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for our FUTURE
Third Grade Math Pacing Guide
2014-2015
Accessing Resources
Investigations Worksheet PDFs Instruction Portal 1) Go to Pearsonsuccessnet.com 1) Go to albany.k12.or.us
2) Enter your username and password. 2) Click on Departments and Services on the left menu
If it is your first time logging in: Scroll down on the log-in screen 3) Click on Curriculum and Instruction on the top menu
and click on Register. See separate handout or ask a math 4) Click on Instruction Portal
leader/administrator if you need assistance with registering and 5) Username: gapsteacher Password: To get the password, talk to
adding your materials the first time. your building’s math leader. 3) Click on the student edition/student activity workbook.
4) Print the worksheets you need
Investigations Common Core additional lessons There are additional lessons and additional teaching notes to better
satisfy all common core state standards. These lessons, teaching
notes, and worksheets are in the book our district purchased last
year titled Investigations and the Common Core State Standards.
Smarter Balanced Sample Summative Items for Teachers http://www.ode.state.or.us/search/page/?id=3747
Balanced Math – The pacing guide represents the minimum set of
skills needed for students to meet the assessment required to receive a
diploma. Therefore, it is important to stay as close to the timing in the
pacing guide as possible. If you get to the end of a unit’s allotted time
and your students have not mastered all of the skills yet, those skills
become a part of the Review section of your lesson and the Conceptual
Lesson section moves with the pacing guide. This enables your
students to reach mastery without slowing the pace of instruction.
Balanced Math Instruction Distribution
Example:
60 minute lesson
15 minutes Review Review 5 minutes Mental Math 25-30% 40 minutes Conceptual
Conceptual Lesson
Lesson
65-70%
Mental Math
5-7%
Acquiring and Maintaining Skills – Throughout the year,
students need to review their addition and subtraction skills to maintain
fluency with their facts. Students are acquiring their multiplication
skills and need to be working on this throughout the year.
Kim Sutton
Use the Kim Sutton 10-block for addition and subtraction as appropriate
for your students.
Use the Kim Sutton 10-block pg. 22-40 starting at the beginning of the
year to build multiplication skills.
Each building has a 10-block binder.
Number Corner
Computational Fluency
Aug. through Jan. reviews addition and subtraction facts.
February through June has multiplication and division activities.
Grade 3 Math 2013-2014 Page 2 Created: July 2013
3rd
Grade Key Concepts and Corresponding Activities
Key Concept Activity Multiplication and Division
Students need to relate multiplication to addition seeing one
meaning of multiplication as repeated addition.
Students need to understand that multiplication is finding an
unknown product using equal groups, arrays, a number line and area
models.
Students need to relate multiplication to division knowing that
division problems are finding an unknown factor.
Factor Pairs and Missing Factor Game
Introduced in Unit 5 Investigation 3.4 (pg. 98)
Continued in Unit 5: 3.6, 4.4, 4.5, 4.6
Fractions
Students work with unit fractions to build other fractions and
increase their understanding that a fraction is a part of a whole that
has been divided into equal groups.
Students combine fractions using visual models.
The Fraction Cookie Game*
Introduced in Unit 7 Investigation 2.2 (pg. 69-71)
Continued in Unit 7: 2.3, 2.4 (extension for advanced student on pg. 86)
*Similar to Kim Sutton’s “Build to One Whole”, and “Strive for Five” in Fractions: a part of the whole book.
Linear and Area Measurement
Students identify area as a measurement of space (covering) and
differentiate this from perimeter with is a measurement of length
(around). They break rectangular areas into rows and columns and
relate multiplication to area.
Real estate game
Kim Sutton Activity+
Introduce in Unit 4 Investigation 2
Continue to use throughout Unit 4
+Directions on Page 23
Bold lessons indicate a discussion or new level of rigor introduced
The above concepts are the key ideas for third grade that students will build on for the years to come. The students need to be familiar with the three
activities so, next year, the fourth grade teachers can use these activities before they start instruction that builds on these concepts. This will allow
fourth grade teachers to hear from the students what they remember from third grade. It will also remind the students what they learned so they can
connect the new learning to what they already know.
Grade 3 Math 2013-2014 Page 3 Created: July 2013
Unit 1: Addition, Subtraction, and the Number System
“Trading Stickers, Combining Coins”
nd thTime: 3.5 weeks September 2 to September 24
Standards to Mastery
None for this unit Standards for which this unit builds foundational skills
3.NBT.2
3.OA.8
Mathematical Practice Standards to Emphasize
Big Ideas
Addition means putting together.
Subtraction means taking away (removal), finding a missing part
(missing addend), and/or the difference between (comparing).
The position of a digit in a number determines its value (place value).
Essential Questions
How do you know when to add or subtract in a problem?
How does the location of a digit affect its value?
Concepts Skills
10 ones is equal to 1 group of 10 Create/find groups of 10
10 groups of ten is equal to 1 group of 100 Subtract using the number line
A digit in the ones place represents that many ones Subtract by adding on
A digit in the tens place represents that many groups of ten Add by place value
A digit in the hundreds place represents that many groups of one Add by breaking one addend into parts
hundred Find sums to 100
Add like values, like groups Identify strategies (near doubles, close to 10, etc) to build fluency with
One-to-one correspondence addition facts (using single digits)
Subtraction is equivalent to an addition problem with a missing addend Add coins to $1.00
There are multiple expressions that give the same sum Relate coin (pictures) to value
Order does not matter when adding Subtract from 100
A number can be broken into smaller parts (decomposing) for example: Solve multiple addend problems
26 = 10 + 10 + 6
26 = 20 + 6
Grade 3 Math 2013-2014 Page 4 Created: July 2013
Resources Standards Expectation by
end of Unit
Vocabulary
Bold are student words
Investigations:
Unit 1 Trading Stickers,
Combining Coins
Session 2.1 can be skipped or
used as intervention
Kim Sutton: Drills to Thrill
Before and After 32-41
Place Value with Pizzaz
Rounding Mountain 27
Place Value Pocket 16-29
Snap Follow Up 50-53
Place Value Clues 112-244
3.NBT.2. Fluently add and subtract within 1000 using
strategies and algorithms based on place value, properties of
operations, and/or the relationship between addition and
subtraction.
Addition and
subtraction to 200
Sum
Addend
Add
Difference
Subtrahend
Minuend
Subtract
Estimate
Round
Digit
Commutative Property of
Addition
Associative Property of
Addition
Identity Property of Addition
Place Value
3.OA.8. 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 rounding. (This standard is
limited to problems posed with whole numbers and having
whole-number answers; students should know how to
perform operations in the conventional order when there are
no parentheses to specify a particular order (Order of
Addition and
subtraction only
Operations). Fact Families
Order of Operations
Expanded Form
Standard Form
Word Form
Pattern
Expression
Equation
Equal
Evaluate
Variable
Altogether
Combine
Total
Inverse
Increase
Decrease
Numeral
Grade 3 Math 2013-2014 Page 5 Created: July 2013
Unit 2: Measurement and Data “Surveys and Line Plots” th thTime: 3.5 weeks September 25 to October 17
Standards to Mastery
3.MD.3
3.MD.4
Standards for which this unit builds foundational skills
None for this unit
Mathematical Practice Standards to Emphasize
Big Ideas
Graphs represent data and can be used to compare data.
Different types of graphs highlight different aspects of a data set.
Essential Questions
What kind of information can be shared in a graph?
Which type of graph would best represent a specific data set?
Concepts
Different data arrangements allow different questions
Graphs can have different scales/keys
Graphs can be used to compare data
The numbers on a line plot represent labels and the X’s are the data A symbol on a pictograph can represent a group of items
A ruler measures length
Skills
Classify data into categories
Pose questions from data
Answer questions posed from data
Create/revise survey questions
Create a pictograph, bar graph, and line graph
Interpret/describe data from a graph
Read and understand the scale/key
Use data to compare while using purposeful phrases
Use a key on a pictograph to interpret the symbols
Use a ruler to measure to the nearest ¼ inch
Grade 3 Math 2013-2014 Page 6 Created: July 2013
Resources Standards Expectation by
end of Unit
Vocabulary
Investigations:
Unit 2 Surveys and Line Plots
add 2.3A lesson pg. CC5-CC9*
2.3 – 2.7 (optional) can be used
as enrichment activity
Additional Resources are
Necessary for more
opportunities to draw bar graphs
and to measure data to the inch,
half inch, and quarter inch.
Number Corner:
Data Collector
December – read and
interpreting graphs
February – interpreting and
comparing charts and graphs
3.MD.3. Draw a scaled picture graph and a scaled bar graph
to represent a data set with several categories. Solve one-
and two-step “how many more” and “how many less”
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.
Mastery Bar Graph
Line Plot
Pictograph/Picture Graph
Key/Legend
Scale
Data
Whole number
Half/Halves
Fourths
Horizontal
Vertical
Customary system
Inch
Foot (Feet)
Yard
Mile
Vocabulary note for teachers:
Standard units of measure
include units within both
customary and metric
systems, non-standard unit
examples include books,
paperclips, etc.
To minimize confusion in
later years and in science, the
Standard System (SI) are the
unit accepted internationally
and used in formulas such as
physics F=ma these units are
metric.
3.MD.4. 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 units— whole numbers,
halves, or quarters.
Mastery
*Additional lessons are in the Investigations and the Common Core State Standards supplement referenced on pg. 2
Grade 3 Math 2013-2014 Page 7 Created: July 2013
Unit 3: Addition, Subtraction, and the Number System
“Collections and Travel Stories”
thTime: 4.5 weeks October 20 to November 21
st
Standards to Mastery
3.NBT.1 Standards for which this unit builds foundational skills
3.NBT.2
3.OA.8
3.OA.9
3.MD.1
Mathematical Practice Standards to Emphasize
Big Ideas
Estimation is a way to show the reasonableness of an answer.
Addition means putting together. Subtraction means taking away
(removal), finding a missing part (missing addend), and/or the
difference between (comparing).
Working with elapsed time is regrouping minutes at 60 instead of 100.
Essential Questions
How do I know if my answer is reasonable?
How do I know when to add and when to subtract in a problem?
How is elapsed time related to addition and subtraction?
Concepts Skills
Ten groups of 100 is equal to 1 group of 1000 Read, write and sequence numbers to 1000
There are different uses for estimates and exact answers Use place value to determine what two multiples of 10 or 100 an
A digit in the ones place represents that many ones number is between
A digit in the tens place represents that many groups of ten Use landmark numbers to locate other numbers on a number line,
A digit in the hundreds place represents that many groups of one hundreds grid, and thousands chart
hundred Estimate the sums of 2 and 3 digit numbers
Subtraction is equivalent to an addition problem with a missing addend Find pairs of numbers that add to 100
Estimation tells about how large an answer will be Tell how many tens are in a 3-digit number
There are 60 minutes in 1 hour Find the difference between two 3-digit numbers using subtraction on a
The meaning of the numbers and the hands on an analog clock number line and/or a 1000 chart.
Rounding is a way to estimate Round to the nearest 10 or 100
Grade 3 Math 2013-2014 Page 8 Created: July 2013
Resources Standards Expectation by
end of Unit
Vocabulary
Investigations:
Unit 3 Collections and Travel
Stories
add 1.7A lesson pg CC14-CC18
definitely include ten-minute
math from Investigations 3 + 4
to hit time standard 3.MD.1
Kim Sutton: Dynamic Dice
Let’s Standardize pg. 126-129
Number Corner:
Calendar Grid
January–Analog+Dig.Clocks
Clocks, Coins + Bills:
October- An Hour or Bust
November–What Time is it Now?
What Time Would it be?
3.NBT.1. Use place value understanding to round whole numbers
to the nearest 10 or 100.
Mastery Sum
Addend
Add
Difference
Subtrahend
Minuend
Subtract
Estimate
Round
Digit
Commutative
Associative
Identity Property
Place Value
Fact Families
Order of Operations
Expanded Form
Standard Form
Word Form
Pattern
Expression
Evaluate
Equation
Solve
Equal
a.m. / p.m.
second/minute/hour
Elapsed Time
Intervals
Quarter Hour
Half Hour
Algorithm
Teacher note:
Expressions are evaluated and
equations are solved.
3.NBT.2. Fluently add and subtract within 1000 using strategies
and algorithms based on place value, properties of operations,
and/or the relationship between addition and subtraction.
Add to 1000 and
subtract from 300.
3.OA.9. 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 addends.
Addition only
3.OA.8. 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
rounding. (Note: This standard is limited to problems posed with
whole numbers and having whole-number answers; students
should know how to perform operations in the conventional order
when there are no parentheses to specify a particular order --Order
of Operations).
Add to 1000 and
subtract from 300.
Use estimation to
justify the
reasonableness of
the answer.
3.MD.1. 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, e.g., by representing
the problem on a number line diagram.
To the nearest 5
minutes.
Grade 3 Math 2013-2014 Page 9 Created: July 2013
Unit 4: 2-D Geometry and Measurement
“Perimeter, Angles, and Area”
thTime: 5 weeks December 1
st to January 16
Standards to Mastery Standards for which this unit builds foundational skills
3.MD.5 3.G.1 3.MD.7
3.MD.6
3.MD.8
Mathematical Practice Standards to Emphasize
Big Ideas
Attributes (number of vertices, perimeter, area, etc) are used to describe
objects.
Perimeter is a linear measurement and is useful when surrounding an
object (framing a picture) while area measurements are useful when
covering an object (painting a wall).
Essential Questions
How can objects be described?
How are area and perimeter different and when is each more useful?
Concepts
Different aspects of a shape can be measured (length, width, perimeter,
area, etc)
Perimeter is the measure around the outside edges of a 2-dimensional
figure
Perimeter is a measurement of length (inches, meters, etc)
Different shapes can have the same perimeter
Area is a measurement of space (square inches, square meters, etc)
Area is additive
Triangles have three sides, three vertices, and three angles
Quadrilaterals have four sides, four vertices, and four angles
The attributes of a shape determine its name
Skills
Measure accurately with standard and metric units
Estimate measurements
Find the perimeter of a figure by measuring the side lengths
Find an unknown side length of a figure when given the other side
lengths and the perimeter.
Draw and label a straight line that represent the perimeter of a figure
Identify congruent figures
Measure area by tiling leaving no gaps or overlaps
Identify different shapes with the same area
Estimate the area and perimeter of irregular figures
Create rectangles with the same area and different perimeters
Create rectangles with the same perimeter and different areas
Identify right angles
Classify angles as less than, greater than, or equal to a right angle
Choose appropriate units to measure
Grade 3 Math 2013-2014 Page 10 Created: July 2013
Resources Standards Expectation by
end of Unit
Vocabulary
Investigations:
Unit 4 Perimeter, Angles, and Area
add 2.5A lesson pg. CC23-CC27
When doing Practicing Place
Value 10-minute math, also have
students write the number in
expanded form and round to the
nearest 10 and 100
Kim Sutton:
3.MD.5. Recognize area as an attribute of plane figures and
understand concepts of area measurement.
a. A square with side length 1 unit, called “a unit square,”
is said to have “one square unit” of area, and can be used
to measure area.
b. 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.
Mastery Measure
Unit
Perimeter
Area
Square Unit
Attribute
Compose
Decompose
Overlapping
Non-
overlapping
Triangle
Square
Rectangle
Rhombus
(Rhombi)
Trapezoid
Parallelogram
Quadrilateral
Pentagon
Hexagon
Octagon
3.MD.6. Measure areas by counting unit squares (square cm,
square m, square in, square ft, and improvised units).
Mastery
3.MD.8. Solve real world and mathematical problems Mastery Dynamic Dice involving perimeters of polygons, including finding the Tiling Polygon
Rolling Polygons 116-117 perimeter given the side lengths, finding an unknown side Plane Figure Perimeter
length, and exhibiting rectangles with the same perimeter and Rectilinear- Sides
Number Corner:
Calendar Grid
November – 2D geometry
different areas or with the same area and different perimeters. Figure
Triangular
Rectangular
Customary
System
Inch
Foot (Feet)
Yard
Mile
Metric System
Centimeter
Meter
Kilometer
Vertex/Vertices
Angles
Acute
Obtuse
Right
Scalene
Isosceles
Equilateral
Equiangular
Parallel Lines
Perpendicular
Congruent
Compare
Line
Line Segment
Ray
2-Dimensional
Symmetry
Side Length
Dimensions
Closed Figure
3.G.1. Understand that shapes in different categories (e.g.,
rhombuses, rectangles, and others) may share attributes (e.g.,
having four sides), and that the shared attributes can define a
larger category (e.g., quadrilaterals). Recognize rhombuses,
rectangles, and squares as examples of quadrilaterals, and
draw examples of quadrilaterals that do not belong to any of
these subcategories.
Mastery
3.MD.7. 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.
d. 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.
Parts b and c will
be addressed in
later units.
Grade 3 Math 2013-2014 Page 11 Created: July 2013
Unit 5: Multiplication and Division “Equal Groups” th thTime: 6.5 weeks January 20 to March 6
Standards to Mastery Standards for which this unit builds foundational skills
3.OA.1 3.OA.5 3.OA.7
3.OA.2 3.OA.6 3.OA.8
3.OA.3 3.NBT.3 3.OA.9
3.OA.4 3.MD.7 3.MD.1
Mathematical Practice Standards to Emphasize
Big Ideas
Multiplication finds the total number of objects when there is an equal
number of objects in each group.
Multiplication is repeated addition.
Division breaks things into equal groups.
Multiplication and division are inverse operations. Division situations
can be written as unknown-factor problems.
Essential Questions
How can we represent situations with equal groups?
How is multiplication related to addition?
How can we represent situations where we are sharing equally?
How are multiplication and division related?
Concepts Skills
Situations where things come in equal groups can be represented with Skip count accurately
multiplication or division Find products using repeated addition/skip counting
Skip counting, repeated addition, arrays, and multiplication are all ways Use multiplication and division notation
of finding a product Identify multiples of 2, 3, 4, 5, 6, and 10 by skip counting
The number of groups and the number of objects in each group are the Use doubles and halves of known products to find related products
factors and the total number is the product Represent a multiplication problem using arrays, equal groups, and
Multiples of a given number share characteristics (e.g. all multiples of number lines
10 have a 0 in the ones place) Identify prime numbers and square numbers
Multiplication and division are inverse operation Manipulate problems using number flexibility to create a solvable
Division is breaking something into equal groups problem (e.g. think of 9 x 4 as 10 x 4 – 4)
Division can be thought of as a missing factor multiplication problem Multiply by multiples of 10
Grade 3 Math 2013-2014 Page 12 Created: July 2013
Resources Standards Expectation by
end of Unit
Vocabulary
Investigations:
Unit 5 Equal Groups
add 3.1A lesson pg CC32-CC36
add 3.5A lesson pg CC37-CC41
add 3.5B lesson pg CC42-CC46
add 3.7A lesson pg CC47-CC51
Make sure to include
10-minute math from
Investigations 1, 3 and 4 to hit
time standard 3.MD.1
Additional Resources are
Necessary to teach products to
100
Number Corner (time acts.):
Clocks, Coins + Bills:
December–How Long Between?
Kim Sutton:
Dynamic Dice
Rolling Your Facts 60, 65-69
Number Line Workbook
My Multiples Book 87-93
Pattern Sticks 35-36
Drills to Thrill
Multiplication Strategies 116-141
Input/Output 150-152
3.OA.1. Interpret products of whole numbers, e.g., interpret 5 × 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 × 7.
Mastery Multiply
Divide
Divisor
Dividend
Quotient
Number Patterns
Equal Groups
Factors
Multiples
Product
Array
Area Model
Measure
Intervals
Number Line
Interpret
Partition
Distributive Property
Parenthesis
Commutative Property
of Multiplication
Associative Property
of Multiplication
Zero Property of
Multiplication
Expression
Evaluate
Equation
Solve
Rounding
Repeated Addition
Repeated
Subtraction
Hundreds Grid
More Vocabulary on
next page
3.OA.2. Interpret whole-number quotients of whole numbers, e.g.,
interpret 56 ÷ 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 ÷ 8.
Mastery
3.OA.3. Use multiplication and division within 100 to solve word
problems in situations involving equal groups, arrays, and measurement
quantities, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem. (See Table 2.)
Mastery
3.OA.4. 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 8 × ? = 48, 5 = ÷ 3, 6 × 6 = ?.
Mastery
3.OA.5. Apply properties of operations as strategies to multiply and
divide. (Students need not use formal terms for these properties.)
Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known.
(Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 ×
5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30.
(Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 ×
2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 =
56. (Distributive property.)
Mastery
3.OA.6. Understand division as an unknown-factor problem. For
example, find 32 ÷ 8 by finding the number that makes 32 when multiplied
by 8.
Mastery
3.NBT.3. Multiply one-digit whole numbers by multiples of 10 in the
range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value
and properties of operations.
More standards for this unit on next page
Mastery
Grade 3 Math 2013-2014 Page 13 Created: July 2013
3.MD.7. 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.
b. 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.
c. 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 × b and a × c.
Use area models to represent the distributive property in mathematical
reasoning.
d. 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.
Mastery Tiling
Additive
Quantity
Decompose
Compose
Rectilinear
Rectangle
Second/Minute/Hour
Elapsed Time
3.OA.7. Fluently multiply and divide within 100, using strategies such as
the relationship between multiplication and division (e.g., knowing that 8
× 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of
Grade 3, know from memory all products of two one-digit numbers.
Students are
building conceptual
understanding and
number fluency.
Working toward
mastery by unit 8
3.OA.8. 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 rounding. (Note: This
standard is limited to problems posed with whole numbers and having
whole-number answers; students should know how to perform operations
in the conventional order when there are no parentheses to specify a
particular order --Order of Operations).
Continue to build
skills working
towards mastery in
unit 8
3.OA.9. 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
addends.
Identify patterns
with multiples on
100 grid
3.MD.1. 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, e.g., by representing the problem
on a number line diagram.
To the nearest
minute
Grade 3 Math 2013-2014 Page 14 Created: July 2013
Unit 7: Fractions and Decimals “Finding Fair Shares” th thTime: 5.5 weeks March 9 to April 24
Standards to Mastery Standards for which this unit builds foundational skills
3.NF.1 3.G.2 None for this unit
3.NF.2 3.MD.1
3.NF.3
Mathematical Practice Standards to Emphasize
Big Ideas
Fractions represent part of a whole.
Fractions are composed of one (unit fraction) or more equal parts which
the whole is divided into. The numerator tells us how many parts we
have and the denominator tells us how many equal parts make one
whole.
Equivalent fractions of the same whole have the same area, and they are
located at the same place on the number line.
Essential Questions
How do we represent amounts that are less than one whole?
What does the numerator and denominator tell us about a fraction?
How do we know if two fractions are equivalent?
Concepts Skills
When breaking a whole into fractional pieces, each piece must be the Name equal parts of one whole with a fraction
same size Divide an area into equal parts
A unit fraction is one equal part of a whole Order unit fractions from largest to smallest
The denominator of a fraction tells how many equal pieces the whole is Create area models for fractions
divided into Create set models for fractions
Larger denominators mean the whole is divided into more pieces Represent fractions on a number line
making each piece smaller Compare fractions using number lines and area models
The numerator of a fraction tells how many equal pieces you have Use inequality notation (<, >) with fractions
If the numerator (number of pieces you have) is equal to the Write equivalent fractions
denominator (number of pieces the whole is broken into) then you have Find fractions that sum to one
one whole Combine fractions using models
Improper fractions represent more than one whole Create a situation to represent a given fraction (use pattern blocks to
Mixed numbers represent some number of wholes and some number of make a design that is half yellow)
fractional pieces
Pieces smaller than one whole can be represented with fractions
Fractions and mixed numbers lie between the whole numbers on the
number line
Grade 3 Math 2013-2014 Page 15 Created: July 2013
Resources Standards Expectation by
end of Unit
Vocabulary
Investigations:
Unit 7 Fractions and Decimals
add 1.4A lesson pg CC57-CC61
add 1.4B lesson pg CC62-CC67
When doing Practicing Place
Value 10-minute math, also
have students write the
number in expanded form
and round to the nearest 10
and 100
Skip Investigation 3
Kim Sutton: Fractions: Part of the Whole
Critical Fraction Questions 8
Fraction Chats 126
Chocolate Fractions pg 44
Circle of Children pg 68
Pattern Block Fraction 90
Number Line Fractions 144
Comparing Fractions after pg 199
Number Corner:
Calendar Grid
April – Equivalent Fractions
May+June–Frac., Dec.+$
3.NF.1. Understand a fraction 1/b as the quantity formed by 1 part when a whole
is partitioned into b equal parts; understand a fraction a/b as the quantity formed
by a parts of size 1/b.
Mastery Unit Fraction
Equivalent Fraction
Numerator
Denominator
Fraction
Equal Parts of:
-whole
-set
-point/distance
Halves
Fourths
Sixths
Eigths
Tenths
Number Line
Compare
Order
Greater Than >
Less Than <
Equal to =
Partition
Diagram
End Point
Point
Increase
Decrease
Mixed Number
Improper Fraction
3.NF.2. Understand a fraction as a number on the number line; represent fractions
on a number line diagram.
a. Represent a fraction 1/b 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 1/b and that the endpoint of the part based at 0 locates the
number 1/b on the number line.
b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b
from 0. Recognize that the resulting interval has size a/b and that its endpoint
locates the number a/b on the number line.
Mastery
3.NF.3. Explain equivalence of fractions in special cases, and compare fractions
by reasoning about their size.
a. Understand two fractions as equivalent (equal) if they are the same size, or the
same point on a number line.
b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3).
Explain why the fractions are equivalent, e.g., by using a visual fraction model.
c. Express whole numbers as fractions, and recognize fractions that are
equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1;
recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line
diagram.
d. 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 >, =, or <, and justify the conclusions, e.g., by using a visual
fraction model.
Mastery
3.G.2. 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 1/4 of the area of the shape.
Mastery
3.MD.1. 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, e.g., by representing the problem on a number line diagram.
Mastery
Grade 3 Math 2013-2014 Page 16 Created: July 2013
Unit 6: Patterns, Functions, and Change
“Stories, Tables, and Graphs”
th thTime: 2 weeks April 27 to May 8
Standards to Mastery Standards for which this unit reinforces skills
3.OA.1 3.OA.8
3.OA.3 3.OA.9
3.OA.5
Mathematical Practice Standards to Emphasize
Big Ideas
Patterns or relationships can be represented using sequences, tables,
graphs, and described with words (and in later grades equations).
The constant rate of change is how many are added each unit (day) it
can also be multiplied by the number of units (days) and then added
to the start amount to find the total at any point in the pattern (on any
given day).
Essential Questions
What are different ways to represent patterns or relationships?
Why is the constant rate of change helpful when working with patterns?
Concepts
Sequences that follow a pattern can be extended based on that pattern
The numbers in the same row of a table are related
Tables are good tools to compare different situations
Graphs are good tools to compare the rate of change in different
situations
In a linear relationship, the total number after a given time depends on
both the starting value and the rate of change (magic marbles)
Variables represent quantities that can change
Skills
Identify the unit of a repeating pattern
Extend a pattern
Skip count by the length of the unit in a pattern
Extend a number sequenced with a constant rate of change (2, 5, 8,. . .)
Identify numbers based on how they are related to the multiples of 3
Recognize and identify a constant rate of change
Use tables to record data
Interpret numbers in a table in terms of the situation that table represents
Generalize a situation where there is a constant rate of change by
writing a rule using variables
Use data from a table to graph a situation in the coordinate plane
Grade 3 Math 2013-2014 Page 17 Created: July 2013
Resources Standards Expectation by
end of Unit
Vocabulary
Investigations:
Unit 6 Stories, Tables, and
Graphs
Skip Investigation 1
Sessions 3.4-3.7 optional
(enrichment)
When doing Practicing Place
Value 10-minute math, also
have students write the
number in expanded form
and round to the nearest 10
and 100
Additional Resources are
Necessary to work with
arithmetic patterns in the
addition and multiplication
tables.
Kim Sutton: Drills to Thrill
Even/Odd Mult. pat.148-149
Input.Output 150-152
Number Corner:
Number Grids
October – Counting Patterns
Data Collector
December – Reading and
Interpreting Graphs
February–Interpreting and
Comparing Charts and Graphs
3.OA.1. Interpret products of whole numbers, e.g., interpret 5 × 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 × 7.
Mastery Sequence
Pattern
-repeating
-growing
-geometric
Horizontal Axis
x-axis
Vertical Axis
y-axis
Table
Row
Column
Properties of Multiplication
Arrays
Equal Groups
Quantity
Variable
Constant Rate of Change
Increase
Decrease
Rule
3.OA.3. Use multiplication and division within 100 to solve word
problems in situations involving equal groups, arrays, and
measurement quantities, e.g., by using drawings and equations
with a symbol for the unknown number to represent the
problem.(See Table 2)
Mastery
3.OA.5. Apply properties of operations as strategies to multiply
and divide. (Students need not use formal terms for these
properties.) Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is
also known. (Commutative property of multiplication.) 3 × 5 × 2
can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10,
then 3 × 10 = 30. (Associative property of multiplication.)
Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8
× (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive
property.)
Mastery
3.OA.8. 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
rounding. (This standard is limited to problems posed with whole
numbers and having whole-number answers; students should
know how to perform operations in the conventional order when
there are no parentheses to specify a particular order (Order of
Operations).
Continue to build
skills working
towards mastery in
unit 8
3.OA.9. 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 addends
Identify patterns in
addition and
multiplication table
Continue to practice fact fluency for 3.OA.7
By the end of Grade 3, know from memory all products of two
one-digit numbers.
Grade 3 Math 2013-2014 Page 18 Created: July 2013
Unit 9: Volume and Mass “Solids and Boxes” th thTime: 1 week May 11 to May 15
Standards to Mastery
3.MD.9 Standards for which this unit builds foundational skills
None for this unit
Mathematical Practice Standards to Emphasize
Big Ideas
The standard units for mass are kilograms and grams.
The standard unit for liquid volume is liters.
Essential Questions
What are the standard units for liquid volume and mass?
Concepts Skills
Liquid volume is the amount of space a liquid takes up Estimate the measure of a liquid volume
1,000 milliliters is 1 liter* Use milliliters and liters appropriately
1,000 gram is 1 kilograms* Estimate the measure of weight and mass
Use grams and kilograms appropriately
*Students do not need to convert units, the relationships are to help them Solve one step word problems involving masses or volumes where
determine the better unit to use (e.g. milliliters are better to describe the measurements are given in the same unit
volume of water in an eyedropper while liters are better to describe the
volume of water in a pool).
Students are not expected to know the difference between weight and
mass at this point in their career but a description for teacher benefit is
on pg. CC78 in the Math Notes in Investigations and the Common Core
State Standards.
Grade 3 Math 2013-2014 Page 19 Created: July 2013
Resources Standards Expectation by
end of Unit
Vocabulary
Investigations:
Unit 9 Solids and Boxes
Additional Sessions ONLY
add 4.1A lesson pg CC73-CC76
add 4.2A lesson pg CC77-CC80
add 4.3A lesson pg CC81-CC84
Number Corner:
Calendar Grids
Aug+Sept – Measuring Tools
3.MD.2. Measure and estimate liquid volumes and masses of objects
using standard units of grams (g), kilograms (kg), and liters (l). 3
(Excludes compound units such as cm and finding the geometric
volume of a container.) Add, subtract, multiply, or divide to solve
one-step word problems involving masses or volumes that are given
in the same units, e.g., by using drawings (such as a beaker with a
measurement scale) to represent the problem. (see Table 2).
Mastery Grams
Kilograms
Milliliters
Liters
Mass
Volume
Units
Continue to practice fact fluency for 3.OA.7
By the end of Grade 3, know from memory all products of two one-
digit numbers.
Grade 3 Math 2013-2014 Page 20 Created: July 2013
Unit 8: Addition, Subtraction, and the Number System
“How Many Hundreds? How Many Miles?"
th thTime: 3.5 weeks May 18 to June 11
Standards to Mastery
3.NBT.2 3.OA.8
3.OA.7 3.OA.9
Standards for which this unit builds foundational skills
Mathematical Practice Standards to Emphasize
Big Ideas
When we change an expression to make it easier to simplify, we must
adjust the answer to maintain equality with the original problem.
The equal sign shows that the expressions on either side represent the
same quantity.
Essential Questions
How can we use what we know to solve harder problems?
What does the equal sign mean?
Concepts
When using a related subtraction problem to solve a more difficult
subtraction problem, if the minuend (# we are taking away) is larger (or
smaller) then difference will be smaller (or larger) by the same amount.
When using a related addition problem to solve a more difficult addition
problem, if an addend is larger (or smaller) the sum will be larger (or
smaller)
When adding and subtracting multiples of 10 (and 100) the ones (and
tens) digit does not change
The equal sign shows the expression on either side represent the same
quantity
Addition and subtraction are inverse operations
Subtraction can have one of three meanings; removal (taking away),
comparison (difference between), or missing part (unknown addend)
Skills
Estimate sums and differences of 3-digit numbers using number
flexibility, the number line, multiples of 10 and 100, etc
Subtract from multiples of 100
Compose and decompose numbers to add and subtract
Combine hundreds to numbers over 1000
Use number lines, hundreds grids, and thousands charts to subtract 3-
digit numbers
Use a known subtraction problem to solve a related problem (for
example 200-75=125, then 200-78=122 because we are taking 3 more
away so the difference is 3 smaller)
Add and subtract multiples of 10 and 100
Fluently multiply and divide within 100
Solve addition problems with more than 2 addends
Create equivalent addition expressions
Explain why 2 expressions are equivalent using context (story situation)
Change the numbers in an addition problem to create an equivalent but
simpler problem
Solve multi-step addition and subtraction problems
Subtract 3-digit numbers by adding on or counting back
Change one or more addends a landmark number and find the sum then
change the sum to compensate for the changes
Grade 3 Math 2013-2014 Page 21 Created: July 2013
Resources Standards Expectation by
end of Unit
Vocabulary
Investigations:
Unit 8 How Many Hundreds? How
Many Miles?
Make sure to include
10-minute math from
Investigations 1, 3 and 4 to hit
time standard 3.MD.1
Kim Sutton: Drills to Thrill
Triangular Relationships pg.100-106
Equations Compared (+/) pg.162-163
Dynamic Dice
Cover the Quantity pg.18-23
First Sum Wins! pg.74-75
Rolling to 99 pg.122-123
3.NBT.2. Fluently add and subtract within 1000 using
strategies and algorithms based on place value,
properties of operations, and/or the relationship
between addition and subtraction.
Mastery Sum
Addend
Add
Altogether
Combine
Increase
Total
Difference
Subtrahend
Minuend
Subtract
Decrease
Inverse
Estimate
Round
Digit
Numeral
Number Line
Hundreds Grid
Thousands Chart
Landmark
Benchmark
Commutative
Associative
Identity Property
Place Value
Fact Families
Multiples
Order of
Operations
Composing
Decomposing
Expanded Form
Standard Form
Word Form
Pattern
Expression
Evaluate
Equation
Solve
Equal
Algorithm
Teacher note:
Expressions are
evaluated and
equations are
solved.
3.OA.7. Fluently multiply and divide within 100,
using strategies such as the relationship between
multiplication and division (e.g., knowing that 8 × 5 =
40, one knows 40 ÷ 5 = 8) or properties of operations.
By the end of Grade 3, know from memory all
products of two one-digit numbers.
Mastery
3.OA.8. 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
rounding. (Note: This standard is limited to problems
posed with whole numbers and having whole-number
answers; students should know how to perform
operations in the conventional order when there are no
parentheses to specify a particular order --Order of
Operations).
Mastery
3.OA.9. 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 addends.
Mastery
Grade 3 Math 2013-2014 Page 22 Created: July 2013
Real Estate Game
Materials
A crayon for each student (different color than their partner)
Game board or centimeter grid paper
Pencil for each student
A double die (or two regular dice) for each pair
Directions
1) First student rolls the double die and builds an array with dimensions equal to the numbers rolled anywhere on
the game board using their color crayon.
2) The student then labels the dimensions of their array and writes the multiplication equations inside their new
property using their pencil.
3) The second student now rolls the double die and builds an array using their color crayon with dimensions equal
to the numbers rolled. Their array can touch, but not overlap the array(s) already on the board.
4) This student then labels the dimension of their array and writes the multiplication equation inside their new
property using their pencil.
5) The first student rolls again and the process repeats alternating between students.
6) If a student rolls dimensions that build an array that will not fit on the board, they lose their turn.
7) When two turns in a row, both students, are unable to find space on the board for their array, the game is over.
8) Students add up the total area in their color crayon and the largest total area wins.
The game can be played for a specific amount of time instead of playing until the board is too full to continue.
Grade 3 Math 2013-2014 Page 23 Created: July 2013
Additional Resources for 3rd
Grade by Unit
Unit 1 Unit 2 Unit 3 Unit 4
Kim Sutton: Drills to Thrill
Before and After 32-41
Equations Compared to 98-99
Dynamic Dice
Cover Up 88-89
Expanded Notation 90-93
Compare Quantities 94-97
Between 10s 104-105
Let’s Standardize! 126-129
Number Roads 132-135
Compare if you Dare 136-143
Computation Practice 144-155
Sorting Numbers 156-159
The Powerful Numbers 0-100
Arrow Math 24-33
Place Value with Pizzaz
Rounding Mountain 27
Place Value Pocket 16-29
Snap Follow Up 50-53
Place Value Clues 112-244
Number Corner:
Data Collector
December – read and interpreting
graphs
February – interpreting and
comparing charts and graphs
Bridges Support Materials:
www.mathlearningcenter.com
Data Analysis E1 Graphing (3 activities)
Kim Sutton: Drills to Thrill
Before and After 32-41
Equations Compared to 98-99
Dynamic Dice
Cover Up 88-89
Expanded Notation 90-93
Compare Quantities 94-97
Between 10s 104-105
Let’s Standardize! 126-129
Number Roads 132-135
Compare if you Dare 136-143
Computation Practice 144-155
Sorting Numbers 156-159
The Powerful Numbers 0-100
Arrow Math 24-33
Place Value with Pizzaz
Rounding Mountain 27
Place Value Pocket 16-29
Snap Follow Up 50-53
Place Value Clues 112-244
Number Corner:
Calendar Grid
January–Analog+Dig.Clocks
Clocks, Coins + Bills:
October- An Hour or Bust
November–What Time is it Now?
What Time Would it be?
December–How Long Between?
March–What Time is it Now? What Time Would it be?
Kim Sutton:
Real Estate Game See Appendix B
Dynamic Dice
Rolling Polygons 116-117
Number Corner:
Calendar Grid
November – 2D geometry
Data Collector
March – Linear Measurement
Bridges Support Materials C1 Parallel, Perpendicular, and
Intersecting Lines (1 activity)
C2 Triangles and More (2 activities)
C4 Quadrilaterals (5 activites)
Discovery Education Streaming:
Discovery math: Geometry (grades 3-
5) 35 segments
Measurement – perimeter
Introduction – Sadman/Batman
Math Mansion; 3.1 All The way Round Rectangles + Perimeter
Grade 3 Math 2013-2014 Page 24 Created: July 2013
Unit 5
Kim Sutton:
Dynamic Dice
Picture This (Groups of) 110-111
Factor Fun 76-81
Lights Out 82-83
Rolling Your Facts 60, 65-69
Even/Odd Outcomes 56-67
Number Line Workbook
My Multiples Book 87-93
Pattern Sticks 35-36
How Many Groups 37-49
Skip Counting
3’s pg. 62-63
6’s pg. 68-69
9’s pg. 74-75
4’s pg. 64-65
8’s pg. 72-733
7’s pg. 70-71
Drills to Thrill
Groups of 212-227
Multiplication Strategies 116-141
Even/Odd Mult. Patterns 148-159
Input/Output 150-152
Triangular Relations 168-172
Powerful Numbers
Sorting Styles 96-103
Matrix Sorting 104-105
Factor Freak Out 106-107
Unit 5 continued
Number Corner:
Number Grid
November – Multiples of 3
Magnetic Board
May/June (1x2 digit mult)
Computational Fluency
February – mult. Workout wheel
March – What’s Missing Bingo April – 10 to Win
Support Materials
Spinning Around Mult. 13
What’s Missing Bingo 16 10 to Win 17
Make Zero 18
Number Corner (time acts.):
Calendar Grid
January–Analog+Dig.Clocks
Clocks, Coins + Bills:
October- An Hour or Bust
November–What Time is it Now?
What Time Would it be?
December–How Long Between?
March–What Time is it Now? What
Time Would it be?
Bridges Support Materials:
www.mathlearningcenter.com
Numbers and Operations
Grade 2 A3 Division (1 activity)
Grade 3 A1 Equal Expressions
A2 Basic Mult. and Division
Unit 7
Kim Sutton: Dynamic Dice
Fraction Match Up 38-50
Make a Fraction 32-35
Fraction Brick Wall 36-37
Fractions:part of the whole
Entire Book!
Number Corner:
Calendar Grid
April – Equivalent Fractions
May+June–Frac., Dec.+$
Magnetic Board
December – Tile Fractions
January–Equivalent Fractions
Bridges Support Materials www.mathlearningcenter.com
Number and Operations
A5 Fractions (1 activity)
Unit 6
Kim Sutton: Drills to Thrill
Even/Odd Mult. pat.148-149
Input.Output 150-152
Number Corner:
Number Grids
October – Counting Patterns
Data Collector
December – Reading and Interpreting
Graphs
February–Interpreting and Comparing
Charts and Graphs
Bridges Support Materials www.mathlearningcenter.com
Data Analysis
E1 Graphing (3 activity)
Discovery Education Videos
Graphing Unit 8
Kim Sutton: Drills to Thrill
Equations Compared To pg.98-99
Triangular Relationships pg.100-106
Equations Compared (+/) pg.162-163
Dynamic Dice
The Difference Game pg.12-13
Sorting Equations pg.16-17
Cover the Quantity pg.18-23
Tic-Fact-Toe pg.72-73
First Sum Wins! pg.74-75
Rolling to 99 pg.122-123
The Powerful Numbers 0-100
Double Up pg.58-61
Unit 9
Number Corner:
Calendar Grids
Aug+Sept – Measuring Tools
Grade 3 Math 2013-2014 Page 25 Created: July 2013