Teacher ediTion and assessmenT Guide sampler On …€¦ · · 2014-02-18Teacher ediTion and...

On Core MathematicsGrade 4

Teacher ediTion and

assessmenT Guide sampler

Teacher Edition and Assessment Guide Sampler includes:

- On Core Program Overview

- Table of Contents for Grade 4

- Teaching Support and Student Lessons

- Assessments

Bridge the gap between your program and the Common Core State Standards. Activities, practice, and assessment for each Common Core State Mathematics Standard.

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Operations and Algebraic ThinkingUse the four operations with whole numbers to solve problems.

Lesson 1 4.OA.1 Algebra • Multiplication Comparisons . . . . . . . . . . . 1Lesson 2 4.OA.2 Algebra • Comparison Problems. . . . . . . . . . . . . . 3Lesson 3 4.OA.3 Problem Solving • Multistep Multiplication Problems . . . 5Lesson 4 4.OA.3 Algebra • Solve Multistep Problems Using Equations . . . 7Lesson 5 4.OA.3 Problem Solving • Multiply 2-Digit Numbers . . . . . . . 9Lesson 6 4.OA.3 Interpret the Remainder . . . . . . . . . . . . . . . . . 11Lesson 7 4.OA.3 Problem Solving • Multistep Division Problems . . . . . 13

Gain familiarity with factors and multiples.

Lesson 8 4.OA.4 Model Factors . . . . . . . . . . . . . . . . . . . . . . 15Lesson 9 4.OA.4 Factors and Divisibility . . . . . . . . . . . . . . . . . . 17Lesson 10 4.OA.4 Problem Solving • Common Factors . . . . . . . . . . 19Lesson 11 4.OA.4 Relate Facts and Multiples . . . . . . . . . . . . . . . . 21Lesson 12 4.OA.4 Prime and Composite Numbers. . . . . . . . . . . . . . 23

Generate and analyze patterns.

Lesson 13 4.OA.5 Algebra • Number Patterns . . . . . . . . . . . . . . . 25Lesson 14 4.OA.5 Problem Solving • Shape Patterns . . . . . . . . . . . 27

Number and Operations in Base TenGeneralize place value understanding for multi-digit whole numbers.

Lesson 15 4.NBT.1 Model Place Value Relationships . . . . . . . . . . . . . 29Lesson 16 4.NBT.1 Rename Numbers . . . . . . . . . . . . . . . . . . . . 31Lesson 17 4.NBT.2 Read and Write Numbers. . . . . . . . . . . . . . . . . 33Lesson 18 4.NBT.2 Compare and Order Numbers . . . . . . . . . . . . . . 35Lesson 19 4.NBT.3 Round Numbers . . . . . . . . . . . . . . . . . . . . . 37

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On Core Mathematics is a comprehensive, ready-made resource providing instruction, practice and assessment for each Common Core State Mathematics Standard at your grade level. Designed to be used hand-in-hand with your current elementary math series, On Core offers you a flexible way to fill in any gaps between your series and the new standards. Whether you use just the lessons you need, or decide use the entire student workbook for comprehensive Common Core coverage, On Core provides a complete Common Core solution in just four components:

student edition: provides a searchable database of additional worksheets, projects, and hands-on activities correlated to the Common Core State Standards. Helps teachers focus on the mathematical practices.

Teacher edition: Instructional support for each Common Core Standards lesson. The three part, research-based lesson plan (Introduce, Teach, and Practice), that uses manipulatives and powerful visual models, provides everything needed to use the content.

assessment Guide: One page of assessment for each standard in multiple-choice, free-response and constructed response formats.

Exam View® online assessment: Administer premade print or online assessments or create your own with this powerful online tool aligned to the Common Core Standards.

What isOn Core Mathematics?

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Grade 4 Table of Contents

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Number and Operations–FractionsExtend understanding of fraction equivalence and ordering.

Lesson 47 4.NF.1 Investigate • Equivalent Fractions . . . . . . . . . . . . 93Lesson 48 4.NF.1 Generate Equivalent Fractions . . . . . . . . . . . . . . 95Lesson 49 4.NF.1 Simplest Form . . . . . . . . . . . . . . . . . . . . . . 97Lesson 50 4.NF.1 Common Denominators . . . . . . . . . . . . . . . . . 99Lesson 51 4.NF.1 Problem Solving • Factors, Multiples,

and Equivalent Fractions . . . . . . . . . . . . . . . . .101Lesson 52 4.NF.2 Compare Fractions Using Benchmarks . . . . . . . . . .103Lesson 53 4.NF.2 Compare Fractions . . . . . . . . . . . . . . . . . . . .105Lesson 54 4.NF.2 Compare and Order Fractions . . . . . . . . . . . . . .107

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

Lesson 55 4.NF.3a Investigate • Join and Separate Fractions . . . . . . . .109Lesson 56 4.NF.3b Write Fractions as Sums . . . . . . . . . . . . . . . . .111Lesson 57 4.NF.3b Rename Fractions and Mixed Numbers . . . . . . . . . .113Lesson 58 4.NF.3c Add and Subtract Mixed Numbers . . . . . . . . . . . .115Lesson 59 4.NF.3c Record Subtraction with Renaming . . . . . . . . . . . .117Lesson 60 4.NF.3c Algebra • Fractions and Properties of Addition . . . . .119Lesson 61 4.NF.3d Add Fractions Using Models . . . . . . . . . . . . . . .121Lesson 62 4.NF.3d Subtract Fractions Using Models . . . . . . . . . . . . .123Lesson 63 4.NF.3d Add and Subtract Fractions. . . . . . . . . . . . . . . .125Lesson 64 4.NF.3d Problem Solving • Multistep Problems

with Fractions . . . . . . . . . . . . . . . . . . . . . .127Lesson 65 4.NF.4a Investigate • Multiples of Unit Fractions. . . . . . . . .129Lesson 66 4.NF.4b Investigate • Multiples of Fractions . . . . . . . . . . .131Lesson 67 4.NF.4b Model Multiplication of a Fraction by a

Whole Number . . . . . . . . . . . . . . . . . . . . . .133Lesson 68 4.NF.4c Multiply a Fraction by a Whole Number . . . . . . . . .135Lesson 69 4.NF.4c Problem Solving • Comparison Problems

with Multiplication . . . . . . . . . . . . . . . . . . . .137

Understand decimal notation for fractions, and compare decimal fractions.

Lesson 70 4.NF.5 Equivalent Fractions Decimals . . . . . . . . . . . . . .139Lesson 71 4.NF.5 Add Fractional Parts of 10 and 100. . . . . . . . . . . .141Lesson 72 4.NF.6 Relate Tenths and Decimals. . . . . . . . . . . . . . . .143Lesson 73 4.NF.6 Relate Hundredths and Decimals . . . . . . . . . . . . .145Lesson 74 4.NF.6 Relate Fractions, Decimals, and Money . . . . . . . . . .147Lesson 75 4.NF.7 Compare Decimals . . . . . . . . . . . . . . . . . . . .149

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Use place value understanding and properties of operations to perform multi-digit arithmetic.

Lesson 20 4.NBT.4 Add Multi-Digit Numbers . . . . . . . . . . . . . . . . 39Lesson 21 4.NBT.4 Subtract Multi-Digit Numbers . . . . . . . . . . . . . . 41Lesson 22 4.NBT.4 Problem Solving • Comparison Problems with

Addition and Subtraction . . . . . . . . . . . . . . . . 43Lesson 23 4.NBT.5 Multiply Tens, Hundreds, and Thousands . . . . . . . . . 45Lesson 24 4.NBT.5 Estimate Products . . . . . . . . . . . . . . . . . . . . 47Lesson 25 4.NBT.5 Investigate • Multiply Using the

Distributive Property . . . . . . . . . . . . . . . . . . . 49Lesson 26 4.NBT.5 Multiply Using Expanded Form . . . . . . . . . . . . . . 51Lesson 27 4.NBT.5 Multiply Using Partial Products . . . . . . . . . . . . . . 53Lesson 28 4.NBT.5 Multiply Using Mental Math . . . . . . . . . . . . . . . 55Lesson 29 4.NBT.5 Multiply 2-Digit Numbers with Regrouping . . . . . . . . 57Lesson 30 4.NBT.5 Multiply 3-Digit and 4-Digit Numbers

with Regrouping . . . . . . . . . . . . . . . . . . . . . 59Lesson 31 4.NBT.5 Multiply Tens . . . . . . . . . . . . . . . . . . . . . . . 61Lesson 32 4.NBT.5 Estimate Products . . . . . . . . . . . . . . . . . . . . 63Lesson 33 4.NBT.5 Investigate • Area Models and Partial Products . . . . . 65Lesson 34 4.NBT.5 Multiply Using Partial Products . . . . . . . . . . . . . . 67Lesson 35 4.NBT.5 Multiply with Regrouping . . . . . . . . . . . . . . . . 69Lesson 36 4.NBT.5 Choose a Multiplication Method . . . . . . . . . . . . . 71Lesson 37 4.NBT.6 Estimate Quotients Using Multiples. . . . . . . . . . . . 73Lesson 38 4.NBT.6 Investigate • Remainders . . . . . . . . . . . . . . . . 75Lesson 39 4.NBT.6 Divide Tens, Hundreds, and Thousands . . . . . . . . . . 77Lesson 40 4.NBT.6 Estimate Quotients Using Compatible Numbers . . . . . 79Lesson 41 4.NBT.6 Investigate • Division and the

Distributive Property . . . . . . . . . . . . . . . . . . . 81Lesson 42 4.NBT.6 Divide Using Repeated Subtraction . . . . . . . . . . . . 83Lesson 43 4.NBT.6 Divide Using Partial Quotients . . . . . . . . . . . . . . 85Lesson 44 4.NBT.6 Investigate • Model Division with Regrouping. . . . . . 87Lesson 45 4.NBT.6 Place the First Digit . . . . . . . . . . . . . . . . . . . . 89Lesson 46 4.NBT.6 Divide by 1-Digit Numbers . . . . . . . . . . . . . . . . 91

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nyNumber and Operations–FractionsExtend understanding of fraction equivalence and ordering.

Lesson 47 4.NF.1 Investigate • Equivalent Fractions . . . . . . . . . . . . 93Lesson 48 4.NF.1 Generate Equivalent Fractions . . . . . . . . . . . . . . 95Lesson 49 4.NF.1 Simplest Form . . . . . . . . . . . . . . . . . . . . . . 97Lesson 50 4.NF.1 Common Denominators . . . . . . . . . . . . . . . . . 99Lesson 51 4.NF.1 Problem Solving • Factors, Multiples,

and Equivalent Fractions . . . . . . . . . . . . . . . . .101Lesson 52 4.NF.2 Compare Fractions Using Benchmarks . . . . . . . . . .103Lesson 53 4.NF.2 Compare Fractions . . . . . . . . . . . . . . . . . . . .105Lesson 54 4.NF.2 Compare and Order Fractions . . . . . . . . . . . . . .107

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

Lesson 55 4.NF.3a Investigate • Join and Separate Fractions . . . . . . . .109Lesson 56 4.NF.3b Write Fractions as Sums . . . . . . . . . . . . . . . . .111Lesson 57 4.NF.3b Rename Fractions and Mixed Numbers . . . . . . . . . .113Lesson 58 4.NF.3c Add and Subtract Mixed Numbers . . . . . . . . . . . .115Lesson 59 4.NF.3c Record Subtraction with Renaming . . . . . . . . . . . .117Lesson 60 4.NF.3c Algebra • Fractions and Properties of Addition . . . . .119Lesson 61 4.NF.3d Add Fractions Using Models . . . . . . . . . . . . . . .121Lesson 62 4.NF.3d Subtract Fractions Using Models . . . . . . . . . . . . .123Lesson 63 4.NF.3d Add and Subtract Fractions. . . . . . . . . . . . . . . .125Lesson 64 4.NF.3d Problem Solving • Multistep Problems

with Fractions . . . . . . . . . . . . . . . . . . . . . .127Lesson 65 4.NF.4a Investigate • Multiples of Unit Fractions. . . . . . . . .129Lesson 66 4.NF.4b Investigate • Multiples of Fractions . . . . . . . . . . .131Lesson 67 4.NF.4b Model Multiplication of a Fraction by a

Whole Number . . . . . . . . . . . . . . . . . . . . . .133Lesson 68 4.NF.4c Multiply a Fraction by a Whole Number . . . . . . . . .135Lesson 69 4.NF.4c Problem Solving • Comparison Problems

with Multiplication . . . . . . . . . . . . . . . . . . . .137

Understand decimal notation for fractions, and compare decimal fractions.

Lesson 70 4.NF.5 Equivalent Fractions Decimals . . . . . . . . . . . . . .139Lesson 71 4.NF.5 Add Fractional Parts of 10 and 100. . . . . . . . . . . .141Lesson 72 4.NF.6 Relate Tenths and Decimals. . . . . . . . . . . . . . . .143Lesson 73 4.NF.6 Relate Hundredths and Decimals . . . . . . . . . . . . .145Lesson 74 4.NF.6 Relate Fractions, Decimals, and Money . . . . . . . . . .147Lesson 75 4.NF.7 Compare Decimals . . . . . . . . . . . . . . . . . . . .149

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GeometryDraw and identify lines and angles, and classify shapes by properties of their lines and angles.

Lesson 98 4.G.1 Lines, Rays, and Angles. . . . . . . . . . . . . . . . . .195Lesson 99 4.G.1 Parallel and Perpendicular Lines . . . . . . . . . . . . .197Lesson 100 4.G.2 Classify Triangles . . . . . . . . . . . . . . . . . . . . .199Lesson 101 4.G.2 Classify Quadrilaterals . . . . . . . . . . . . . . . . . .201Lesson 102 4.G.3 Line Symmetry . . . . . . . . . . . . . . . . . . . . . .203Lesson 103 4.G.3 Find and Draw Lines of Symmetry . . . . . . . . . . . .205

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Measurement and DataSolve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

Lesson 76 4.MD.1 Measurement Benchmarks . . . . . . . . . . . . . . . .151Lesson 77 4.MD.1 Customary Units of Length . . . . . . . . . . . . . . . .153Lesson 78 4.MD.1 Customary Units of Weight . . . . . . . . . . . . . . .155Lesson 79 4.MD.1 Customary Units of Liquid Volume . . . . . . . . . . . .157Lesson 80 4.MD.1 Investigate • Metric Units of Length . . . . . . . . . .159Lesson 81 4.MD.1 Metric Units of Liquid Volume and Mass . . . . . . . . .161Lesson 82 4.MD.1 Time . . . . . . . . . . . . . . . . . . . . . . . . . . .163Lesson 83 4.MD.1 Patterns in Measurement Units . . . . . . . . . . . . . .165Lesson 84 4.MD.2 Problem Solving • Money . . . . . . . . . . . . . . .167Lesson 85 4.MD.2 Problem Solving • Elapsed Time . . . . . . . . . . . .169Lesson 86 4.MD.2 Solve Problems with Mixed Measures. . . . . . . . . . .171Lesson 87 4.MD.3 Perimeter. . . . . . . . . . . . . . . . . . . . . . . . .173Lesson 88 4.MD.3 Area . . . . . . . . . . . . . . . . . . . . . . . . . . .175Lesson 89 4.MD.3 Area of Combined Rectangles . . . . . . . . . . . . . .177Lesson 90 4.MD.3 Find Unknown Measures . . . . . . . . . . . . . . . . .179Lesson 91 4.MD.3 Problem Solving • Find the Area . . . . . . . . . . . .181

Represent and interpret data.

Lesson 92 4.MD.4 Line Plots . . . . . . . . . . . . . . . . . . . . . . . . .183

Geometric measurement: understand concepts of angle and measure angles.

Lesson 93 4.MD.5a Investigate • Angles and Fractional Parts of a Circle. . .185Lesson 94 4.MD.5b Degrees . . . . . . . . . . . . . . . . . . . . . . . . .187Lesson 95 4.MD.6 Measure and Draw Angles . . . . . . . . . . . . . . . .189Lesson 96 4.MD.7 Join and Separate Angles. . . . . . . . . . . . . . . . .191Lesson 97 4.MD.7 Problem Solving • Angle Equations . . . . . . . . . . .193

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Lesson 98 4.G.1 Lines, Rays, and Angles. . . . . . . . . . . . . . . . . .195Lesson 99 4.G.1 Parallel and Perpendicular Lines . . . . . . . . . . . . .197Lesson 100 4.G.2 Classify Triangles . . . . . . . . . . . . . . . . . . . . .199Lesson 101 4.G.2 Classify Quadrilaterals . . . . . . . . . . . . . . . . . .201Lesson 102 4.G.3 Line Symmetry . . . . . . . . . . . . . . . . . . . . . .203Lesson 103 4.G.3 Find and Draw Lines of Symmetry . . . . . . . . . . . .205

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7Operations and Algebraic Thinking 3

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Operations and Algebraic Thinking 3

Lesson 2COMMON CORE STANDARD CC.4.OA.2

Lesson Objective: Solve problems involving multiplicative comparison and additive comparison.

Comparison Problems

Grade 4Reteach

Jamie has 3 times as many baseball cards as Rick. Together, they have 20 baseball cards. How many cards does Jamie have?

The words “3 times as many” show you can use a multiplication model to solve.

Step 1 Draw a box with the letter n in it to show that Rick has an unknown number of cards. Jamie has 3 times as many cards as Rick, so draw three identical boxes to represent Jamie’s cards.

Step 2 Use the model to write an equation.

Think: There are 4 equal bars. The number in each bar is n.

There are a total of 20 cards. So, 3 n 5

Step 3 Solve the equation to fi nd the value of n.

Think: 4 times what number is 20?

Since 4 3 5 20, the value of n is .

Step 4 Find how many cards Jamie has.

Think: 5 is the number of cards Rick has. Jamie has 3 times as many.

So, Jamie has 3 3 5 baseball cards.

Draw a model. Write an equation and solve.

1. Maddie has 2 times as many stickers on her notebook as Meg. Together, they have 15 stickers. How many stickers are on Maddie’s notebook?

2. How many more stickers are on Maddie’s notebook than on Meg’s notebook?

4 20

5

5 15

5

3n 5 15, n 5 5; There are 10 stickers on Maddie’s

notebook.

5 more stickers on Maddie’s notebook

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Lesson 2.2Comparison Problems


1. Stacey made a necklace using 4 times as many blue beads as red beads. She used a total of 40 beads. How many blue beads did Stacey use?

Think: The words “times as many as” means multiplication. Let n represent the number of red beads.

2. At the zoo, there were 3 times as many monkeys as lions. Tom counted 24 total monkeys and lions. How many monkeys were there?

3. Fred’s frog jumped 7 times as far as Al’s frog. The two frogs jumped a total of 56 inches. How far did Fred’s frog jump?

4. Sheila has 5 times as many markers as Dave. Together, they have 18 markers. How many markers does Sheila have?

5. Rafael counted a total of 40 white cars and yellow cars. There were 9 times as many white cars as yellow cars. How many white cars did Rafael count?

6. Sue scored a total of 35 points in two games. She scored 6 times as many points in the second game as in the first. How many points did she score in the second game?

COMMON CORE STANDARD 4.OA.2

Use the four operations with whole numbers to solve problems.

5n 5 40, n 5 8; 32 blue beads

YellowCars

WhiteCars

n

n n n n n n n n n

40

Lions

Monkeys

n

n n n

24

Dave

Sheila

n

n n n n n

18

First Game

Second Game

n

n nn n n n

35

Al’s Frog

Fred’s Frog

n

n nnn n n n

56

Red

Blue

n

n n n n

40

7n 5 35; 30 points

6n 5 18; 15 markers

4n 5 24, n 5 6; 18 monkeys

10n 5 40; 36 white cars

8n 5 56; 49 inches

Lesson 2CC.4.OA.2

About the MathWhen a problem describes one quantity as being a certain number of times as great as another, multiplication is being used as a means of comparison. To solve the problem, the comparison can be represented visually by using a bar model. Then the model can be used to write an algebraic equation. Solving problems in this way develops students’ ability to model with mathematics and to determine whether results make sense.

The LessonIntroduce Remind students that multiplication can be used as a way to compare numbers. Give students one or two examples of multiplication comparisons to review the concept. Tell students that they will learn how to use multiplication comparisons to write equations and solve problems.

Teach Make sure students understand that, when writing an equation, a letter like n is used to represent an unknown amount. Ask why 4 3 n 5 20 is an appropriate equation for the problem at the top of the page. Discuss why the solution of the equation, n 5 5, is not the solution of the problem.

To extend the process, ask how many more cards Jamie has than Rick has. Point out that the answer to this question involves comparing by subtraction.

Practice Have students complete page 4. Encourage students to always reread a problem to check that the proposed answer makes sense.

Comparison ProblemsLESSON 2Pages 3–4Page 2, Assessment Guide

COMMON CORE STANDARDCC.4.OA.2

OBJECTIVESolve problems involving multiplicative comparison and additive comparison.

ESSENTIAL QUESTIONHow does a model help you solve a comparison problem?

VOCABULARY

MATERIALS

PREREQUISITESInterpret multiplication as a comparison.

Write a multiplication comparison statement as an equation.

Multiply with whole numbers through 10.

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Comparison Problems

Grade 4Reteach
















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Comparison Problems

Grade 4Reteach
















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notebook.



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Lesson 2.2Comparison Problems


1. Stacey made a necklace using 4 times as many blue beads as red beads. She used a total of 40 beads. How many blue beads did Stacey use?

Think: The words “times as many as” means multiplication. Let n represent the number of red beads.

2. At the zoo, there were 3 times as many monkeys as lions. Tom counted 24 total monkeys and lions. How many monkeys were there?

3. Fred’s frog jumped 7 times as far as Al’s frog. The two frogs jumped a total of 56 inches. How far did Fred’s frog jump?

4. Sheila has 5 times as many markers as Dave. Together, they have 18 markers. How many markers does Sheila have?

5. Rafael counted a total of 40 white cars and yellow cars. There were 9 times as many white cars as yellow cars. How many white cars did Rafael count?

6. Sue scored a total of 35 points in two games. She scored 6 times as many points in the second game as in the first. How many points did she score in the second game?


Use the four operations with whole numbers to solve problems.

5n 5 40, n 5 8; 32 blue beads

YellowCars

WhiteCars

n

n n n n n n n n n

40

Lions

Monkeys

n

n n n

24

Dave

Sheila

n

n n n n n

18

First Game

Second Game

n

n nn n n n

35

Al’s Frog

Fred’s Frog

n

n nnn n n n

56

Red

Blue

n

n n n n

40

7n 5 35; 30 points

6n 5 18; 15 markers

4n 5 24, n 5 6; 18 monkeys

10n 5 40; 36 white cars

8n 5 56; 49 inches

Lesson 2CC.4.OA.2

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Lesson 5.3Problem Solving • Common Factors

Solve each problem.

1. Grace is preparing grab bags for her store’s open house. She has 24 candles, 16 pens, and 40 figurines. Each grab bag will have the same number of items, and all the items in a bag will be the same. How many items can Grace put in each bag?

____

2. Simon is making wreaths to sell. He has 60 bows, 36 silk roses, and 48 silk carnations. He wants to put the same number of items on each wreath. All the items on a wreath will be the same type. How many items can Simon put on each wreath?

____

3. Justin has 20 pencils, 25 erasers, and 40 paper clips. He organizes them into groups with the same number of items in each group. All the items in a group will be the same type. How many items can he put in each group?

____

4. A food bank has 50 cans of vegetables, 30 loaves of bread, and 100 bottles of water. The volunteers will put the items into boxes. Each box will have the same number of food items and all the items in a box will be the same type. How many items can they put in each box?

____

5. A debate competition has participants from three different schools: 15 from James Elementary, 18 from George Washington School, and 12 from the MLK Jr. Academy. All teams must have the same number of students. Each team can have only students from the same school. How many students can be on each team?

____

Find the common factors of 24, 16, and 40.



1, 2, 3, 4, 6, or 12 items

1 or 5 items

1, 2, 4, or 8 items

1, 2, 5, or 10 items

1 or 3 students

Lesson 10CC.4.OA.4

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Lesson Objective: Solve problems by using the strategy make a list.Problem Solving • Common Factors

Factorsof 35

Factorsof 21

Factorsof 49

1

5

7

35

1

3

7

21

1

7

49

Susan sorts a collection of beads. There are 35 blue, 49 red, and 21 pink beads. She arranges all the beads into rows. Each row will have the same number of beads and all the beads in a row will be the same color. How many beads can she put in each row?

1. Allyson has 60 purple buttons, 36 black buttons, and 24 green buttons. She wants to put all of the buttons in bins. She wants each bin to have only one color and all bins to have the same number of buttons. How many buttons can Allyson put in one bin?

2. Ricardo has a marble collection with 54 blue marbles, 24 red marbles, and 18 yellow marbles. He arranges the marbles into equal rows. The marbles in each row will be the same color. How many marbles can he put in one row?

Read the Problem Solve the Problem

What do I need to fi nd?

I need to fi nd

.

What information do I need to use?

I need to use

.

How will I use the information?

I can make a list to fi nd all of the

factors of

which I can use to fi nd the

.

The common factors are .

So, Susan can put or

beads in each row.

the number of beads in each row, if each row is equal and has only one color

and 21 pink beads

common factors

1, 2, 3, 4, 6, or 12 buttons 1, 2, 3, or 6 marbles

35, 49, and 21

35 blue, 49 red

17

1 and 7

About the MathProblem-solving strategies offer students organized methods of approaching problems in mathematics. In this lesson, students use the make a list strategy to list the factors of three whole numbers and make identifying the common factor easier. Applying this problem-solving strategy helps students develop their ability to make sense of problems and persevere in solving them.

The LessonIntroduce Read the given problem. Have students identify what the problem asks them to find and what information they are given that could help them answer the question. Talk about possible strategies for solving the problem.

Teach Help student define common factor as a number that is a factor of two or more numbers. Discuss the words or phrases in the problem that indicate that the solution must be a common factor of 35, 49, and 21. Students should recognize that making organized lists of factors from least to greatest is an efficient strategy to identify factors common to all three numbers of beads.

Practice Have students complete page 20. Encourage them to check that their lists are complete so that they don’t overlook any solutions.

Problem Solving • Common Factors


OBJECTIVESolve problems by using the strategy make a list.

ESSENTIAL QUESTIONWhen can you use the make a list strategy to solve a problem?

VOCABULARYcommon factor

MATERIALS

PREREQUISITESFind all the factors of a number.

LESSON 10Pages 19–20Page 10, Assessment Guide

4_MNLAEWB591179_TE_L010.indd Sec2:11 12/16/10 4:14:42 PM


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20


Solve each problem.


____


____


____


____


____




1, 2, 3, 4, 6, or 12 items

1 or 5 items

1, 2, 4, or 8 items

1, 2, 5, or 10 items

1 or 3 students

Lesson 10CC.4.OA.4

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Factorsof 35

Factorsof 21

Factorsof 49

1

5

7

35

1

3

7

21

1

7

49






I need to fi nd

.


I need to use

.



factors of


.



beads in each row.


and 21 pink beads

common factors


35, 49, and 21

35 blue, 49 red

17

1 and 7

About the MathProblem-solving strategies offer students organized methods of approaching problems in mathematics. In this lesson, students use the make a list strategy to list the factors of three whole numbers and make identifying the common factor easier. Applying this problem-solving strategy helps students develop their ability to make sense of problems and persevere in solving them.

The LessonIntroduce Read the given problem. Have students identify what the problem asks them to find and what information they are given that could help them answer the question. Talk about possible strategies for solving the problem.

Teach Help student define common factor as a number that is a factor of two or more numbers. Discuss the words or phrases in the problem that indicate that the solution must be a common factor of 35, 49, and 21. Students should recognize that making organized lists of factors from least to greatest is an efficient strategy to identify factors common to all three numbers of beads.

Practice Have students complete page 20. Encourage them to check that their lists are complete so that they don’t overlook any solutions.

Problem Solving • Common Factors


OBJECTIVESolve problems by using the strategy make a list.

ESSENTIAL QUESTIONWhen can you use the make a list strategy to solve a problem?

VOCABULARYcommon factor

MATERIALS

PREREQUISITESFind all the factors of a number.

LESSON 10Pages 19–20Page 10, Assessment Guide

4_MNLAEWB591179_TE_L010.indd Sec2:11 12/16/10 4:14:42 PM

12

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Factorsof 35

Factorsof 21

Factorsof 49

1

5

7

35

1

3

7

21

1

7

49






I need to fi nd

.


I need to use

.



factors of


.



beads in each row.


and 21 pink beads

common factors


35, 49, and 21

35 blue, 49 red

17

1 and 7


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20


Solve each problem.


____


____


____


____


____




1, 2, 3, 4, 6, or 12 items

1 or 5 items

1, 2, 4, or 8 items

1, 2, 5, or 10 items

1 or 3 students

Lesson 10CC.4.OA.4


13

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Factorsof 35

Factorsof 21

Factorsof 49

1

5

7

35

1

3

7

21

1

7

49






I need to fi nd

.


I need to use

.



factors of


.



beads in each row.


and 21 pink beads

common factors


35, 49, and 21

35 blue, 49 red

17

1 and 7


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20


Solve each problem.


____


____


____


____


____




1, 2, 3, 4, 6, or 12 items

1 or 5 items

1, 2, 4, or 8 items

1, 2, 5, or 10 items

1 or 3 students

Lesson 10CC.4.OA.4



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Lesson Objective: Determine whether a number is prime or composite.Prime and Composite Numbers

A prime number is a whole number greater than 1 with exactly two factors, 1 and the number itself.

A composite number is a whole number greater than 1 with more thantwo factors.

You can use division to find the factors of a number and tell whether the number is prime or composite.

Tell whether 55 is prime or composite.

Use division to find all the numbers by which 55 divides evenly without a remainder. Those numbers are the factors of 55.

55 4 1 5 55, so 1 and 55 are factors.


The factors of 55 are 1, 5, 11, and 55.

Because 55 has more than two factors, 55 is a composite number.




There are no other numbers that divide into 61 evenly without a remainder.

The factors of 61 are 1 and 61.

Because 61 has exactly two factors, 61 is a prime number.

Tell whether the number is prime or composite.

1. 44 Think: 44 is an even number. Is it divisible by any number other than 1 and 44?

2. 53 Think: Does 31 have other factors besides 1 and itself?

3. 12 4. 50 5. 24 6. 67

7. 83 8. 27 9. 34 10. 78

composite

composite

prime

composite

composite

composite

composite composite

prime

prime

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24

Prime and Composite Numbers


1. 47

____

2. 68

____

3. 52

____

4. 63

_ _ _ _

5. 75

_ _ _ _

6. 31

_ _ _ _

7. 77

____

8. 59

____

9. 87

____

prime

13. Could 85 pounds of butter be divided evenly into containers that hold 5 pounds each? Explain.

14. Could 43 eggs be evenly distributed into egg cartons holding 6 eggs each? Explain.

10. 72

_ _ _ _

11. 49

_ _ _ _

12. 73

_ _ _ _



Think: Does 47 have other factors besides 1 and itself?

composite

composite

composite

composite

composite

composite prime

prime

composite composite prime

Yes. Five is a factor of 85. So, the butter could be divided evenly into 17 containers.

No. Six is not a factor of 43. 43 is a prime number.

CC.4.OA.4

Lesson 12

About the MathAll whole numbers greater than 1 are either prime or composite numbers. To help determine whether a number is prime or composite, students can find all factor pairs for the number. Recognizing that some numbers have exactly one pair of factors and others have more than one pair of factors develops the ability to look for and make use of structure, which will be helpful with fraction equivalence concepts.

The LessonIntroduce Remind students that a factor is a number that is multiplied by another number to get a product. Since a number is divisible by its factors, division can be used to find all factor pairs for a number and to determine whether the number is prime or composite.

Teach Discuss the meanings of prime and composite. Explain that the numbers 0 and 1 are neither prime nor composite. Review how to find all factor pairs for a number. Start with the factor 1. Determine if it divides evenly into the number without a remainder. Then try the factor 2 and so on until pairs of factors start to repeat. Students should see that 1 and the number itself always form a factor pair for a number and that this is the only factor pair for prime numbers.

Practice Have students complete page 24. You may wish to work through the first exercise with the class.

Prime and Composite NumbersLESSON 12Pages 23–24Page 12, Assessment Guide


OBJECTIVEDetermine whether a number is prime or composite.

ESSENTIAL QUESTIONHow can you tell whether a number is prime or composite?

VOCABULARYcomposite numberprime number

MATERIALS

PREREQUISITESFind factors of numbers.

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3. 12 4. 50 5. 24 6. 67

7. 83 8. 27 9. 34 10. 78

composite

composite

prime

composite

composite

composite

composite composite

prime

prime


17

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3. 12 4. 50 5. 24 6. 67

7. 83 8. 27 9. 34 10. 78

composite

composite

prime

composite

composite

composite

composite composite

prime

prime


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24

Prime and Composite Numbers


1. 47

____

2. 68

____

3. 52

____

4. 63

_ _ _ _

5. 75

_ _ _ _

6. 31

_ _ _ _

7. 77

____

8. 59

____

9. 87

____

prime

13. Could 85 pounds of butter be divided evenly into containers that hold 5 pounds each? Explain.

14. Could 43 eggs be evenly distributed into egg cartons holding 6 eggs each? Explain.

10. 72

_ _ _ _

11. 49

_ _ _ _

12. 73

_ _ _ _



Think: Does 47 have other factors besides 1 and itself?

composite

composite

composite

composite

composite

composite prime

prime

composite composite prime

Yes. Five is a factor of 85. So, the butter could be divided evenly into 17 containers.

No. Six is not a factor of 43. 43 is a prime number.

CC.4.OA.4

Lesson 12


18

The following pages from the On Core Assessment Guide

support the student lessons presented earlier in this sampler:

lesson 2: comparison problems

Lesson 10: Problem Solving • Common Factors

lesson 12: prime and composite numbers

Assessment Guide Sample Pages

19

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2 Operations and Algebraic Thinking

CC.4.OA.2Lesson 2

1. Maria has 4 times as many necklaces as Sheila. Together, they have 25 necklaces. How many necklaces does Maria have?

A 4

B 5

C 15

D 20

2. Fernando ran 3 times as far as Aaron. They ran a total of 12 miles. How many miles did Fernando run?

A 2 miles

B 3 miles

C 6 miles

D 9 miles

3. Mr. Anson made a walkway using 4 times as many red bricks as gray bricks. He used a total of 80 bricks. How many red bricks did Mr. Anson use?

A 5

B 8

C 16

D 64

4. Sam worked a total of 36 hours over two weeks. He worked twice as many hours in the second week as the first. How many hours did he work in the first week?

A 6

B 12

C 24

D 36

5. Michael and Tom sold magazine subscriptions for a school fundraising event. Michael sold 3 times as many magazine subscriptions as Tom. Their teacher asked if they sold 27 subscriptions in all. Should Michael and Tom have answered their teacher’s question with a yes or a no? Explain your answer.

They should have answered their teacher’s question with a

no. Because Michael sold three times as many subscriptions

as Tom, the total number of subscriptions they both sold

must be a multiple of 4, and 27 is not a multiple of 4.

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20

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CC.4.OA.4Lesson 10

1. Miles has 36 engines, 54 boxcars, and 18 cabooses. He wants to arrange the train cars in equal rows, with one type of car in each row. How many train cars can he put in each row?

A 1 or 18

B 1, 2, 9, or 18

C 1, 2, 3, 6, 9, or 18

D 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, or 54

2. Gina made a list of all the factors of 24 and 36. Which list shows the common factors of 24 and 36?

A 1, 2, 3, 4, 6, 8, 12, 24

B 1, 2, 4, 6, 8, 9, 12, 24

C 1, 2, 3, 4, 6, 12

D 1, 6, 8, 12

3. Kendall has 45 dolphin stickers, 15 shark stickers, and 20 whale stickers to put in gift bags. If she wants to put the same number of each type of sticker in all the bags, how many bags can she fill?

A 1

B 1 or 5

C 1, 3, 4, or 5

D 1, 2, 3, 4, 5, 9, 10, 15, 20, or 45

4. Which of the following is not a common factor of 24, 32, and 64?

A 12

B 8

C 4

D 2

5. Karen is making two displays. One display has 57 red mugs. The other display has 76 sports mugs. The rows of each display must have the same number of mugs. What would be the greatest number of mugs possible to have in a row? Explain your answer.

The greatest number possible to have in a row is 19. The

number of mugs in a row must be a factor of 76 and 57.

The factors of 57 are 1, 3, 19, and 57. The factors of 76 are

1, 2, 4, 19, 38, and 76. The greatest common factor is 19.


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CC.4.OA.4Lesson 12

1. Ms. Chan asked Dwight if 6 is a prime number or a composite number. How should he answer?

A 6 is prime.

B 6 is composite.

C 6 is neither prime nor composite.

D 6 is both prime and composite.

2. Cal wants to put 17 baseballs in a display case. Which arrangement can he use?

A 4 rows of 4 baseballs

B 8 rows of 2 baseballs

C 1 row of 17 baseballs

D 3 rows of 6 baseballs

3. Elina used 10 tiles in the shape of a rectangle to make a design. She drew a model of the design.

1

2

5

10

What can Elina conclude about the number 10 from her model?

A 10 is a prime number.

B 10 is a composite number.



4. Maria’s friend wrote 4 numbers and asked Maria to identify the prime number. Which is the prime number?

A 21 C 25

B 23 D 27

5. There are 93 students in the marching band. Mr. Burns wants the same number of students in each row when the band performs. How many students can he put in each row? Explain your answer.

The factors of 93 are 1, 93, 3, and 31. Mr. Burns can put all

93 students in 1 row, or 31 students in each of 3 rows.


21

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CC.4.OA.4Lesson 12

1. Ms. Chan asked Dwight if 6 is a prime number or a composite number. How should he answer?

A 6 is prime.

B 6 is composite.



2. Cal wants to put 17 baseballs in a display case. Which arrangement can he use?

A 4 rows of 4 baseballs

B 8 rows of 2 baseballs

C 1 row of 17 baseballs

D 3 rows of 6 baseballs

3. Elina used 10 tiles in the shape of a rectangle to make a design. She drew a model of the design.

1

2

5

10

What can Elina conclude about the number 10 from her model?

A 10 is a prime number.

B 10 is a composite number.



4. Maria’s friend wrote 4 numbers and asked Maria to identify the prime number. Which is the prime number?

A 21 C 25

B 23 D 27

5. There are 93 students in the marching band. Mr. Burns wants the same number of students in each row when the band performs. How many students can he put in each row? Explain your answer.

The factors of 93 are 1, 93, 3, and 31. Mr. Burns can put all

93 students in 1 row, or 31 students in each of 3 rows.


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