problems identified through symbol representationEx Complete word problems that have pictures rather than wordsEx Solve by adding (eg ldquoThere are three ducks in the pond two more joined How many ducks are in the pondrdquo [picture representation])
Level I Students willEE3OA8 Identify the object(s) that appear in a real world one-step story problemEx Given a simple word problem and asked ldquoWhat is the problem aboutrdquo point to an object from a choice of two that represents what the problem was about (eg box toy)Ex Indicate which object a word problem is about from an array of two choices
Version 3 2015-2016 24
solutions
Multiplication is putting together equal sized groups
Division is sharing into equal-sized shares or as sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models and representations
Solutions can be evaluated by using reasoning to compare the actual solution with estimated solutions
CCSS Math Pacing Guide
Version 3 2015-2016 25
Grade 3
Grade Level 3rdStandard with code 3OA9 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations For example observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addendsDomain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmeticQuarter 1
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 2
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 3
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 26
Students
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations (eg observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends)
Students know
Characteristics of numbers and properties of operations (eg odd even)
Properties from Table 3 etc
Students understand thatare able to
Identify arithmetic patterns in number sequences in the addition table or multiplication table
Use logical reasoning and properties of numbers and operations to explain arithmetic patterns
Characteristics of numbers and properties of operations justify patterns which can be used to reason about mathematical situations form conjectures and solve problems
EE3OA9 Identify arithmetic patterns
Level IV Students willEE3OA9 Complete a complex arithmetic patternEx Complete the pattern using more than two numbers (ie A B C A B C)Ex Using a 100s number chart complete the pattern identified
Level III Students willEE3OA9 Identify arithmetic patternsEx When provided arithmetic patterns on a 100s chart identify the next number in the patternEx When given two number stamps stamp an arithmetic pattern
Level II Students willEE3OA9 Identify a patternEx Make pattern jumps on a number lineEx Sing songs and identify the pattern in the song
Level I Students willEE3OA9 Follow patternsEx Sing ldquoHead Shoulders Knees and Toesrdquo and mimic the patternEx Using tactile objects (fur sand sand fur) in a pattern repeat the patternEx Using manipulatives mimic the teacher to create a pattern
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 27
Grade Level 3rdStandard with code 3NBT1 Use place value understanding to round whole numbers to the nearest 10 or 100Domain Number and Operations in Base Ten
Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 28
StudentsGiven any number less than 1000
Round it to the nearest 10 or 100 and justify the answer using place value vocabulary (eg Rounding 147 to the nearest 10 is 150 because 147 is between 140 and 150 and is more than half way to 150)
Students know
Place value (ones tens hundreds)
Rounding
Students understand thatare able to
Count by 10s and 100s
Determine what is halfway between two multiples of 10 or 100
Round to the nearest 10 or 100
Use place value vocabulary and logical reasoning to justify solutions to rounding problems
Rounding and place value can be used to estimate quantities by changing the original number to the closest multiple of a power of 10
EE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)
Level IV Students willEE3NBT1 Identify the two 10s a number comes in between and tell which is closest (numbers 0-50)Ex Use a color beaded number line to identify the number and round to the closest 10Ex Given a number line separated into tens (0-10 10-20 etc) stand on a number and identify the 10 that is closer
Level III Students willEE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)Ex Use a color beaded number line to identify the two 10s a number falls betweenEx Given the number 14 they would identify 10 and 20
Level II Students willEE3NBT1 Identify tens on a number lineEx Given a number line circle the tensEx Stand on a number chart on 10 20 30 etc
Level I Students willEE3NBT1 Identify a numberEx Point to any number from one to three on a number lineEx Participate in a cake walk When the music stops look to see if they are on the number that is called outEx Identify a number when point to or presented on a cardEx Given a number from one to three point to the number symbolRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 29
Grade Level 3rdStandard with code 3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtractionDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 30
Students
Fluently add and subtract within 1000 using strategies based on place values properties of operations andor the relationship between addition and subtraction
Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning
Students know
Tools for modeling addition and subtraction
Strategies for solving addition and subtraction problems
Methods for symbolically (numerically) recording strategies for solving addition and subtraction problems
Students understand thatare able to
Model addition and subtraction problems using appropriate tools
Record strategies for solving addition and subtraction problems
Communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems
Relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and solution strategies
EE3NBT2 Identify place value to tens
Level IV Students willEE3NBT2 Identify place value to 50Ex Build numbers with place value piecesEx Identify the number in the ones and tens place value (ie the price of an item)Ex Write the number in expanded form ndash 43 = 40 + 3
Level III Students willEE3NBT2 Identify place value to tensEx When given two-digit number cards identify the number in the tens place valueEx When given a group of 10 frame models arrange and count the value of the numberI saw three groups of 10 and five extras so three groups of 10 = 30 and 5 more makes 35
Level II Students willEE3NBT2 Count to 10 using one-to-one correspondenceEx Given a bag of Skittles pull 10 Skittles out of the bagEx Select a domino and tell what number the dots representEx Shown a set of 10 objects create a duplicate collectionEx Given a container of pennies count out 10 from the container
Level I Students willEE3NBT2 Identify more or lessEx Given two collections of objects (group of 10 group of 20) indicate ldquoWhich has morerdquoEx Given math manipulatives representing a single unit and multiple units point to the multiple unit representation when asked ldquowhich is morerdquoRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 31
Grade Level 3rdStandard with code 3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operationsDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 32
Students
Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers
Students know
Place value models for multiplying numbers (eg open arrays place value blocks)
Strategies for multiplying one-digit numbers
Strategies for mentally multiplying one-digit numbers by multiples of powers of 10
Students understand thatare able to
Use mental strategies based on an understanding of place value properties of operations and knowledge of one-digit multiplication to find products
Use a variety of place value models of multiplication problems to justify strategies and solutions
Patterns in the place value system and properties of operations can be used to efficiently compute products
EE3NBT3 Count by tens using money
Level IV Students willEE3NBT3 Compare the value of money based on place valueEx Use money (dimes and pennies) to represent place valueEx Given 15 pennies create a one group of 10 and a group of five ones
Level III Students willEE3NBT3 Count by tens using moneyEx Given three dimes count by 10 to determine totalEx Given five dimes count by 10 to determine total
Level II Students willEE3NBT3 Identify whole numbers to 10Ex Given sets of 10 pennies pair with numbersEx Given sets of 10 pennies pair with dimes
Level I Students willEE3NBT3 Count pennies to 10
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 33
Grade Level 3rdStandard with code 3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1bDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 34
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
StudentsGiven a variety of two-step word problems involving all four operations
Apply their understanding of operations to explain and justify solutions and solution paths using the connections among a variety of representations including equations with symbols for unknown quantities
Apply their understanding of operations and estimation strategies including rounding to evaluate the reasonableness of their solutions (eg The answer had to be around 125 because its a put together problem and 72 is close to 75 and 56 is close to 50 and 75 plus 50 is 125)
Students know
Characteristics of addition subtraction multiplication and division situations
Addition subtraction multiplication and division strategies
Strategies for mentally computing and estimating sums differences products and quotients
Students understand thatare able to
Strategically use a variety of representations to solve two-step word problems involving all four operations
Use symbols to represent unknown quantities in equations that relate to word problem contexts
Use mathematical language and contextual situations to communicate the connections among the four operations and related physical pictorial or symbolic representations and justify solutionssolution paths
Accurately compute sums differences products and quotients
Use logical reasoning mental computation strategies and estimation strategies to justify the reasonableness of
EE3OA8 Add to solve real world one-step story problems from 0-30
Level IV Students willEE3OA8 Add to solve real world one-step story problems with sums up to 50 using various problem-solving modelsEx Solve by adding (eg ldquoThere are 25 birds in a tree and 10 more joined them How many birds are in a treerdquo)Ex Solve by adding (eg ldquoI have 15 snacks on the cart and 25 snacks in the cupboard how many snacks do I have all together)Ex Solve by adding (eg ldquoAdd the pencils in two boxes and tell how many pencils we haverdquo)
Level III Students willEE3OA8 Add to solve real world one-step story problems from 0-30 Represent the problem in pictures or with objectsEx Solve by adding (eg ldquoHere are 10 pencils We need 10 more for each person to get a pencil How many will we need in allrdquo)Ex Solve by adding (eg ldquoConnie had five marbles Juan gave her eight more marbles How many marbles does Connie have all togetherrdquo)Ex Solve by adding (eg ldquoAdd the crayons in these two boxes and show me how many we have in allrdquo)
Level II Students willEE3OA8 Add to solve word problems identified through symbol representationEx Complete word problems that have pictures rather than wordsEx Solve by adding (eg ldquoThere are three ducks in the pond two more joined How many ducks are in the pondrdquo [picture representation])
Level I Students willEE3OA8 Identify the object(s) that appear in a real world one-step story problemEx Given a simple word problem and asked ldquoWhat is the problem aboutrdquo point to an object from a choice of two that represents what the problem was about (eg box toy)Ex Indicate which object a word problem is about from an array of two choices
Version 3 2015-2016 24
solutions
Multiplication is putting together equal sized groups
Division is sharing into equal-sized shares or as sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models and representations
Solutions can be evaluated by using reasoning to compare the actual solution with estimated solutions
CCSS Math Pacing Guide
Version 3 2015-2016 25
Grade 3
Grade Level 3rdStandard with code 3OA9 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations For example observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addendsDomain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmeticQuarter 1
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 2
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 3
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 26
Students
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations (eg observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends)
Students know
Characteristics of numbers and properties of operations (eg odd even)
Properties from Table 3 etc
Students understand thatare able to
Identify arithmetic patterns in number sequences in the addition table or multiplication table
Use logical reasoning and properties of numbers and operations to explain arithmetic patterns
Characteristics of numbers and properties of operations justify patterns which can be used to reason about mathematical situations form conjectures and solve problems
EE3OA9 Identify arithmetic patterns
Level IV Students willEE3OA9 Complete a complex arithmetic patternEx Complete the pattern using more than two numbers (ie A B C A B C)Ex Using a 100s number chart complete the pattern identified
Level III Students willEE3OA9 Identify arithmetic patternsEx When provided arithmetic patterns on a 100s chart identify the next number in the patternEx When given two number stamps stamp an arithmetic pattern
Level II Students willEE3OA9 Identify a patternEx Make pattern jumps on a number lineEx Sing songs and identify the pattern in the song
Level I Students willEE3OA9 Follow patternsEx Sing ldquoHead Shoulders Knees and Toesrdquo and mimic the patternEx Using tactile objects (fur sand sand fur) in a pattern repeat the patternEx Using manipulatives mimic the teacher to create a pattern
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 27
Grade Level 3rdStandard with code 3NBT1 Use place value understanding to round whole numbers to the nearest 10 or 100Domain Number and Operations in Base Ten
Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 28
StudentsGiven any number less than 1000
Round it to the nearest 10 or 100 and justify the answer using place value vocabulary (eg Rounding 147 to the nearest 10 is 150 because 147 is between 140 and 150 and is more than half way to 150)
Students know
Place value (ones tens hundreds)
Rounding
Students understand thatare able to
Count by 10s and 100s
Determine what is halfway between two multiples of 10 or 100
Round to the nearest 10 or 100
Use place value vocabulary and logical reasoning to justify solutions to rounding problems
Rounding and place value can be used to estimate quantities by changing the original number to the closest multiple of a power of 10
EE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)
Level IV Students willEE3NBT1 Identify the two 10s a number comes in between and tell which is closest (numbers 0-50)Ex Use a color beaded number line to identify the number and round to the closest 10Ex Given a number line separated into tens (0-10 10-20 etc) stand on a number and identify the 10 that is closer
Level III Students willEE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)Ex Use a color beaded number line to identify the two 10s a number falls betweenEx Given the number 14 they would identify 10 and 20
Level II Students willEE3NBT1 Identify tens on a number lineEx Given a number line circle the tensEx Stand on a number chart on 10 20 30 etc
Level I Students willEE3NBT1 Identify a numberEx Point to any number from one to three on a number lineEx Participate in a cake walk When the music stops look to see if they are on the number that is called outEx Identify a number when point to or presented on a cardEx Given a number from one to three point to the number symbolRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 29
Grade Level 3rdStandard with code 3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtractionDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 30
Students
Fluently add and subtract within 1000 using strategies based on place values properties of operations andor the relationship between addition and subtraction
Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning
Students know
Tools for modeling addition and subtraction
Strategies for solving addition and subtraction problems
Methods for symbolically (numerically) recording strategies for solving addition and subtraction problems
Students understand thatare able to
Model addition and subtraction problems using appropriate tools
Record strategies for solving addition and subtraction problems
Communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems
Relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and solution strategies
EE3NBT2 Identify place value to tens
Level IV Students willEE3NBT2 Identify place value to 50Ex Build numbers with place value piecesEx Identify the number in the ones and tens place value (ie the price of an item)Ex Write the number in expanded form ndash 43 = 40 + 3
Level III Students willEE3NBT2 Identify place value to tensEx When given two-digit number cards identify the number in the tens place valueEx When given a group of 10 frame models arrange and count the value of the numberI saw three groups of 10 and five extras so three groups of 10 = 30 and 5 more makes 35
Level II Students willEE3NBT2 Count to 10 using one-to-one correspondenceEx Given a bag of Skittles pull 10 Skittles out of the bagEx Select a domino and tell what number the dots representEx Shown a set of 10 objects create a duplicate collectionEx Given a container of pennies count out 10 from the container
Level I Students willEE3NBT2 Identify more or lessEx Given two collections of objects (group of 10 group of 20) indicate ldquoWhich has morerdquoEx Given math manipulatives representing a single unit and multiple units point to the multiple unit representation when asked ldquowhich is morerdquoRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 31
Grade Level 3rdStandard with code 3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operationsDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 32
Students
Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers
Students know
Place value models for multiplying numbers (eg open arrays place value blocks)
Strategies for multiplying one-digit numbers
Strategies for mentally multiplying one-digit numbers by multiples of powers of 10
Students understand thatare able to
Use mental strategies based on an understanding of place value properties of operations and knowledge of one-digit multiplication to find products
Use a variety of place value models of multiplication problems to justify strategies and solutions
Patterns in the place value system and properties of operations can be used to efficiently compute products
EE3NBT3 Count by tens using money
Level IV Students willEE3NBT3 Compare the value of money based on place valueEx Use money (dimes and pennies) to represent place valueEx Given 15 pennies create a one group of 10 and a group of five ones
Level III Students willEE3NBT3 Count by tens using moneyEx Given three dimes count by 10 to determine totalEx Given five dimes count by 10 to determine total
Level II Students willEE3NBT3 Identify whole numbers to 10Ex Given sets of 10 pennies pair with numbersEx Given sets of 10 pennies pair with dimes
Level I Students willEE3NBT3 Count pennies to 10
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 33
Grade Level 3rdStandard with code 3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1bDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 34
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
solutions
Multiplication is putting together equal sized groups
Division is sharing into equal-sized shares or as sharing equally among a given number of groups
Mathematical problems can be solved using a variety of strategies models and representations
Solutions can be evaluated by using reasoning to compare the actual solution with estimated solutions
CCSS Math Pacing Guide
Version 3 2015-2016 25
Grade 3
Grade Level 3rdStandard with code 3OA9 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations For example observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addendsDomain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmeticQuarter 1
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 2
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 3
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 26
Students
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations (eg observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends)
Students know
Characteristics of numbers and properties of operations (eg odd even)
Properties from Table 3 etc
Students understand thatare able to
Identify arithmetic patterns in number sequences in the addition table or multiplication table
Use logical reasoning and properties of numbers and operations to explain arithmetic patterns
Characteristics of numbers and properties of operations justify patterns which can be used to reason about mathematical situations form conjectures and solve problems
EE3OA9 Identify arithmetic patterns
Level IV Students willEE3OA9 Complete a complex arithmetic patternEx Complete the pattern using more than two numbers (ie A B C A B C)Ex Using a 100s number chart complete the pattern identified
Level III Students willEE3OA9 Identify arithmetic patternsEx When provided arithmetic patterns on a 100s chart identify the next number in the patternEx When given two number stamps stamp an arithmetic pattern
Level II Students willEE3OA9 Identify a patternEx Make pattern jumps on a number lineEx Sing songs and identify the pattern in the song
Level I Students willEE3OA9 Follow patternsEx Sing ldquoHead Shoulders Knees and Toesrdquo and mimic the patternEx Using tactile objects (fur sand sand fur) in a pattern repeat the patternEx Using manipulatives mimic the teacher to create a pattern
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 27
Grade Level 3rdStandard with code 3NBT1 Use place value understanding to round whole numbers to the nearest 10 or 100Domain Number and Operations in Base Ten
Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 28
StudentsGiven any number less than 1000
Round it to the nearest 10 or 100 and justify the answer using place value vocabulary (eg Rounding 147 to the nearest 10 is 150 because 147 is between 140 and 150 and is more than half way to 150)
Students know
Place value (ones tens hundreds)
Rounding
Students understand thatare able to
Count by 10s and 100s
Determine what is halfway between two multiples of 10 or 100
Round to the nearest 10 or 100
Use place value vocabulary and logical reasoning to justify solutions to rounding problems
Rounding and place value can be used to estimate quantities by changing the original number to the closest multiple of a power of 10
EE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)
Level IV Students willEE3NBT1 Identify the two 10s a number comes in between and tell which is closest (numbers 0-50)Ex Use a color beaded number line to identify the number and round to the closest 10Ex Given a number line separated into tens (0-10 10-20 etc) stand on a number and identify the 10 that is closer
Level III Students willEE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)Ex Use a color beaded number line to identify the two 10s a number falls betweenEx Given the number 14 they would identify 10 and 20
Level II Students willEE3NBT1 Identify tens on a number lineEx Given a number line circle the tensEx Stand on a number chart on 10 20 30 etc
Level I Students willEE3NBT1 Identify a numberEx Point to any number from one to three on a number lineEx Participate in a cake walk When the music stops look to see if they are on the number that is called outEx Identify a number when point to or presented on a cardEx Given a number from one to three point to the number symbolRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 29
Grade Level 3rdStandard with code 3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtractionDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 30
Students
Fluently add and subtract within 1000 using strategies based on place values properties of operations andor the relationship between addition and subtraction
Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning
Students know
Tools for modeling addition and subtraction
Strategies for solving addition and subtraction problems
Methods for symbolically (numerically) recording strategies for solving addition and subtraction problems
Students understand thatare able to
Model addition and subtraction problems using appropriate tools
Record strategies for solving addition and subtraction problems
Communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems
Relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and solution strategies
EE3NBT2 Identify place value to tens
Level IV Students willEE3NBT2 Identify place value to 50Ex Build numbers with place value piecesEx Identify the number in the ones and tens place value (ie the price of an item)Ex Write the number in expanded form ndash 43 = 40 + 3
Level III Students willEE3NBT2 Identify place value to tensEx When given two-digit number cards identify the number in the tens place valueEx When given a group of 10 frame models arrange and count the value of the numberI saw three groups of 10 and five extras so three groups of 10 = 30 and 5 more makes 35
Level II Students willEE3NBT2 Count to 10 using one-to-one correspondenceEx Given a bag of Skittles pull 10 Skittles out of the bagEx Select a domino and tell what number the dots representEx Shown a set of 10 objects create a duplicate collectionEx Given a container of pennies count out 10 from the container
Level I Students willEE3NBT2 Identify more or lessEx Given two collections of objects (group of 10 group of 20) indicate ldquoWhich has morerdquoEx Given math manipulatives representing a single unit and multiple units point to the multiple unit representation when asked ldquowhich is morerdquoRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 31
Grade Level 3rdStandard with code 3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operationsDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 32
Students
Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers
Students know
Place value models for multiplying numbers (eg open arrays place value blocks)
Strategies for multiplying one-digit numbers
Strategies for mentally multiplying one-digit numbers by multiples of powers of 10
Students understand thatare able to
Use mental strategies based on an understanding of place value properties of operations and knowledge of one-digit multiplication to find products
Use a variety of place value models of multiplication problems to justify strategies and solutions
Patterns in the place value system and properties of operations can be used to efficiently compute products
EE3NBT3 Count by tens using money
Level IV Students willEE3NBT3 Compare the value of money based on place valueEx Use money (dimes and pennies) to represent place valueEx Given 15 pennies create a one group of 10 and a group of five ones
Level III Students willEE3NBT3 Count by tens using moneyEx Given three dimes count by 10 to determine totalEx Given five dimes count by 10 to determine total
Level II Students willEE3NBT3 Identify whole numbers to 10Ex Given sets of 10 pennies pair with numbersEx Given sets of 10 pennies pair with dimes
Level I Students willEE3NBT3 Count pennies to 10
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 33
Grade Level 3rdStandard with code 3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1bDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 34
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Grade 3
Grade Level 3rdStandard with code 3OA9 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations For example observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addendsDomain Operations and Algebraic Thinking Cluster Solve problems involving the four operations and identify and explain patterns in arithmeticQuarter 1
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 2
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 3
Identify arithmetic patterns (such as even and odd numbers patterns in an addition table patterns in a multiplication table patterns regarding multiples and sums)
Explain rules for a pattern using properties of operations (Properties of operations glossary page 90 Common Core State Standards)
Explain relationships between the numbers in a pattern
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 26
Students
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations (eg observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends)
Students know
Characteristics of numbers and properties of operations (eg odd even)
Properties from Table 3 etc
Students understand thatare able to
Identify arithmetic patterns in number sequences in the addition table or multiplication table
Use logical reasoning and properties of numbers and operations to explain arithmetic patterns
Characteristics of numbers and properties of operations justify patterns which can be used to reason about mathematical situations form conjectures and solve problems
EE3OA9 Identify arithmetic patterns
Level IV Students willEE3OA9 Complete a complex arithmetic patternEx Complete the pattern using more than two numbers (ie A B C A B C)Ex Using a 100s number chart complete the pattern identified
Level III Students willEE3OA9 Identify arithmetic patternsEx When provided arithmetic patterns on a 100s chart identify the next number in the patternEx When given two number stamps stamp an arithmetic pattern
Level II Students willEE3OA9 Identify a patternEx Make pattern jumps on a number lineEx Sing songs and identify the pattern in the song
Level I Students willEE3OA9 Follow patternsEx Sing ldquoHead Shoulders Knees and Toesrdquo and mimic the patternEx Using tactile objects (fur sand sand fur) in a pattern repeat the patternEx Using manipulatives mimic the teacher to create a pattern
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 27
Grade Level 3rdStandard with code 3NBT1 Use place value understanding to round whole numbers to the nearest 10 or 100Domain Number and Operations in Base Ten
Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 28
StudentsGiven any number less than 1000
Round it to the nearest 10 or 100 and justify the answer using place value vocabulary (eg Rounding 147 to the nearest 10 is 150 because 147 is between 140 and 150 and is more than half way to 150)
Students know
Place value (ones tens hundreds)
Rounding
Students understand thatare able to
Count by 10s and 100s
Determine what is halfway between two multiples of 10 or 100
Round to the nearest 10 or 100
Use place value vocabulary and logical reasoning to justify solutions to rounding problems
Rounding and place value can be used to estimate quantities by changing the original number to the closest multiple of a power of 10
EE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)
Level IV Students willEE3NBT1 Identify the two 10s a number comes in between and tell which is closest (numbers 0-50)Ex Use a color beaded number line to identify the number and round to the closest 10Ex Given a number line separated into tens (0-10 10-20 etc) stand on a number and identify the 10 that is closer
Level III Students willEE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)Ex Use a color beaded number line to identify the two 10s a number falls betweenEx Given the number 14 they would identify 10 and 20
Level II Students willEE3NBT1 Identify tens on a number lineEx Given a number line circle the tensEx Stand on a number chart on 10 20 30 etc
Level I Students willEE3NBT1 Identify a numberEx Point to any number from one to three on a number lineEx Participate in a cake walk When the music stops look to see if they are on the number that is called outEx Identify a number when point to or presented on a cardEx Given a number from one to three point to the number symbolRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 29
Grade Level 3rdStandard with code 3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtractionDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 30
Students
Fluently add and subtract within 1000 using strategies based on place values properties of operations andor the relationship between addition and subtraction
Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning
Students know
Tools for modeling addition and subtraction
Strategies for solving addition and subtraction problems
Methods for symbolically (numerically) recording strategies for solving addition and subtraction problems
Students understand thatare able to
Model addition and subtraction problems using appropriate tools
Record strategies for solving addition and subtraction problems
Communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems
Relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and solution strategies
EE3NBT2 Identify place value to tens
Level IV Students willEE3NBT2 Identify place value to 50Ex Build numbers with place value piecesEx Identify the number in the ones and tens place value (ie the price of an item)Ex Write the number in expanded form ndash 43 = 40 + 3
Level III Students willEE3NBT2 Identify place value to tensEx When given two-digit number cards identify the number in the tens place valueEx When given a group of 10 frame models arrange and count the value of the numberI saw three groups of 10 and five extras so three groups of 10 = 30 and 5 more makes 35
Level II Students willEE3NBT2 Count to 10 using one-to-one correspondenceEx Given a bag of Skittles pull 10 Skittles out of the bagEx Select a domino and tell what number the dots representEx Shown a set of 10 objects create a duplicate collectionEx Given a container of pennies count out 10 from the container
Level I Students willEE3NBT2 Identify more or lessEx Given two collections of objects (group of 10 group of 20) indicate ldquoWhich has morerdquoEx Given math manipulatives representing a single unit and multiple units point to the multiple unit representation when asked ldquowhich is morerdquoRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 31
Grade Level 3rdStandard with code 3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operationsDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 32
Students
Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers
Students know
Place value models for multiplying numbers (eg open arrays place value blocks)
Strategies for multiplying one-digit numbers
Strategies for mentally multiplying one-digit numbers by multiples of powers of 10
Students understand thatare able to
Use mental strategies based on an understanding of place value properties of operations and knowledge of one-digit multiplication to find products
Use a variety of place value models of multiplication problems to justify strategies and solutions
Patterns in the place value system and properties of operations can be used to efficiently compute products
EE3NBT3 Count by tens using money
Level IV Students willEE3NBT3 Compare the value of money based on place valueEx Use money (dimes and pennies) to represent place valueEx Given 15 pennies create a one group of 10 and a group of five ones
Level III Students willEE3NBT3 Count by tens using moneyEx Given three dimes count by 10 to determine totalEx Given five dimes count by 10 to determine total
Level II Students willEE3NBT3 Identify whole numbers to 10Ex Given sets of 10 pennies pair with numbersEx Given sets of 10 pennies pair with dimes
Level I Students willEE3NBT3 Count pennies to 10
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 33
Grade Level 3rdStandard with code 3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1bDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 34
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Students
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations (eg observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends)
Students know
Characteristics of numbers and properties of operations (eg odd even)
Properties from Table 3 etc
Students understand thatare able to
Identify arithmetic patterns in number sequences in the addition table or multiplication table
Use logical reasoning and properties of numbers and operations to explain arithmetic patterns
Characteristics of numbers and properties of operations justify patterns which can be used to reason about mathematical situations form conjectures and solve problems
EE3OA9 Identify arithmetic patterns
Level IV Students willEE3OA9 Complete a complex arithmetic patternEx Complete the pattern using more than two numbers (ie A B C A B C)Ex Using a 100s number chart complete the pattern identified
Level III Students willEE3OA9 Identify arithmetic patternsEx When provided arithmetic patterns on a 100s chart identify the next number in the patternEx When given two number stamps stamp an arithmetic pattern
Level II Students willEE3OA9 Identify a patternEx Make pattern jumps on a number lineEx Sing songs and identify the pattern in the song
Level I Students willEE3OA9 Follow patternsEx Sing ldquoHead Shoulders Knees and Toesrdquo and mimic the patternEx Using tactile objects (fur sand sand fur) in a pattern repeat the patternEx Using manipulatives mimic the teacher to create a pattern
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 27
Grade Level 3rdStandard with code 3NBT1 Use place value understanding to round whole numbers to the nearest 10 or 100Domain Number and Operations in Base Ten
Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 28
StudentsGiven any number less than 1000
Round it to the nearest 10 or 100 and justify the answer using place value vocabulary (eg Rounding 147 to the nearest 10 is 150 because 147 is between 140 and 150 and is more than half way to 150)
Students know
Place value (ones tens hundreds)
Rounding
Students understand thatare able to
Count by 10s and 100s
Determine what is halfway between two multiples of 10 or 100
Round to the nearest 10 or 100
Use place value vocabulary and logical reasoning to justify solutions to rounding problems
Rounding and place value can be used to estimate quantities by changing the original number to the closest multiple of a power of 10
EE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)
Level IV Students willEE3NBT1 Identify the two 10s a number comes in between and tell which is closest (numbers 0-50)Ex Use a color beaded number line to identify the number and round to the closest 10Ex Given a number line separated into tens (0-10 10-20 etc) stand on a number and identify the 10 that is closer
Level III Students willEE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)Ex Use a color beaded number line to identify the two 10s a number falls betweenEx Given the number 14 they would identify 10 and 20
Level II Students willEE3NBT1 Identify tens on a number lineEx Given a number line circle the tensEx Stand on a number chart on 10 20 30 etc
Level I Students willEE3NBT1 Identify a numberEx Point to any number from one to three on a number lineEx Participate in a cake walk When the music stops look to see if they are on the number that is called outEx Identify a number when point to or presented on a cardEx Given a number from one to three point to the number symbolRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 29
Grade Level 3rdStandard with code 3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtractionDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 30
Students
Fluently add and subtract within 1000 using strategies based on place values properties of operations andor the relationship between addition and subtraction
Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning
Students know
Tools for modeling addition and subtraction
Strategies for solving addition and subtraction problems
Methods for symbolically (numerically) recording strategies for solving addition and subtraction problems
Students understand thatare able to
Model addition and subtraction problems using appropriate tools
Record strategies for solving addition and subtraction problems
Communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems
Relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and solution strategies
EE3NBT2 Identify place value to tens
Level IV Students willEE3NBT2 Identify place value to 50Ex Build numbers with place value piecesEx Identify the number in the ones and tens place value (ie the price of an item)Ex Write the number in expanded form ndash 43 = 40 + 3
Level III Students willEE3NBT2 Identify place value to tensEx When given two-digit number cards identify the number in the tens place valueEx When given a group of 10 frame models arrange and count the value of the numberI saw three groups of 10 and five extras so three groups of 10 = 30 and 5 more makes 35
Level II Students willEE3NBT2 Count to 10 using one-to-one correspondenceEx Given a bag of Skittles pull 10 Skittles out of the bagEx Select a domino and tell what number the dots representEx Shown a set of 10 objects create a duplicate collectionEx Given a container of pennies count out 10 from the container
Level I Students willEE3NBT2 Identify more or lessEx Given two collections of objects (group of 10 group of 20) indicate ldquoWhich has morerdquoEx Given math manipulatives representing a single unit and multiple units point to the multiple unit representation when asked ldquowhich is morerdquoRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 31
Grade Level 3rdStandard with code 3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operationsDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 32
Students
Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers
Students know
Place value models for multiplying numbers (eg open arrays place value blocks)
Strategies for multiplying one-digit numbers
Strategies for mentally multiplying one-digit numbers by multiples of powers of 10
Students understand thatare able to
Use mental strategies based on an understanding of place value properties of operations and knowledge of one-digit multiplication to find products
Use a variety of place value models of multiplication problems to justify strategies and solutions
Patterns in the place value system and properties of operations can be used to efficiently compute products
EE3NBT3 Count by tens using money
Level IV Students willEE3NBT3 Compare the value of money based on place valueEx Use money (dimes and pennies) to represent place valueEx Given 15 pennies create a one group of 10 and a group of five ones
Level III Students willEE3NBT3 Count by tens using moneyEx Given three dimes count by 10 to determine totalEx Given five dimes count by 10 to determine total
Level II Students willEE3NBT3 Identify whole numbers to 10Ex Given sets of 10 pennies pair with numbersEx Given sets of 10 pennies pair with dimes
Level I Students willEE3NBT3 Count pennies to 10
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 33
Grade Level 3rdStandard with code 3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1bDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 34
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Grade Level 3rdStandard with code 3NBT1 Use place value understanding to round whole numbers to the nearest 10 or 100Domain Number and Operations in Base Ten
Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 28
StudentsGiven any number less than 1000
Round it to the nearest 10 or 100 and justify the answer using place value vocabulary (eg Rounding 147 to the nearest 10 is 150 because 147 is between 140 and 150 and is more than half way to 150)
Students know
Place value (ones tens hundreds)
Rounding
Students understand thatare able to
Count by 10s and 100s
Determine what is halfway between two multiples of 10 or 100
Round to the nearest 10 or 100
Use place value vocabulary and logical reasoning to justify solutions to rounding problems
Rounding and place value can be used to estimate quantities by changing the original number to the closest multiple of a power of 10
EE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)
Level IV Students willEE3NBT1 Identify the two 10s a number comes in between and tell which is closest (numbers 0-50)Ex Use a color beaded number line to identify the number and round to the closest 10Ex Given a number line separated into tens (0-10 10-20 etc) stand on a number and identify the 10 that is closer
Level III Students willEE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)Ex Use a color beaded number line to identify the two 10s a number falls betweenEx Given the number 14 they would identify 10 and 20
Level II Students willEE3NBT1 Identify tens on a number lineEx Given a number line circle the tensEx Stand on a number chart on 10 20 30 etc
Level I Students willEE3NBT1 Identify a numberEx Point to any number from one to three on a number lineEx Participate in a cake walk When the music stops look to see if they are on the number that is called outEx Identify a number when point to or presented on a cardEx Given a number from one to three point to the number symbolRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 29
Grade Level 3rdStandard with code 3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtractionDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 30
Students
Fluently add and subtract within 1000 using strategies based on place values properties of operations andor the relationship between addition and subtraction
Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning
Students know
Tools for modeling addition and subtraction
Strategies for solving addition and subtraction problems
Methods for symbolically (numerically) recording strategies for solving addition and subtraction problems
Students understand thatare able to
Model addition and subtraction problems using appropriate tools
Record strategies for solving addition and subtraction problems
Communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems
Relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and solution strategies
EE3NBT2 Identify place value to tens
Level IV Students willEE3NBT2 Identify place value to 50Ex Build numbers with place value piecesEx Identify the number in the ones and tens place value (ie the price of an item)Ex Write the number in expanded form ndash 43 = 40 + 3
Level III Students willEE3NBT2 Identify place value to tensEx When given two-digit number cards identify the number in the tens place valueEx When given a group of 10 frame models arrange and count the value of the numberI saw three groups of 10 and five extras so three groups of 10 = 30 and 5 more makes 35
Level II Students willEE3NBT2 Count to 10 using one-to-one correspondenceEx Given a bag of Skittles pull 10 Skittles out of the bagEx Select a domino and tell what number the dots representEx Shown a set of 10 objects create a duplicate collectionEx Given a container of pennies count out 10 from the container
Level I Students willEE3NBT2 Identify more or lessEx Given two collections of objects (group of 10 group of 20) indicate ldquoWhich has morerdquoEx Given math manipulatives representing a single unit and multiple units point to the multiple unit representation when asked ldquowhich is morerdquoRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 31
Grade Level 3rdStandard with code 3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operationsDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 32
Students
Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers
Students know
Place value models for multiplying numbers (eg open arrays place value blocks)
Strategies for multiplying one-digit numbers
Strategies for mentally multiplying one-digit numbers by multiples of powers of 10
Students understand thatare able to
Use mental strategies based on an understanding of place value properties of operations and knowledge of one-digit multiplication to find products
Use a variety of place value models of multiplication problems to justify strategies and solutions
Patterns in the place value system and properties of operations can be used to efficiently compute products
EE3NBT3 Count by tens using money
Level IV Students willEE3NBT3 Compare the value of money based on place valueEx Use money (dimes and pennies) to represent place valueEx Given 15 pennies create a one group of 10 and a group of five ones
Level III Students willEE3NBT3 Count by tens using moneyEx Given three dimes count by 10 to determine totalEx Given five dimes count by 10 to determine total
Level II Students willEE3NBT3 Identify whole numbers to 10Ex Given sets of 10 pennies pair with numbersEx Given sets of 10 pennies pair with dimes
Level I Students willEE3NBT3 Count pennies to 10
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 33
Grade Level 3rdStandard with code 3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1bDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 34
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
StudentsGiven any number less than 1000
Round it to the nearest 10 or 100 and justify the answer using place value vocabulary (eg Rounding 147 to the nearest 10 is 150 because 147 is between 140 and 150 and is more than half way to 150)
Students know
Place value (ones tens hundreds)
Rounding
Students understand thatare able to
Count by 10s and 100s
Determine what is halfway between two multiples of 10 or 100
Round to the nearest 10 or 100
Use place value vocabulary and logical reasoning to justify solutions to rounding problems
Rounding and place value can be used to estimate quantities by changing the original number to the closest multiple of a power of 10
EE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)
Level IV Students willEE3NBT1 Identify the two 10s a number comes in between and tell which is closest (numbers 0-50)Ex Use a color beaded number line to identify the number and round to the closest 10Ex Given a number line separated into tens (0-10 10-20 etc) stand on a number and identify the 10 that is closer
Level III Students willEE3NBT1 Identify the two 10s a number comes in between on a number line (numbers 0-30)Ex Use a color beaded number line to identify the two 10s a number falls betweenEx Given the number 14 they would identify 10 and 20
Level II Students willEE3NBT1 Identify tens on a number lineEx Given a number line circle the tensEx Stand on a number chart on 10 20 30 etc
Level I Students willEE3NBT1 Identify a numberEx Point to any number from one to three on a number lineEx Participate in a cake walk When the music stops look to see if they are on the number that is called outEx Identify a number when point to or presented on a cardEx Given a number from one to three point to the number symbolRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 29
Grade Level 3rdStandard with code 3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtractionDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 30
Students
Fluently add and subtract within 1000 using strategies based on place values properties of operations andor the relationship between addition and subtraction
Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning
Students know
Tools for modeling addition and subtraction
Strategies for solving addition and subtraction problems
Methods for symbolically (numerically) recording strategies for solving addition and subtraction problems
Students understand thatare able to
Model addition and subtraction problems using appropriate tools
Record strategies for solving addition and subtraction problems
Communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems
Relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and solution strategies
EE3NBT2 Identify place value to tens
Level IV Students willEE3NBT2 Identify place value to 50Ex Build numbers with place value piecesEx Identify the number in the ones and tens place value (ie the price of an item)Ex Write the number in expanded form ndash 43 = 40 + 3
Level III Students willEE3NBT2 Identify place value to tensEx When given two-digit number cards identify the number in the tens place valueEx When given a group of 10 frame models arrange and count the value of the numberI saw three groups of 10 and five extras so three groups of 10 = 30 and 5 more makes 35
Level II Students willEE3NBT2 Count to 10 using one-to-one correspondenceEx Given a bag of Skittles pull 10 Skittles out of the bagEx Select a domino and tell what number the dots representEx Shown a set of 10 objects create a duplicate collectionEx Given a container of pennies count out 10 from the container
Level I Students willEE3NBT2 Identify more or lessEx Given two collections of objects (group of 10 group of 20) indicate ldquoWhich has morerdquoEx Given math manipulatives representing a single unit and multiple units point to the multiple unit representation when asked ldquowhich is morerdquoRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 31
Grade Level 3rdStandard with code 3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operationsDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 32
Students
Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers
Students know
Place value models for multiplying numbers (eg open arrays place value blocks)
Strategies for multiplying one-digit numbers
Strategies for mentally multiplying one-digit numbers by multiples of powers of 10
Students understand thatare able to
Use mental strategies based on an understanding of place value properties of operations and knowledge of one-digit multiplication to find products
Use a variety of place value models of multiplication problems to justify strategies and solutions
Patterns in the place value system and properties of operations can be used to efficiently compute products
EE3NBT3 Count by tens using money
Level IV Students willEE3NBT3 Compare the value of money based on place valueEx Use money (dimes and pennies) to represent place valueEx Given 15 pennies create a one group of 10 and a group of five ones
Level III Students willEE3NBT3 Count by tens using moneyEx Given three dimes count by 10 to determine totalEx Given five dimes count by 10 to determine total
Level II Students willEE3NBT3 Identify whole numbers to 10Ex Given sets of 10 pennies pair with numbersEx Given sets of 10 pennies pair with dimes
Level I Students willEE3NBT3 Count pennies to 10
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 33
Grade Level 3rdStandard with code 3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1bDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 34
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Grade Level 3rdStandard with code 3NBT2 Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations andor the relationship between addition and subtractionDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 30
Students
Fluently add and subtract within 1000 using strategies based on place values properties of operations andor the relationship between addition and subtraction
Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning
Students know
Tools for modeling addition and subtraction
Strategies for solving addition and subtraction problems
Methods for symbolically (numerically) recording strategies for solving addition and subtraction problems
Students understand thatare able to
Model addition and subtraction problems using appropriate tools
Record strategies for solving addition and subtraction problems
Communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems
Relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and solution strategies
EE3NBT2 Identify place value to tens
Level IV Students willEE3NBT2 Identify place value to 50Ex Build numbers with place value piecesEx Identify the number in the ones and tens place value (ie the price of an item)Ex Write the number in expanded form ndash 43 = 40 + 3
Level III Students willEE3NBT2 Identify place value to tensEx When given two-digit number cards identify the number in the tens place valueEx When given a group of 10 frame models arrange and count the value of the numberI saw three groups of 10 and five extras so three groups of 10 = 30 and 5 more makes 35
Level II Students willEE3NBT2 Count to 10 using one-to-one correspondenceEx Given a bag of Skittles pull 10 Skittles out of the bagEx Select a domino and tell what number the dots representEx Shown a set of 10 objects create a duplicate collectionEx Given a container of pennies count out 10 from the container
Level I Students willEE3NBT2 Identify more or lessEx Given two collections of objects (group of 10 group of 20) indicate ldquoWhich has morerdquoEx Given math manipulatives representing a single unit and multiple units point to the multiple unit representation when asked ldquowhich is morerdquoRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 31
Grade Level 3rdStandard with code 3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operationsDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 32
Students
Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers
Students know
Place value models for multiplying numbers (eg open arrays place value blocks)
Strategies for multiplying one-digit numbers
Strategies for mentally multiplying one-digit numbers by multiples of powers of 10
Students understand thatare able to
Use mental strategies based on an understanding of place value properties of operations and knowledge of one-digit multiplication to find products
Use a variety of place value models of multiplication problems to justify strategies and solutions
Patterns in the place value system and properties of operations can be used to efficiently compute products
EE3NBT3 Count by tens using money
Level IV Students willEE3NBT3 Compare the value of money based on place valueEx Use money (dimes and pennies) to represent place valueEx Given 15 pennies create a one group of 10 and a group of five ones
Level III Students willEE3NBT3 Count by tens using moneyEx Given three dimes count by 10 to determine totalEx Given five dimes count by 10 to determine total
Level II Students willEE3NBT3 Identify whole numbers to 10Ex Given sets of 10 pennies pair with numbersEx Given sets of 10 pennies pair with dimes
Level I Students willEE3NBT3 Count pennies to 10
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 33
Grade Level 3rdStandard with code 3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1bDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 34
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Students
Fluently add and subtract within 1000 using strategies based on place values properties of operations andor the relationship between addition and subtraction
Justify solutions including those which required regrouping by relating the strategy to a written method and explain the reasoning
Students know
Tools for modeling addition and subtraction
Strategies for solving addition and subtraction problems
Methods for symbolically (numerically) recording strategies for solving addition and subtraction problems
Students understand thatare able to
Model addition and subtraction problems using appropriate tools
Record strategies for solving addition and subtraction problems
Communicate the relationship between models and symbolic (numeric) representations of solutions to addition and subtraction problems
Relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and solution strategies
EE3NBT2 Identify place value to tens
Level IV Students willEE3NBT2 Identify place value to 50Ex Build numbers with place value piecesEx Identify the number in the ones and tens place value (ie the price of an item)Ex Write the number in expanded form ndash 43 = 40 + 3
Level III Students willEE3NBT2 Identify place value to tensEx When given two-digit number cards identify the number in the tens place valueEx When given a group of 10 frame models arrange and count the value of the numberI saw three groups of 10 and five extras so three groups of 10 = 30 and 5 more makes 35
Level II Students willEE3NBT2 Count to 10 using one-to-one correspondenceEx Given a bag of Skittles pull 10 Skittles out of the bagEx Select a domino and tell what number the dots representEx Shown a set of 10 objects create a duplicate collectionEx Given a container of pennies count out 10 from the container
Level I Students willEE3NBT2 Identify more or lessEx Given two collections of objects (group of 10 group of 20) indicate ldquoWhich has morerdquoEx Given math manipulatives representing a single unit and multiple units point to the multiple unit representation when asked ldquowhich is morerdquoRefer to the Common Core Essential Elements document for diagram
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 31
Grade Level 3rdStandard with code 3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operationsDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 32
Students
Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers
Students know
Place value models for multiplying numbers (eg open arrays place value blocks)
Strategies for multiplying one-digit numbers
Strategies for mentally multiplying one-digit numbers by multiples of powers of 10
Students understand thatare able to
Use mental strategies based on an understanding of place value properties of operations and knowledge of one-digit multiplication to find products
Use a variety of place value models of multiplication problems to justify strategies and solutions
Patterns in the place value system and properties of operations can be used to efficiently compute products
EE3NBT3 Count by tens using money
Level IV Students willEE3NBT3 Compare the value of money based on place valueEx Use money (dimes and pennies) to represent place valueEx Given 15 pennies create a one group of 10 and a group of five ones
Level III Students willEE3NBT3 Count by tens using moneyEx Given three dimes count by 10 to determine totalEx Given five dimes count by 10 to determine total
Level II Students willEE3NBT3 Identify whole numbers to 10Ex Given sets of 10 pennies pair with numbersEx Given sets of 10 pennies pair with dimes
Level I Students willEE3NBT3 Count pennies to 10
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 33
Grade Level 3rdStandard with code 3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1bDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 34
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Grade Level 3rdStandard with code 3NBT3 Multiply one-digit whole numbers by multiples of 10 in the range 10ndash90 (eg 9 times 80 5 times 60) using strategies based on place value and properties of operationsDomain Number and Operations in Base Ten Cluster Use place value understanding and properties of operations to perform multi-digit arithmetic4
Quarter 1
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 2 Quarter 3 Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 32
Students
Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers
Students know
Place value models for multiplying numbers (eg open arrays place value blocks)
Strategies for multiplying one-digit numbers
Strategies for mentally multiplying one-digit numbers by multiples of powers of 10
Students understand thatare able to
Use mental strategies based on an understanding of place value properties of operations and knowledge of one-digit multiplication to find products
Use a variety of place value models of multiplication problems to justify strategies and solutions
Patterns in the place value system and properties of operations can be used to efficiently compute products
EE3NBT3 Count by tens using money
Level IV Students willEE3NBT3 Compare the value of money based on place valueEx Use money (dimes and pennies) to represent place valueEx Given 15 pennies create a one group of 10 and a group of five ones
Level III Students willEE3NBT3 Count by tens using moneyEx Given three dimes count by 10 to determine totalEx Given five dimes count by 10 to determine total
Level II Students willEE3NBT3 Identify whole numbers to 10Ex Given sets of 10 pennies pair with numbersEx Given sets of 10 pennies pair with dimes
Level I Students willEE3NBT3 Count pennies to 10
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 33
Grade Level 3rdStandard with code 3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1bDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 34
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Students
Efficiently use strategies based on place value and properties of operations to multiply one-digit numbers by multiples of 10 (from 10-90) and justify their answers
Students know
Place value models for multiplying numbers (eg open arrays place value blocks)
Strategies for multiplying one-digit numbers
Strategies for mentally multiplying one-digit numbers by multiples of powers of 10
Students understand thatare able to
Use mental strategies based on an understanding of place value properties of operations and knowledge of one-digit multiplication to find products
Use a variety of place value models of multiplication problems to justify strategies and solutions
Patterns in the place value system and properties of operations can be used to efficiently compute products
EE3NBT3 Count by tens using money
Level IV Students willEE3NBT3 Compare the value of money based on place valueEx Use money (dimes and pennies) to represent place valueEx Given 15 pennies create a one group of 10 and a group of five ones
Level III Students willEE3NBT3 Count by tens using moneyEx Given three dimes count by 10 to determine totalEx Given five dimes count by 10 to determine total
Level II Students willEE3NBT3 Identify whole numbers to 10Ex Given sets of 10 pennies pair with numbersEx Given sets of 10 pennies pair with dimes
Level I Students willEE3NBT3 Count pennies to 10
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 33
Grade Level 3rdStandard with code 3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1bDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 34
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Grade Level 3rdStandard with code 3NF1 Understand a fraction 1b as the quantity formed by 1 part when a whole is partitioned into b equal parts understand a fraction ab as the quantity formed by a parts of size 1bDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Define ldquoround or roundingrdquo in relation to place value
Round a whole number to the nearest 10
Round a whole number to the nearest 100
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 34
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
StudentsGiven any fraction in the form ab
Create a model of the fraction and explain the relationship between the fraction and the model including the corresponding sum of unit fractions (fractions with numerator = 1) (eg 35 = 15 + 15 + 15)
Given a model of a fraction
Write the corresponding fraction and explain the relationship of the numerator and denominator to the model
Students know
Fractions
Strategies for creating models of fractional quantities (eg folding repeatedly dividing the whole in half etc)
Students understand thatare able to
Write fractions that correspond to pictorial or physical models
Create models of fractions that correspond to fractions written in the form ab
Communicate the relationship between models of fractions and the corresponding written fraction
Fractional parts are created when a whole is partitioned into equal sized pieces (using up the whole)
The unit fraction (1b) names the size of the unit with respect to the referenced whole
The numerator counts the parts referenced and that the denominator tells the number of parts into which the whole was partitioned
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 35
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Grade Level 3rdStandard with code 3NF2 Understand a fraction as a number on the number line represent fractions on a number line diagrama Represent a fraction 1b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts Recognize that each part has size 1b and that the endpoint of the part based at 0 locates the number 1b on the number lineb Represent a fraction ab on a number line diagram by marking off a lengths 1b from 0 Recognize that the resulting interval has size ab and that its endpoint locates the number ab on the number lineDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3Know strategies and algorithms for adding and subtracting within 1000
Fluently add and subtract within 1000
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Students know Students understand EE3NF1-3 Level IV Students will
Version 3 2015-2016 36
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Given any common fraction ab between 0 and 1 (denominators of 2 3 4 6 8)
Create a number line diagram and justify the partitioning of the interval from 0 to 1 and the placement of the point that corresponds to the fraction
Fractions
Strategies for creating number line models of fractions less than 1 (eg marking off equal lengths by estimation recursive halving)
thatare able to
Represent fractions in the form ab on a number line including correctly partitioning the interval from 0 to 1 into b equal parts and counting a parts to place the fraction
Explain and justify the creation and placement of a fraction less than 1 on a number line
A fractional quantity can be modeled using a variety of representations (eg part of a whole part of a group a distance on a numberline) each of which may reveal important features of given contexts
Differentiate a fractional part from a whole
EE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 37
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Grade Level 3rdStandard with code 3NF3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their sizea Understand two fractions as equivalent (equal) if they are the same size or the same point on a number lineb Recognize and generate simple equivalent fractions eg 12 = 24 46 = 23) Explain why the fractions are equivalent eg by using a visual fraction modelc Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers Examples Express 3 in the form 3 = 31 recognize that 61 = 6 locate 44 and 1 at the same point of a number line diagramd Compare two fractions with the same numerator or the same denominator by reasoning about their size Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with the symbols gt = or lt and justify the conclusions eg by using a visual fraction modelDomain Number and Operations-Fractions5 Cluster Develop understanding of fractions as numbers
Quarter 1 Quarter 2 Quarter 3
Know strategies to multiply one-digit numbers by multiples of 10 (up to 90)
Apply knowledge of place value to multiply one-digit whole numbers by multiples of 10 in the range 10-90
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Use visual models (eg fraction manipulatives number lines or pictures) to generate simple equivalent fractions including fractions
Students know
Strategies for comparing fractions (eg comparing numerators of like fractions comparing denominators of fractions with like numerators comparing to landmark
Students understand thatare able to
Generate simple equivalent fractions using visual models
Express the same whole number in
EE3NF1-3 Differentiate a fractional part from a whole
Level IV Students willEE3NF1-3 Identify halves or fourths as related to the wholeEx Identify pictures or objects that are split into fourthsEx Fold a square piece of paper into four equal parts and identify it as four parts of a wholeEx Complete a picture of half an object with the other half to make the wholeEx Given a set of pictures color a half of each wholeEx Shown four halves assemble them into two wholes and state the number of wholes
Version 3 2015-2016 38
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
equivalent to whole numbers
Given two fractions use logical reasoning and a variety of models to represent and order the fractions (using lt = gt) and justify their answers
Communicate the reason why it is not valid to make a comparison between fractions that refer to different wholes (eg why it may not be valid to say 12 gt14 if the 12 refers to a small pizza and the 14 refers to an extra-large pizza or Susie said her 16 pizza was bigger than my 12 pizza is she correct)
fractions such as 12)
Strategies for generating equivalent fractions using visual models (eg fraction circles fraction bars diagrams pictures etc)
multiple ways as fractions (4 = 41 = 82 = 164) and explain their answers
Strategically choose and apply a variety of representations or use logical reasoning to justify the comparison of two fractions
Represent the comparison of fractions using lt = and gt notation
Two fractions are equivalent if they are the same portion of the same whole or are the same point on the number line
Comparisons of fractions are valid only when the two fractions refer to the same whole
Any fraction can be named in many ways (equivalent fractions) and different names are useful for different problem situations
Level III Students willEE3NF1-3 Differentiate a fractional part from a wholeEx Sort pictures of whole objects and parts into the appropriate categoryEx Use a variety of real-world objects (pizza segmented chocolate bar etc) to demonstrate that each piece represents a part of the wholeEx Shown four halves assemble them into two wholes
Level II Students willEE3NF1-3 Recognize that fractions are part of a wholeEx Using a self-sticking non-adhesive shape take apart and put together fractional parts of a wholeEx Utilize wooden shapes separate into halves and put back together into whole
Level I Students willEE3NF1-3 Identify a wholeEx Given a part of and the whole real-world object (pizza segmented chocolate bar segmented toy pie etc) point to the wholeEx Given a puzzle with missing pieces and a puzzle with complete pieces identify the whole
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 39
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Grade Level 3rdStandard with code 3MD1 Tell and write time to the nearest minute and measure time intervals in minutes Solve word problems involving addition and subtraction of time intervals in minutes eg by representing the problem on a number line diagramDomain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objectsQuarter 1 Quarter 2 Quarter 3
Recognize minute marks on analog clock face and minute position on digital clock face
Know how to write time to the minute
Tell time to the minute
Compare an analog clock face with a number line diagram
Use a number line diagram to add and subtract time intervals in minutes
Solve word problems involving addition and subtraction of time intervals in minutes
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements
Instructional Achievement Level Descriptors
Students Students know Students understand thatare able to
EE3MD1 Tell time to the hour on a digital
Level IV Students willEE3MD1 Tell time to the half hour using a digital clock
Version 3 2015-2016 40
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Tell and write time to the nearest minute using analog and digital clocks
Use strategies (eg watch the movement of a second or minute hand count the changing of digits) to estimate and measure time intervals in minutes
Solve word problems involving addition and subtraction of time intervals using representations of time passage such as arrows on open number lines
Conventions for time notation
Time sequence patterns
Strategies for determining elapsed time (eg using number lines)
Accurately read and write time to the nearest minute from analog and digital clocks
Measure time intervals in minutes
Strategically select and apply methods for showing elapsed time to solve word problems
Analog and digital clocks represent the time at any particular moment
Clocks show the passage of time with the movement of the hands or the changing of digits
Representations for use in solving problems are selected based on the context and numbers in the problem
clock Ex Look at a digital clock and read the timeEx When looking at a schedule identify the hour
Level III Students willEE3MD1 Tell time to the hour on a digital clockEx Given a time written to the hour write the digital timeEx Identify the time of a digital clock that is set to the hourEx Given a time on a digital clock say the time to the hour
Level II Students willEE3MD1 Identify which is the hour on a digital clockEx Relate the hour with the time on their daily scheduleEx Given cards showing digital clocks - with one clock having the hour circled and one clock with the minutes circled indicate the clock with the hour circled
Level I Students willEE3MD1 Differentiate a digital clock from other measurement tools as a tool for telling timeEx Given a digital clock and a measuring cup identify the clock for telling timeEx Asked ldquoHow do we know when it is time to go to lunchrdquo indicate a clock
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 41
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Grade Level 3rdStandard with code 3MD2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)6 Add subtract multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units eg by using drawings (such as a beaker with a measurement scale) to represent the problem7Domain Measurement and Data Cluster Solve problems involving measurement and estimation of intervals of time liquid volumes and masses of objects
Quarter 1 Quarter 2 Quarter 3Explain how to measure liquid volume in liters
Explain how to measure mass in grams and kilograms
Add subtract multiply and divide units of liters grams and kilograms
Know various strategies to represent a word problem involving liquid volume or mass
Solve one step word problems involving masses given in the same units
Solve one step word problems involving liquid volume given in the same units
Measure liquid volumes using standard units of liters
Measure mass of objects using standard units of grams (g) and kilograms (kg)
Quarter 4
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 42
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Students
Accurately measure the liquid volume and mass of objects by selecting and using appropriate tools such as balance and spring scales graduated cylinders beakers and measuring cups to determine measures to the nearest whole unit
Given a variety of one-step word problems involving same unit volume or mass measurements
Explain and justify solutions using a variety of representations
Liquid volume
Mass
Students know
Personal benchmarks for metric standard units of mass (gram amp kilogram) and liquid volume (liter) measure and the use of related tools for measurement to those units
Characteristics of addition subtraction multiplication and division contexts that involve measurements
Students understand thatare able to
Measure liquid volume and mass in metric standard units
Choose appropriate measurement tools and units of measure
Represent quantities and operations physically pictorially or symbolically
Strategically use a variety of representations to solve one-step word problems that involve measurement
The liquid volume of the object is expressed as the number of unit volumes needed to fill the same space
The mass of an object is expressed as the number of standard units needed to balance the object
Mathematical problems can be solved using a variety of strategies models and representations
EE3MD2 Identify standard units of measure for mass and liquid
Level IV Students willEE3MD2 Measure liquid volumes and masses of objects using standard units of grams (g) kilograms (kg) and liters (l)Ex Measure out items in a recipeEx Compare the mass of two items using a two-pan balance (balance scale)Ex Given a standard unit scale weigh 10 grams of sand
Level III Students willEE3MD2 Identify standard units of measure for mass and liquidEx Sort the following real-world items as being measured by grams or liters when shown the measurement tools (apple measured in grams and juice in liters)Ex When shown pictures of the tool identify what would be measured grams or liters
Level II Students willEE3MD2 Select the appropriate tool to measure a solid or a liquidEx When provided two pictures one showing a ruler and one showing a scale identify which tool measures massEx When provided two tools a measuring cup and a scale identify which tool measures liquidEx Select from a variety of tools the appropriate tool to measure either mass or volumeEx Given a rock and a glass of water identify which would be measured using a measuring cup
Level I Students willEE3MD2 Determine if an object is a solid and a liquidEx Place objects from the room into the appropriate measurement category (solid or liquid)Ex Given a rock and a glass of water identify which is solid
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 43
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Grade Level 3rdStandard with code 3MD3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories Solve one- and two-step ldquohow many morerdquo and ldquohow many lessrdquo problems using information presented in scaled bar graphs For example draw a bar graph in which each square in the bar graph might represent 5 petsDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Explain the scale of a graph with a scale greater than one
Identify the scale of a graph with a scale greater than one
Analyze a graph with a scale greater than one
Choose a proper scale for a bar graph or picture graph
Interpret a barpicture graph to solve one or two step problems asking ldquohow many morerdquo and ldquohow many lessrdquo
Create a scaled picture graph to show data
Create a scaled bar graph to show dataMake sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 44
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Students
Organize and represent data with several categories using picture graphs (pictographs) and bar graphs with scales other than 1
Reason quantitatively to answer one- and two-step how many more and how many less problems using information presented in the scaled pictographs and bar graph
Scaled pictograph
Scaled bar graph
Students know
Strategies for collecting organizing and recording data (including scaled pictographs and scaled bar graphs)
Strategies for counting and comparing quantities
Strategies for solving addition and subtraction one and two-step problems
Students understand thatare able to
Choose and apply appropriate strategies for organizing and recording data
Read and interpret graphical representations (pictographs and bar graphs with scales other than 1) of data
Communicate and defend solutions and solutions paths
Questions concerning mathematical contexts can be answered by collecting and organizing data scaled pictographs and bar graphs
Understand that logical reasoning and connections between representations provide justifications for solutions
EE3MD3 Use picture or bar graph data to answer questions about data
Level IV Students willEE3MD3 Interpret data to answer questionsEx Identify how they know there were no rainy days that week based on the chartEx State two facts about the data on a graph
Level III Students willEE3MD3 Use picture or bar graph data to answer questions about dataEx Identify from a picture or bar graph how many students in the class were identified as wearing blue shirtsEx State how many days were sunny as charted on a weather chart
Level II Students willEE3MD3 Organize dataEx Take data collected from the lunch choices and place data into appropriate categoriesEx Place data on a chart to represent the data collected
Level I Students willEE3MD3 Collect dataEx Using two posters one for the students with brown hair and one for the students with ldquoyellowrdquo hair place their picture on the poster board that indicates what color hair they haveEx Use a daily survey to collect data on different interest
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 45
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Grade Level 3rdStandard with code 3MD4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch Show the data by making a line plot where the horizontal scale is marked off in appropriate unitsmdash whole numbers halves or quartersDomain Measurement and Data Cluster Represent and interpret data
Quarter 1 Quarter 2 Quarter 3 Quarter 4Define horizontal axis
Identify each plot on the line as data or a number of objects
Analyze data from a line plot
Determine appropriate unit of measurement
Determine appropriate scale for line plot
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch
Create a line plot where the horizontal scale is marked off in appropriate units- whole numbers halves or quarters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students Line plots Students know Students understand thatare EE3MD4 Measure Level IV Students will
Version 3 2015-2016 46
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Make and use line plots (scale to match unit of measure) to represent data generated by measuring lengths (to the nearest inch half inch or quarter inch) of several objects (eg measure the length of all class members fingers) or by making repeated measurements (eg measuring how far a marble rolls under certain conditions)
Communicate questions and descriptions related to the data display
Line plots
Standard units
Related tools for measuring length
able to
Use standard units and the related tools to measure length to the nearest quarter inch
Organize and represent length measurement data on a line plot
Form conjectures based on the display of the data
Questions concerning mathematical contexts can be answered by collecting organizing and analyzing data and data displays
length of objects using standard tools such as rulers yardsticks and meter sticks
EE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticks by repeating the use of the measurement toolunitEx Given a row of three tile squares on the floor measure the length of the tiles by repeating a ruler end to endEx Given a hallway from the classroom to the bathroom across the hall measure the distance with a yardstick by repeating the yardstick from end to endEx Give one ruler length of yarn to each classmate for a project
Level III Students willEE3MD4 Measure length of objects using standard tools such as rulers yardsticks and meter sticksEx Given an object and a measuring tool use the tool to mark the length of the objectEx Given a ruler and snowfall mark the depth of the snow with a rulerEx Given a yardstick measure different lengths or widths of the room and record the measurement
Level II Students willEE3MD4 Measure length with non-standard units of measurementEx Identify the length of items in the classroom using a yardstick end-to-end and record as number of yardsticksEx When provided two non-standard measuring units identify which one is most appropriate for what is to be measured (pencil or long stick to measure the length of the classroom)
Level I Students willEE3MD4 Place a standard measuring tool where one would begin to measure the length of an objectEx Given a string place the ruler at the end of the string where one would begin a measureEx Shown a picture of a boy standing against a height measure and asked where you would look to find the boyrsquos height indicate the top of the boyrsquos headEx Given a bookshelf and a ruler place the ruler on the lower left corner of the bookshelf front (Anything with a definite lower left edge that will not allow the student to go beyond it will work)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 47
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Grade Level 3rdStandard with code 3MD5 Recognize area as an attribute of plane figures and understand concepts of area measurementa A square with side length 1 unit called ldquoa unit squarerdquo is said to have ldquoone square unitrdquo of area and can be used to measure areab A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square unitsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to additionQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define ldquounit squarerdquo
Define area
Relate the number (n) of unit squares to the area of a plane figure
Cover the area of a plane figure with unit squares without gaps or overlaps
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
Version 3 2015-2016 48
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Students
Explain the result of measuring the area of a plane figure as a number of unit squares needed to cover the object without gaps or overlaps
Area
Plane figure
Unit square
Students know
Measureable attributes of objects specifically area
Units of measure for area (unit squares)
Students understand thatare able to
Measure area using manipulative square units to cover a plane figure
Explain and justify procedures for determining the area of a plane figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 49
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Grade Level 3rdStandard with code 3MD6 Measure areas by counting unit squares (square cm square m square in square ft and improvised units)Domain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Measure areas by counting unit squares
Use unit squares of cm m in ft and other sizes of unit squares to measure area
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
Students Given a variety Students know Students understand EE3MD5-7 NA (Area EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 50
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
of plane figures
Accurately measure area by counting standard (square centimeter square meter square inch and square foot) and non-standard unit squares (eg orange pattern blocks floor tiles etc)
Measurable attributes of objects specifically area
Strategies for measuring area
thatare able to
Accurately measure area using standard and non-standard square units (to the nearest whole unit)
The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure
begins at grade 6)
CCSS Math Pacing GuideGrade 3
Version 3 2015-2016 51
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Grade Level 3rdStandard with code 3MD7a Relate area to the operations of multiplication and additiona Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengthsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Find the area of a rectangle by tiling it in unit squares
Find the side lengths of a rectangle in units
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core Essential
Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 52
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3Grade Level 3rd
Version 3 2015-2016 53
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Standard with code 3MD7b Relate area to the operations of multiplication and additionb Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply side lengths to find areas of rectangles
Solve real world and mathematical area problems by multiplying side lengths of rectangles
Use rectangular arrays to represent whole-number products in multiplication problems
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment
Vocabulary Knowledge Skills Common Core Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 54
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 55
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7c Relate area to the operations of multiplication and additionc Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a times b and a times c Use area models to represent the distributive property in mathematical reasoningDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Multiply using an area model (array)
Relate area of a rectangle to multiplication and addition by modeling the distributive property
Version 3 2015-2016 56
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Area of a Rectangle 3 x (5+2) = 3x5 + 3x2
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 57
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD7 Relate area to the operations of multiplication and additiond Recognize area as additive Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts applying this technique to solve real world problemsDomain Measurement and Data Cluster Geometric measurement understand concepts of area and relate area to multiplication and to addition
Quarter 1 Quarter 2 Quarter 3 Quarter 4Find areas of rectangles
Add areas of rectangles
Recognize that areas of each rectangle in a
Version 3 2015-2016 58
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
rectilinear (straight line) figure can be added together to find the area of the figure
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems
Decompose rectilinear figures into non-overlapping rectangles
For example this shape decomposes into
these two rectangles
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven a polygon that may be decomposed into 2 or more rectangles
Find the total area by decomposing the figure into non-overlapping rectangles finding the area of each and find the sum of the areas
Distributive Property
Rectilinear figures
Students know
Relationships between rectangular arrays and the corresponding multiplication problems (counting unit squares in rows and columns compared to multiplying length by width)
Strategies for finding sums and products of whole numbers
Students understand thatare able to
Communicate the relationships between rectangular array models of areas and multiplication and addition problems including modeling the Distributive Property
Model the area of
EE3MD5-7 NA (Area begins at grade 6)
EE3MD5-7 NA (Area begins at grade 6)
Version 3 2015-2016 59
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Given a rectangle with whole number length sides
Find and justify the area of the rectangle by relating a tile covered model to a corresponding multiplication problem (counting unit squares in rows and columns compared to multiplying length by width)
Using array cards or tiles
Create and explain rectangular models to show that the area of a rectangle with whole-number side lengths a and d (where d=b+c) is the same as the area of two smaller rectangles with area a x b and a x c (the Distributive Property)
rectangles using manipulatives or graph paper
Strategically and fluently choose strategies for finding sums and products
Accurately compute sums and products
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
Multiplication is putting together equal sized groups
Rectangular arrays represent groups (rows) of equal size (number of columns)
Multiplication is distributive over the addition of whole numbers
Version 3 2015-2016 60
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3MD8 Solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimetersDomain Measurement and Data Cluster Geometric measurement recognize perimeter as an attribute of plane figures and distinguish between linear and area
measuresQuarter 1 Quarter 2 Quarter 3 Quarter 4
Define a polygon
Define perimeter
Find the perimeter when given the length of sides
Version 3 2015-2016 61
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Find the perimeter when there is an unknown side length
Exhibit (design create draw model etc) rectangles with the same perimeter and different areas
Exhibit rectangles with the same area and different perimeters
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Find and justify solutions to real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths finding an unknown side length and exhibiting rectangles with the
Perimeter
Area
Polygons
Students know
Measureable attributes of objects specifically perimeter and area
Strategies for modeling measurement problems involving perimeter and area
Strategies for representing and computing perimeter and area
Students understand thatare able to
Strategically use a variety of models and representations to solve measurement problems involving area and perimeter
Accurately compute using whole numbers
Use logical reasoning to justify solutions and
EE3MD8 NA (Perimeter begins at grade 7)
EE3MD8 NA (Perimeter begins at grade 7)
Version 3 2015-2016 62
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
same perimeter and different areas or with the same area and different perimeters
solution paths by connecting models to equations and computations
Perimeter is measured in length units and is the distance around a 2-D figure
The area of a plane figure is measured by the number of same-size squares that exactly cover the interior space of the figure
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G1 Understand that shapes in different categories (eg rhombuses rectangles and others) may share attributes (eg having four sides) and that the shared attributes can define a larger category (eg quadrilaterals) Recognize rhombuses rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4Identify and define rhombuses rectangles and squares as examples of quadrilaterals based on their attributes
Describe analyze and compare
Version 3 2015-2016 63
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
properties of two-dimensional shapes
Compare and classify shapes by attributes sides and angles
Group shapes with shared attributes to define a larger category (eg quadrilaterals)
Draw examples of quadrilaterals that do and do not belong to any of the subcategories
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
Students
Justify their identificationsorting of shapes (triangles quadrilaterals pentagons hexagons squares rectangles rhombuses) by referring to their shared attributes
Draw corresponding
Rhombus
Rectangle
Square
Quadrilateral
Students know
Names for 2-D shapes (eg triangle quadrilateral pentagon hexagon square rectangle rhombus)
Defining attributes for 2-D shapes (eg right angles equal length sides parallel sides straight sides closed figure)
Students understand thatare able to
Identify attributes of 2-D shapes (eg number of sides equal sides right angles parallel sides)
Classify 2-D shapes based on their attributes
Draw shapes based on
EE3G1 Recognize that shapes in different categories can share attributes
Level IV Students willEE3G1 Identify the shared attributes of shapes in different categoriesEx Given a Venn diagram sort attributes of shapes (ie straight edges curved edges both)Ex Trace the shared attributes of two different shapes
Level III Students willEE3G1 Recognize that shapes in different categories can share attributesEx Shown different shapes answers ldquoWhat is the samerdquoEx Place in the appropriate category shapes with common attributes
Level II Students willEE3G1 Sort shapes by attributesEx Given a sorting map sort shapes by given attributes
Version 3 2015-2016 64
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
shapes when given a list of attributes
specified attributes
Shapes may be assigned to different categories of shapes based on different selections of shared attributes and that the shared attributes can define a larger category
Ex Given a sorting map sort different size same shapes into the same category (eg large and small triangle would go in the same category)
Level I Students willEE3G1 Match shapes (eg squares rectangles circles triangles)Ex Match shapes to the shape of objects within the classroomEx Match shapes that are the same
CCSS Math Pacing GuideGrade 3
Grade Level 3rdStandard with code 3G2 Partition shapes into parts with equal areas Express the area of each part as a unit fraction of the whole For example partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shapeDomain Geometry Cluster Reason with shapes and their attributes
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Know that shapes can be partitioned into equal areas
Version 3 2015-2016 65
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
Describe the area of each part as a fractional part of the whole
Relate fractions to geometry by expressing the area of part of a shape as a unit fraction of the whole (See 3rd grade introduction)
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Evidence of Student Attainment Vocabulary Knowledge Skills Common Core
Essential Elements Instructional Achievement Level Descriptors
StudentsGiven squares rectangles or circles
Cut or draw lines to divide the shapes into equal shares and justify their divisions by reasoning about
Area
Partition
Students know
Strategies for decomposing shapes into equal shares
Fraction vocabulary halves thirds fourths quarters fifths eighths and tenths
Students understand thatare able to
Decompose circles squares and rectangles into equal shares
Communicate the size of shares using the appropriate
EE3G2 Recognize that shapes can be partitioned into equal areas
Level IV Students willEE3G2 Given shapes with multiple lines of symmetry will be able to identify equal areasEx Complete simple tangram puzzles with tangram piecesEx Identify equal areas on complex shapes (ie stars rectangle cut on the diagonal)
Level III Students willEE3G2 Recognize that shapes can be partitioned into equal areasEx Given a shape cut the shape into equal areasEx Cut a pizza into equal areas to hand out to students in the class
Version 3 2015-2016 66
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67
equal area
Express the area of each part as a unit fraction of the whole (eg partition a shape into 4 parts with equal area and describe the area of each part as 14 of the area of the shape)
fraction terminology
Justify equal area of congruent and non-congruent shares as equal shares of the same size whole
The same fractional parts of same- size 2-D shapes have equal area but do not have to be congruent (eg When two same-size rectangles are cut in half vertically horizontally or diagonally the pieces are all one half of the original rectangle have equal area but are not all congruent)
Level II Students willEE3G2 Create shapesEx Work a pattern block puzzle that results in a shapeEx Given three small rectangles rearrange them into a larger rectangle
Level I Students willEE3G2 Match shapesEx Match a picture of a shape to a shape in the classroomEx Match two shapes from an array of three in which one is differentRefer to the Common Core Essential Elements document for diagram
Version 3 2015-2016 67