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Grade 5CAP

Grade 5 - Common Core MathPlacing the Standards in the Math

Curriculum

July 2011

Jane Hodge – Cap CoordinatorStacey Matulewicz

Carol NeherLissette Pellegrino

Table of ContentsAbstract ......................................................................... 2

Rationale ......................................................................... 3

New York State Standards ....................................... 4

8 Common Core Practices ........................................... 10

Common Core State Standards.................................. 36

Grade 5 Pacing Calendar .............................................. 40

Abstract

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Grade 5Fifth Grade Common Core - Math

July 2011

This CAP was developed to provide greater focus on mathematical experiences in the classroom. With an eye on integrating the Common Core Standards into our existing pacing calendar it will help prepare the students and teachers for this year and the following school year when the Common Core is implemented. The Common Core fosters a greater in-depth understanding of mathematical concepts and their connections to everyday life.

The Common Core Standards have been integrated into the math curriculum through the pacing calendar. These standards provide for a greater examination of the math concepts by the students.

Additionally, this CAP includes a teacher friendly guide to the eight Common Core practices and aligns the New York State Standards to the Common Core. This will help enhance the students’ learning and to better prepare them for the May assessments and for real world applications.

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RATIONALEGrade 5

Fifth Grade Common Core Math - CAP

July 2011

Now with the New York State Math Assessment being aligned to the Common Core it is essential for all elementary teachers to have a pacing calendar that not only addresses the New York State Standards but also integrates the Common Core into their teaching. The Common Core practices seek to develop math proficiency in students and establish a thorough understanding of math practices.

With classroom instructional time being so precious, our intent was to provide a concise curriculum calendar integrating the core curriculum with the New York State Standards. We knew our students would benefit greatly by incorporating the Common Core Standards with our math pacing calendar. Also, included in the CAP is an explanation of the Common Core Standards.

This CAP will help teachers and students acclimate to the new Common Core Curriculum.

Standards for Grade 5

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Number Sense and Operations Strand

Students will understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems.

Number Systems

5.N.1 Read and write whole numbers to millions5.N.2 Compare and order numbers to millions5.N.3 Understand the place value structure of the base ten number

system

10 ones = 1 ten10 tens = 1 hundred10 hundreds = 1 thousand10 thousands = 1 ten thousand10 ten thousands = 1 hundred thousand10 hundred thousands = 1 million

5.N.4 Create equivalent fractions, given a fraction5.N.5 Compare and order fractions including unlike denominators

(with and without the use of a number line) Note: Commonly used fractions such as those that might be indicated on ruler, measuring cup, etc.

5.N.6 Understand the concept of ratio5.N.7 Express ratios in different forms5.N.8 Read, write, and order decimals to thousandths5.N.9 Compare fractions using <, >, or =5.N.10 Compare decimals using <, >, or =5.N.11 Understand that percent means part of 100, and write

percents as fractions and decimals

Number Theory

5.N.12 Recognize that some numbers are only divisible by one and themselves (prime) and others have multiple divisors (composite)

5.N.13 Calculate multiples of a whole number and the least common multiple of two numbers

5.N.14 Identify the factors of a given number5.N.15 Find the common factors and the greatest common factor of

two numbers

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Students will understand meanings of operations and procedures, and how they relate to one another.

Operations

5.N.16 Use a variety of strategies to multiply three-digit by three-digit numbers Note: Multiplication by anything greater than a three-digit multiplier/ multiplicand should be done using technology.

5.N.17 Use a variety of strategies to divide three-digit numbers by one- and two-digit numbers Note: Division by anything greater than a two-digit divisor should be done using technology.

5.N.18 Evaluate an arithmetic expression using order of operations including multiplication, division, addition, subtraction and parentheses

5.N.19 Simplify fractions to lowest terms5.N.20 Convert improper fractions to mixed numbers, and mixed

numbers to improper fractions5.N.21 Use a variety of strategies to add and subtract fractions with

like denominators5.N.22 Add and subtract mixed numbers with like denominators5.N.23 Use a variety of strategies to add, subtract, multiply, and

divide decimals to thousandths

Students will compute accurately and make reasonable estimates.

Estimation

5.N.24 Round numbers to the nearest hundredth and up to 10,0005.N.25 Estimate sums and differences of fractions with like

denominators .5.N.26 Estimate sums, differences, products, and quotients of

decimals5.N.27 Justify the reasonableness of answers using estimation

Algebra Strand

Students will represent and analyze algebraically a wide variety of problem solving situations.

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Variables and Expressions

5.A.1 Define and use appropriate terminology when referring to constants, variables, and algebraic expressions

5.A.2 Translate simple verbal expressions into algebraic expressions

Students will perform algebraic procedures accurately.

Variables and Expressions

5.A.3 Substitute assigned values into variable expressions and evaluate using order of operations

Equations and Inequalities

5.A.4 Solve simple one-step equations using basic whole-number facts

5.A.5 Solve and explain simple one-step equations using inverse operations involving whole numbers

5.A.6 Evaluate the perimeter formula for given input values

Students will recognize, use, and represent algebraically patterns, relations, and functions.

Patterns, Functions, and Relations

5.A.7 Create and explain patterns and algebraic relationships (e,g.,2,4,6,8...) algebraically: 2n (doubling)

5.A.8 Create algebraic or geometric patterns using concrete objects or visual drawings (e.g., rotate and shade geometric shapes)

Geometry Strand

Students will use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes.

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Shapes

5.G.1 Calculate the perimeter of regular and irregular polygons

Students will identify and justify geometric relationships, formally and informally.

Geometric Relationships

5.G.2 Identify pairs of similar triangles5.G.3 Identify the ratio of corresponding sides of similar triangles5.G.4 Classify quadrilaterals by properties of their angles and sides5.G.5 Know that the sum of the interior angles of a quadrilateral is

360 degrees5.G.6 Classify triangles by properties of their angles and sides5.G.7 Know that the sum of the interior angles of a triangle is 180

degrees5.G.8 Find a missing angle when given two angles of a triangle5.G.9 Identify pairs of congruent triangles5.G.10 Identify corresponding parts of congruent triangles

Students will apply transformations and symmetry to analyze problem solving situations.

Transformational Geometry

5.G.11 Identify and draw lines of symmetry of basic geometric shapes

Students will apply coordinate geometry to analyze problem solving situations.

Coordinate Geometry

5.G.12 Identify and plot points in the first quadrant5.G.13 Plot points to form basic geometric shapes (identify and

classify)5.G.14 Calculate perimeter of basic geometric shapes drawn on a

coordinate plane (rectangles and shapes composed of rectangles having sides with integer lengths and parallel to the axes)

Measurement Strand

Students will determine what can be measured and how, using appropriate methods and formulas.

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Units of Measurement

5.M.1

Use a ruler to measure to the nearest inch, and inch5.M.2 Identify customary equivalent units of length5.M.3 Measure to the nearest centimeter5.M.4 Identify equivalent metric units of length5.M.5 Convert measurement within a given system

Tools and Methods

5.M.6 Determine the tool and technique to measure with an appropriate level of precision: lengths and angles

Students will use units to give meaning to measurements.

Units

5.M.7 Calculate elapsed time in hours and minutes5.M.8 Measure and draw angles using a protractor

Students will develop strategies for estimating measurements.

Estimation

5.M.9 Determine personal references for customary units of length (e.g., your pace is approximately 3 feet, your height is approximately 5 feet, etc.)

5.M.10 Determine personal references for metric units of length5.M.11 Justify the reasonableness of estimates

Statistics and Probability Strand

Students will collect, organize, display, and analyze data.

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Collection of Data

5.S.1 Collect and record data from a variety of sources (e.g., newspapers, magazines, polls, charts, and surveys)

Organization and Display of Data

5.S.2 Display data in a line graph to show an increase or decrease over time

Analysis of Data

5.S.3 Calculate the mean for a given set of data and use to describe a set of data

Students will make predictions that are based upon data analysis.

Predictions from Data

5.S.4 Formulate conclusions and make predictions from graphs

Students will understand and apply concepts of probability.

Probability

5.S.5 List the possible outcomes for a single-event experiment5.S.6 Record experiment results using fractions/ratios5.S.7 Create a sample space and determine the probability of a

single event, given a simple experiment (e.g., rolling a number cube)

Mathematics: Standards for Mathematical Practice

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The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).

1. Make sense of problems and persevere in solving them.Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

2. Reason abstractly and quantitatively.Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems

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involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

3. Construct viable arguments and critique the reasoning of others.Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments ofothers. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

4. Model with mathematics.Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this

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might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

5. Use appropriate tools strategically.Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.

6. Attend to precision.

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Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.

7. Look for and make use of structure.Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

8. Look for and express regularity in repeated reasoning.Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x2 + x + 1), and (x – 1)(x3 + x2 + x + 1) might lead them to the

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general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.

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Implementing Standards for

Mathematical Practice:

Instructional Strategies for

Grade 5

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Mathematics – Grade 5: Introduction

In Grade 5, instructional time should focus on three critical areas: (1) developing fluency with addition and subtractions of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions); (2) extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations; and (3) developing understanding of volume.

1. Students apply their understanding of fractions and fraction models to represent the addition and subtraction of fractions with unlike denominators as equivalent calculations with like denominators. They develop fluency in calculating sums and differences of fractions, and make reasonable estimates of them. Students also use the meaning of fractions, of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for multiplying and dividing fractions make sense. (Note: this is limited to the case of dividing unit fractions by whole numbners and whole numbers by unit fractions.)

2. Students develop understanding of why division procedures work based on the meaning of base-ten numerals and properties of operations. They finalized fluency with multi-digit addition, subtraction, multiplication, and division. They apply their understanding of models for decimals, decimal notation, and properties of operations to add and subtract decimals to hundredths. They develop fluency in these computations and make reasonable estimates of their results. Students use the relationship between decimals and fractions, as well as the relationship between finite decimals and whole numbers (i.e., a finite decimal multiplied by an appropriate power of 10 is a whole number), to understand and explain why the procedures for multiplying and dividing finite decimals make sense. They compute products and quotients of decimals to hundredths efficiently and accurately.

3. Students recognized volume as an attribute of three-dimensional space. They understand that volume can be measured by finding the total number of same-size units of volume required to fill the space without gaps or overlaps. They underatand that a 1-unit by 1-unit by 1-unit cube is the standard unit for measuring volume. The select appropriate units, strategies, and tools for solving problems that involve estimating and measuring volume. The decompose three-dimensional shapes and find volumes of right rectangulars prisms by viewing them as decomposed into layers of arrays of cubes. They measure necessary attributes of shapes in order to determine volumes to solve real world and mathematical problems.

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Mathematical Practices1. Make sense of problems and persevere in solving them.2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated reasoning.

Grade Five Overview

Operations and Algebraic Thinking Write and interpret numerical expressions Analyze patterns and relationships

Numbers and Operations in Base Ten Understand the place value system Perform operations with multi-digit whole numbers and with decimals to hundredths

Number and Operation – Fractions Use equivalent fractions as a strategy to add and subtract fractions. Apply and extend previous understandings of multiplication and division to multiply

and divide fractions.

Measurement and Data Convert like measurment units within a given measurement system. Represent and interpret data. Geometric measurement: Understand concepts of volume and relate volume to

addition.

Geometry Graph points in the coordinate plane to solve real world and mathematical problems. Classify two-dimensional figures into categories based on their properties.

Operations & Algebraic Thinking 5.OA

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Write and interpret numerical expressions.1. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.2. Write simple expressions that record calculations with numbers, and interpret numerical expressions withoutevaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

Analyze patterns and relationships.3. Generate two numerical patterns using two given rules. Identify apparent relationships between correspondingterms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” an the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

Number & Operations in Base Ten 5.NBT

Understand the place value system.1. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in theplace to its right and 1/10 of what it represents in the place to its left.2. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole number exponents to denote powers of 10.3. Read, write, and compare decimals to thousandths.a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g.,347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <symbols to record the results of comparisons.4. Use place value understanding to round decimals to any place.

Perform operations with multi-digit whole numbers and with decimals to hundredths.5. Fluently multiply multi-digit whole numbers using the standard algorithm.6. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, usingstrategies based on place value, the properties of operations, and/or the relationship between multiplication anddivision. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.7. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategiesbased on place value, properties of operations, and/or the relationship between addition and subtraction; relate thestrategy to a written method and explain the reasoning used.

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Number & Operations—Fractions 5.NF

Use equivalent fractions as a strategy to add and subtract fractions.1. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.3. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?4. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of asequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, andcreate a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) =ac/bd.)b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unitfraction side lengths, and show that the area is the same as would be found by multiplying the side lengths.Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangularareas.5. Interpret multiplication as scaling (resizing), by:a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, withoutperforming the indicated multiplication.b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than thegiven number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explainingwhy multiplying a given number by a fraction less than 1 results in a product smaller than the givennumber; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplyinga/b by 1.

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6. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.7. Apply and extend previous understandings of division to divide unit fractions by whole numbers and wholenumbers by unit fractions.1a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example,create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use therelationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create astory context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationshipbetween multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division ofwhole numbers by unit fractions, e.g., by using visual fraction models and equations to represent theproblem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolateequally? How many 1/3-cup servings are in 2 cups of raisins?

_________________1 Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.

Measurement & Data 5.MD

Convert like measurement units within a given measurement system.1. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

Represent and interpret data.2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations onfractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.3. Recognize volume as an attribute of solid figures and understand concepts of volume measurement.a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can beused to measure volume.b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume ofn cubic units.4. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

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5. Relate volume to the operations of multiplication and addition and solve real world and mathematical problemsinvolving volume.a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes,and show that the volume is the same as would be found by multiplying the edge lengths, equivalently bymultiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g.,to represent the associative property of multiplication.b. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangularprisms with whole-number edge lengths in the context of solving real world and mathematical problems.c. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping rightrectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solvereal world problems.

Geometry 5.G

Graph points on the coordinate plane to solve real-world and mathematical problems.1. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and xcoordinate, y-axis and y-coordinate).2. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

Classify two-dimensional figures into categories based on their properties.3. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories ofthat category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.4. Classify two-dimensional figures in a hierarchy based on properties.

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MondaySeptember 5

TuesdaySeptember 6

WednesdaySeptember 7

ThursdaySeptember 8

FridaySeptember 9

NYS Standard 5.S.1Common Core

NYS Standard 4.S.4, 5.S.4Common Core


First Day of School

Description:Reading graphsCollect dataOrganize & analyze data

Description:Line graphs

Description:Display data in a line graph

SF # 1-1Coach Lesson 39, 40Crosswalk Lesson

SF # 1-2Coach Lesson 41Crosswalk Lesson


MondaySeptember 12

TuesdaySeptember 13


ThursdaySeptember 15

FridaySeptember 16


NYS StandardCommon Core 5.MD.2

NYS StandardCommon Core 5.G.1

NYS Standard 5.A.1, 5.A.2Common Core

NYS Standard 5.N.1, 5.N.3Common Core

Description:Display data in a line graph

Description:Line Plots – Reading and using a line plot to solve word problems and analyze data

Description:Coo rdinate Geometry

Description:Translate words into algebraic expressions

Description:Place value to millionsRead/Write whole #’sCompare & order whole numbers


SF # 1-4Coach LessonCrosswalk Lesson 29

SF #Coach Lesson 32Crosswalk Lesson 30


SF # 2-1, 2-2Coach Lesson 1Crosswalk Lesson

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September 2011

MondaySeptember 19

TuesdaySeptember 20



FridaySeptember 23

NYS Standard 5.N.3Common Core


NYS Standard 5.N.24Common Core 5.NBT.4


NYS StandardCommon Core 5.OA.3

Description:Place value structure

Description:Compare/order numbers to millions

Description:Rounding whole numbersSupplement materials(Ready-Lesson 19: Round Whole Numbers and Decimals page 119-124)

Description:Rounding whole numbers

Description:Graph Patterns-Creating a graph on a coordinate plane to show relationship between two values

SF # 2-3Coach LessonCrosswalk Lesson


SF #Coach LessonCrosswalk Lesson


SF #Coach LessonCrosswalk Lesson 5

MondaySeptember 26

TuesdaySeptember 27



FridaySeptember 30

NYS StandardCommon Core



Description:Review supplement materials

Description:Spiral Test #1

Description:Tenths & Hundredths Rosh

HashanahRosh

Hashanah




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September 2011

MondayOctober 3

TuesdayOctober 4

WednesdayOctober 5

ThursdayOctober 6

FridayOctober 7

NYS Standard 4.N.10, 4.N.12

Common CoreNYS Standard 5.N.8Common Core 5.NBT.3.a

NYS Standard 5.N.10Common Core 5.NBT.3.b


NYS Standard 5.N.10Common Core 5.NBT.3.b

Description:Equivalent Decimals

Description:Read/write decimals to thousandths & read/write decimals in expanded form

Description:Decimals on a number line & comparing decimals using >, <, =

Description:Comparing decimal fractions and percentsSupplement materials

Description:Compare and order decimals


SF # 2-9Coach Lesson 13Crosswalk Lesson 9




MondayOctober 10

TuesdayOctober 11

WednesdayOctober 12

ThursdayOctober 13

FridayOctober 14





Columbus Day

Description:Rounding decimals

Description:Rounding decimals

Description:Estimate sums and differences

Description:Adding whole numbers





42

October 2011

MondayOctober 17

TuesdayOctober 18

WednesdayOctober 19

ThursdayOctober 20

FridayOctober 21






Description:Subtracting whole numbers

Description:Add decimals & explain relationship between addition & subtraction

Description:Subtract decimals & explain relationship between addition & subtraction

Description:Problem solving strategiesDraw a picture

Description:Review supplement materials


SF # 2-16, 2-17Coach Lesson 15Crosswalk Lesson 13




MondayOctober 24

TuesdayOctober 25

WednesdayOctober 26

ThursdayOctober 27

FridayOctober 28






Description:ReviewSupplement materials


Description:Multiplication Properties

Description:Estimate products

Description:Multiplying whole numbers






43

October 2011

MondayOctober 31

TuesdayNovember 1

WednesdayNovember 2

ThursdayNovember 3

FridayNovember 4

NYS Standard 5.N.13Common Core 4.OA.4

NYS Standard 5.N.23Common Core 5.NBT.7, 2




Description:LCM

Description:Exploring decimal patterns (multiply) & explain zeros in the product when multiplying by powers of 10

Description:Estimating decimal products

Description:Multipying whole #’s and decimals

Description:Problem Solving: Choose an operationMultiple Step





SF # 1-6, 2-19Coach LessonCrosswalk Lesson

MondayNovember 7

TuesdayNovember 8

WednesdayNovember 9

ThursdayNovember 10

FridayNovember 11




Description:MultiplyDecimal x Decimal Election Day

Description:Review for Spiral #3

Description:Spiral Test #3 Veterans

Day




44

October/November 2011

Benchmark I TBA

MondayNovember 14

TuesdayNovember 15

WednesdayNovember 16

ThursdayNovember 17

FridayNovember 18






Description:Decimals x Zeros

Description:Meaning/Patterns of Division

Description:Estimating Quotients

Description:Division1-Digit Divisors

Description:Problem Solving: Interpret Remainders






MondayNovember 21

TuesdayNovember 22


ThursdayNovember 24

FridayNovember 25



NYS Standard 5.S.3Common Core 6.SP.5

Description:Quotient/Digit Placement

Description:Zero in Quotient

Description:Exploring Mean Thanksgiving

RecessThanksgiving

Recess




45

November 2011

46

December 2011MondayNovember 28

TuesdayNovember 29


ThursdayDecember 1

FridayDecember 2




NYS Standard 5.N.15Common Core 6.NS.4


Description:Dividing Money

Description:Dividing decimals

Description:Factors & Divisibility

Description:Greatest Common Factor

Description:Prime & Composite






MondayDecember 5

TuesdayDecember 6

WednesdayDecember 7

ThursdayDecember 8

FridayDecember 9





Description:Problem Solving-Working Backwards

Description:Problem Solving: Make a Table

NO SCHOOL -Parent Teacher

Conferences

Description:Review






November/ December 2011

MondayDecember 12

TuesdayDecember 13

WednesdayDecember 14

ThursdayDecember 15

FridayDecember 16






Description:Estimate Quotients with 2-digit divisiors

Description:Division 2-Digit Divisors

Description:Zeros in Quotient

Description:Dividing Money with a two-digit divisor

Description:Decimal Division Patterns






MondayDecember 19

TuesdayDecember 20


ThursdayDecember 22

FridayDecember 23

NYS Standard 5.A.2Common Core 6.EE.2.a




Description:Explore Algebra

Description:Order of OperationsSupplement Materials

Description:Order of OperationsSupplement Materials

Description:Spiral Test # 5 Holiday

Recess





47

MondayDecember 26

TuesdayDecember 27


ThursdayDecember 29

FridayDecember 30

Holiday Recess

Holiday Recess

Holiday Recess

Holiday Recess

Holiday Recess

MondayJanuary 2

TuesdayJanuary 3

WednesdayJanuary 4

ThursdayJanuary 5

FridayJanuary 6



NYS Standard 4.G.6, 7,8Common Core 4.G.1

NYS Standard 5.M., 6, 8Common Core 4.G.1

Holiday Recess

Description:Review Test Spiral #5

Description:Crosswalk Diagnostic Assessment Lessons #6-16

Description:Lines & Angles

Description:Measuring Angles


SF #Coach LessonCrosswalk Lesson pg. 44 & 45

SF # 6-1Coach Lesson 25, 26Crosswalk Lesson


48

December/ January 2011-12

MondayJanuary 9

TuesdayJanuary 10

WednesdayJanuary 11

ThursdayJanuary 12

FridayJanuary 13

NYS Standard 5.G.6Common Core 5.G.3, 5.G.4

NYS Standard 5.G.7, 8Common Core 5.G.3



NYS Standard 5.G.9, 10Common Core

Description:Classify Triangles

Description:Triangle Angles

Description:Quadrilaterals

Description:Quadrilateral Angles

Description:Similar/Congruent


SF #Coach Lesson 27Crosswalk Lesson




MondayJanuary 16

TuesdayJanuary 17

WednesdayJanuary 18

ThursdayJanuary 19

FridayJanuary 20

NYS Standard 5.G.11,4.G.3, 5Common Core

NYS Standard 5.A.6, 5.G.1, 4.MD.3Common Core


NYS Standard 5.N.4Common Core 5.NF.1

Martin Luther King

Day

Description:SymmetryText 6-8

Description:Perimeter

Description:Fraction Review

Description:Equivalent Fractions





49

January 2012

MondayJanuary 23

TuesdayJanuary 24

WednesdayJanuary 25

ThursdayJanuary 26

FridayJanuary 27

NYS Standard 4. N.4, 14Common Core

NYS Standard 4.N.7, 9Common Core

NYS Standard 5.N.5, 9Common Core



Description:Simplest Form

Description:Compare & Order Fractions

Description:Compare & Order Fractions

Description:Review

Description:Spiral #6






MondayJanuary 30

TuesdayJanuary 31

WednesdayFebruary 1

ThursdayFebruary 2

FridayFebruary 3


NYS Standard 5.N.20Common Core 5.NF.1, 5.NF.2

NYS Standard 5.N.9Common Core 5.NF.1, 5.NF.2


NYS StandardCommon Core 5.NF.3

Description:Explore Mixed Numbers

Description:Mixed Numbers

Description:Compare & Order Mixed Numbers

Description:Explore Percent

Description:Fraction As Division






50

January/ February 2012 Benchmark 2 TBA

MondayFebruary 6

TuesdayFebruary 7

WednesdayFebruary 8

ThursdayFebruary 9

FridayFebruary 10

NYS Standard 5.N.11Common Core 6.RP.3d

NYS Standard 5.N.11Common Core 6.RP.3d

NYS Standard 5.N.21, 22Common Core 5.NF.1, NF2

NYS Standard 5.N.21, 22Common Core 5.NF.1, 5.NF.2


Description:Connecting Fractions, Decimals and Percent

Description:Connecting Fractions, Decimals and Percent

Description:Add & Subtract Fractions

Description:Add & Subtract Fractions

Description:Fractions: Estimate Sums/Differences



SF # 8-1Coach Lesson 11Crosswalk Lesson 19, 20

SF # 8-1Coach Lesson 11Crosswalk Lesson 19, 20


MondayFebruary 13

TuesdayFebruary 14

WednesdayFebruary 15

ThursdayFebruary 16

FridayFebruary 17



NYS Standard 5.M.1, 6, 9Common Core

NYS Standard 5.M.1, 6, 9Common Core

NYS Standard 5.M.2, 5Common Core 5.MD.1

Description:Review


Description:Measure Using Inches

Description:Measure Using Inches

Description:Converting Units of Measurement






51

February 2012

MondayFebruary 20

TuesdayFebruary 21


ThursdayFebruary 23

FridayFebruary 24

Winter Recess

Winter Recess

Winter Recess

Winter Recess

Winter Recess

MondayFebruary 27

TuesdayFebruary 28


ThursdayMarch 1

FridayMarch 2

NYS Standard 5.M.3, 6, 10Common Core 4.MD.1

NYS Standard 5.M.2, 4, 5Common Core 5.MD.1

NYS Standard 5.M.5Common Core 5.MD.1



Description:MeasureLengthMetric Units

Description:Identifying Equivalent Metric Units of Length

Description:Converting Measurement in a System

Description:Elapsed timeSupplement Material

Description:Elapsed TimeSupplement Material






MondayMarch 5

TuesdayMarch 6

WednesdayMarch 7

ThursdayMarch 8

FridayMarch 9

52

February/ March 2012

March 2012



NYS Standard 5.M.11Common Core

NYS Standard 5.N.6, 7Common Core 6.RP.1

NYS Standard 5.A, 7, 8Common Core

Description:Review Supplement Material


Description:Justify Reasonableness of EstimatesSupplement Materials

Description:Ratio

Description:Ratios, algebraic and geometric patterns






MondayMarch 12

TuesdayMarch 13

WednesdayMarch 14

ThursdayMarch 15

FridayMarch 16

NYS Standard 5.G.2, 3Common Core

NYS Standard 5.A.2Common Core


NYS Standard 5.A.4, 5Common Core

NYS Standard 5.A.4, 5Common Core

Description:Ratio of Corresponding Sides of Similar Triangles

Description:Translate words into algebraic expressions

Description:Evaluate Using Order of Operations

Description:Solve Equations

Description:Review






53

MondayMarch 19

TuesdayMarch 20

WednesdayMarch 21

ThursdayMarch 22

FridayMarch 23

54

March 2012 Benchmark 3 TBA





Description:ReviewSupplement Material


Description:Balancing Equations Review for

NYS Math Assessment

Description:-Jumpstart-NY Ready-Previous State Assessments-Review Benchmark #s 1, 2, 3





MondayMarch 26

TuesdayMarch 27

WednesdayMarch 28

ThursdayMarch 29

FridayMarch 30




Description:Coach Book ReviewsStrand 1 Review p. 127Strand 2 Review p. 157Strand 3 Review p. 221

Description:Strand 4 Review p. 261Strand 5 Review p. 304,(note: *Possible Outcomes and Probability are post May)

Description:Coach Practice TestsPractice Test 1 p. 317Practice Test 2 p. 333

Review for NYS Math Assessment





MondayApril 2

TuesdayApril 3

WednesdayApril 4

ThursdayApril 5

FridayApril 6

55

April 2012




Spring Recess

Spring Recess

MondayApril 9

TuesdayApril 10

WednesdayApril 11

ThursdayApril 12

FridayApril 13

Spring Recess

Spring Recess

Spring Recess

Spring Recess

Spring Recess

MondayApril 16

TuesdayApril 17

WednesdayApril 18

ThursdayApril 19

FridayApril 20

56

April 2012






MondayApril 23

TuesdayApril 24

WednesdayApril 25

ThursdayApril 26

FridayApril 27






MondayApril 30

TuesdayMay 1

WednesdayMay 2

ThursdayMay 3

FridayMay 4

57

April/ May 2012



ELA State Tests


ELA State Tests


ELA State Tests


MondayMay 7

TuesdayMay 8

WednesdayMay 9

ThursdayMay 10

FridayMay 11



Math State Tests Math State Tests Math State Tests

MondayMay 14

TuesdayMay 15

WednesdayMay 16

ThursdayMay 17

FridayMay 18

NYS Standard 5.G.12Common Core 5.G.1,2


NYS Standard 5.G.13, 14Common Core 6.G.3

NYS Standard 5.S.5, 7Common Core


58

May 2012

Description:Identify and Plot Points in the First QuadrantSupplement Materials

Description:Identify and Plot Points in the First QuadrantSupplement Materials

Description:Draw shapes on a grid

Description:ProbabilityPossible Outcomes

Description:Predicting Samples




SF #Coach Lesson 43, 44Crosswalk Lesson


MondayMay 21

TuesdayMay 22

WednesdayMay 23

ThursdayMay 24

FridayMay 25




NYS StandardCommon Core 5.NF.5.a, 5.NF.5.b

NYS StandardCommon Core5.NF.4.a,b & 5.NF.6

Description:Predicting From Experiments

Description:Probability as a fraction

Description:Probability as a fraction

Description:Understanding multiplication of fractions

Description:Multiplying fractions & word problems using fractions






MondayMay 28

TuesdayMay 29

WednesdayMay 30

ThursdayMay 31

FridayJune 1

NYS Standard 6.N.17 & 6.N.18

NYS Standard 6.N.17 & 6.N.18

NYS Standard 6.N.19Common Core 5.NF.7.a,

NYS Standard 6.N.19Common Core 5.NF.7.a,

59

May/ June 2012

Common Core5.NF.4.a & 5.NF.6

Common Core 5.NF.4 & 5.NF.4.a

5.NF.7.b, 5.NF.7.c 5.NF.7.b, 5.NF.7.c

Memorial Day

Description:Multiplying whole numbers and a fraction

Description:Multiplying whole numbers and mixed numbers

Description:Dividing fractions

Description:Dividing fractions





MondayJune 4

TuesdayJune 5

WednesdayJune 6

ThursdayJune 7

FridayJune 8

NYS Standard 6.M.1Common Core 5.MD.3.a, 5.MD.3.b, 5.MD.4., 5MD.5.a

NYS Standard 6.M.1Common Core 5.MD.4, 5.MD.5.b, 5.MD.5.c

NYS StandardCommon Core5.MD.4.c



Description:Understanding Volume

Description:Volumes of Rectangular Prisms

Description:Volumes of Rectangular Prisms Word ProblemsSupplemental Materials

Description:

Review for Spiral Test #10

Description:

Spiral Test #10






MondayJune 11

TuesdayJune 12

WednesdayJune 13

ThursdayJune 14

FridayJune 15

60

June 2012

Mixed Review Mixed Review Mixed Review Mixed Review Mixed Review

MondayJune 18

TuesdayJune 19

WednesdayJune 20

ThursdayJune 21

FridayJune 22

Mixed Review Mixed Review Mixed Review

Last Day of School

61

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