Teacher ediTion and assessmenT Guide sampler On...

On Core MathematicsGrade 3

Teacher ediTion and

assessmenT Guide sampler

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

Teacher Edition and Assessment Guide Sampler includes:

- On Core Program Overview

- Table of Contents for Grade 3

- Teaching Support and Student Lessons

- Assessments

iii

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny

Operations and Algebraic ThinkingRepresent and solve problems involving multiplication and division.

Lesson 1 3.OA.1 Count Equal Groups . . . . . . . . . . . . . . . . . . . . 1Lesson 2 3.OA.1 Algebra • Relate Addition and Multiplication . . . . . . . 3Lesson 3 3.OA.2 Size of Equal Groups . . . . . . . . . . . . . . . . . . . . 5Lesson 4 3.OA.2 Number of Equal Groups . . . . . . . . . . . . . . . . . . 7Lesson 5 3.OA.2 Model with Bar Models. . . . . . . . . . . . . . . . . . . 9Lesson 6 3.OA.3 Skip Count on a Number Line . . . . . . . . . . . . . . 11Lesson 7 3.OA.3 Model with Arrays . . . . . . . . . . . . . . . . . . . . 13Lesson 8 3.OA.3 Multiply with 2 and 4 . . . . . . . . . . . . . . . . . . 15Lesson 9 3.OA.3 Multiply with 5 and 10 . . . . . . . . . . . . . . . . . . 17Lesson 10 3.OA.3 Multiply with 3 and 6 . . . . . . . . . . . . . . . . . . 19Lesson 11 3.OA.3 Problem Solving • Model Division . . . . . . . . . . . 21Lesson 12 3.OA.3 Algebra • Relate Subtraction and Division . . . . . . . . 23Lesson 13 3.OA.3 Investigate • Model with Arrays. . . . . . . . . . . . . 25Lesson 14 3.OA.3 Divide by 2 . . . . . . . . . . . . . . . . . . . . . . . 27Lesson 15 3.OA.3 Divide by 5 . . . . . . . . . . . . . . . . . . . . . . . . 29Lesson 16 3.OA.4 Algebra • Find Unknown Factors . . . . . . . . . . . . 31Lesson 17 3.OA.4 Divide by 8 . . . . . . . . . . . . . . . . . . . . . . . . 33

Understand properties of multiplication and the relationship betweenmultiplication and division.

Lesson 18 3.OA.5 Algebra • Commutative Property of Multiplication . . . . . . . . . . . . . . . . . . . . . 35

Lesson 19 3.OA.5 Algebra • Multiply with 1 and 0 . . . . . . . . . . . . . 37Lesson 20 3.OA.5 Algebra • Distributive Property . . . . . . . . . . . . . 39Lesson 21 3.OA.5 Algebra • Associative Property of Multiplication . . . . . 41Lesson 22 3.OA.5 Algebra • Division Rules for 1 and 0 . . . . . . . . . . . 43Lesson 23 3.OA.6 Algebra • Relate Multiplication and Division . . . . . . . 45

→

→

3_MNLAESEXXXXXX_TOC.indd iii 12/8/10 5:20:26 AM

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?

1 iii

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

nyOperations and Algebraic ThinkingRepresent and solve problems involving multiplication and division.





→

→

3_MNLAESEXXXXXX_TOC.indd iii 12/8/10 5:20:26 AMiii

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny






→

→


iii

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny






→

→


Grade 3 Table of Contents

2iv

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny

Multiply and divide within 100.

Lesson 24 3.OA.7 Multiply with 7 . . . . . . . . . . . . . . . . . . . . . . 47Lesson 25 3.OA.7 Multiply with 8 . . . . . . . . . . . . . . . . . . . . . . 49Lesson 26 3.OA.7 Multiply with 9 . . . . . . . . . . . . . . . . . . . . . . 51Lesson 27 3.OA.7 Algebra • Write Related Facts . . . . . . . . . . . . . . 53Lesson 28 3.OA.7 Divide by 10 . . . . . . . . . . . . . . . . . . . . . . . 55Lesson 29 3.OA.7 Divide by 3 . . . . . . . . . . . . . . . . . . . . . . . . 57Lesson 30 3.OA.7 Divide by 4 . . . . . . . . . . . . . . . . . . . . . . . . 59Lesson 31 3.OA.7 Divide by 6 . . . . . . . . . . . . . . . . . . . . . . . . 61Lesson 32 3.OA.7 Divide by 7 . . . . . . . . . . . . . . . . . . . . . . . . 63Lesson 33 3.OA.7 Divide by 9 . . . . . . . . . . . . . . . . . . . . . . . . 65

Solve problems involving the four operations, and identify and explainpatterns in arithmetic.

Lesson 34 3.OA.8 Problem Solving • Addition and Subtraction . . . . . . 67Lesson 35 3.OA.8 Problem Solving • Model Multiplication . . . . . . . . 69Lesson 36 3.OA.8 Problem Solving • Multiplication . . . . . . . . . . . . 71Lesson 37 3.OA.8 Problem Solving • Two-Step Problems . . . . . . . . . 73Lesson 38 3.OA.8 Investigate • Order of Operations . . . . . . . . . . . . 75Lesson 39 3.OA.9 Algebra • Number Patterns . . . . . . . . . . . . . . . 77Lesson 40 3.OA.9 Algebra • Patterns on the Multiplication Table . . . . . . 79Lesson 41 3.OA.9 Algebra • Describe Patterns . . . . . . . . . . . . . . . 81

→

→

3_MNLAESEXXXXXX_TOC.indd iv 12/8/10 5:20:27 AM

v

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny

Number and Operations in Base TenUse place value understanding and properties of operations to performmulti-digit arithmetic.

Lesson 42 3.NBT.1 Round to the Nearest Ten or Hundred . . . . . . . . . . 83Lesson 43 3.NBT.1 Estimate Sums . . . . . . . . . . . . . . . . . . . . . . 85Lesson 44 3.NBT.1 Estimate Differences . . . . . . . . . . . . . . . . . . . 87Lesson 45 3.NBT.2 Mental Math Strategies for Addition . . . . . . . . . . . 89Lesson 46 3.NBT.2 Algebra • Use Properties to Add. . . . . . . . . . . . . 91Lesson 47 3.NBT.2 Use the Break Apart Strategy to Add . . . . . . . . . . . 93Lesson 48 3.NBT.2 Use Place Value to Add . . . . . . . . . . . . . . . . . . 95Lesson 49 3.NBT.2 Mental Math Strategies for Subtraction . . . . . . . . . 97Lesson 50 3.NBT.2 Use Place Value to Subtract. . . . . . . . . . . . . . . . 99Lesson 51 3.NBT.2 Combine Place Values to Subtract . . . . . . . . . . . .101Lesson 52 3.NBT.3 Problem Solving • Use the Distributive Property . . . .103Lesson 53 3.NBT.3 Multiplication Strategies with Multiples of 10 . . . . . .105Lesson 54 3.NBT.3 Multiply Multiples of 10 by 1-Digit Numbers . . . . . . .107

Number and Operations–FractionsDevelop understanding of fractions as numbers.

Lesson 55 3.NF.1 Equal Parts of a Whole . . . . . . . . . . . . . . . . . .109Lesson 56 3.NF.1 Equal Shares . . . . . . . . . . . . . . . . . . . . . . .111Lesson 57 3.NF.1 Unit Fractions of a Whole . . . . . . . . . . . . . . . .113Lesson 58 3.NF.1 Fractions of a Whole . . . . . . . . . . . . . . . . . . .115Lesson 59 3.NF.1 Fractions of a Group . . . . . . . . . . . . . . . . . . .117Lesson 60 3.NF.1 Find Part of a Group Using Unit Fractions. . . . . . . . .119Lesson 61 3.NF.1 Problem Solving • Find the Whole Group Using

Unit Fractions . . . . . . . . . . . . . . . . . . . . . .121Lesson 62 3.NF.2a Fractions on a Number Line . . . . . . . . . . . . . . .123

3.NF.2bLesson 63 3.NF.3a Investigate • Model Equivalent Fractions . . . . . . . .125Lesson 64 3.NF.3b Equivalent Fractions . . . . . . . . . . . . . . . . . . .127Lesson 65 3.NF.3c Relate Fractions and Whole Numbers. . . . . . . . . . .129Lesson 66 3.NF.3d Problem Solving • Compare Fractions . . . . . . . . .131Lesson 67 3.NF.3d Compare Fractions with the Same Denominator . . . . .133Lesson 68 3.NF.3d Compare Fractions with the Same Numerator . . . . . .135Lesson 69 3.NF.3d Compare Fractions . . . . . . . . . . . . . . . . . . . .137Lesson 70 3.NF.3d Compare and Order Fractions . . . . . . . . . . . . . .139

→

→

3_MNLAESEXXXXXX_TOC.indd v 12/8/10 5:20:27 AM

3 v

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

nyNumber and Operations in Base TenUse place value understanding and properties of operations to performmulti-digit arithmetic.

Lesson 42 3.NBT.1 Round to the Nearest Ten or Hundred . . . . . . . . . . 83Lesson 43 3.NBT.1 Estimate Sums . . . . . . . . . . . . . . . . . . . . . . 85Lesson 44 3.NBT.1 Estimate Differences . . . . . . . . . . . . . . . . . . . 87Lesson 45 3.NBT.2 Mental Math Strategies for Addition . . . . . . . . . . . 89Lesson 46 3.NBT.2 Algebra • Use Properties to Add. . . . . . . . . . . . . 91Lesson 47 3.NBT.2 Use the Break Apart Strategy to Add . . . . . . . . . . . 93Lesson 48 3.NBT.2 Use Place Value to Add . . . . . . . . . . . . . . . . . . 95Lesson 49 3.NBT.2 Mental Math Strategies for Subtraction . . . . . . . . . 97Lesson 50 3.NBT.2 Use Place Value to Subtract. . . . . . . . . . . . . . . . 99Lesson 51 3.NBT.2 Combine Place Values to Subtract . . . . . . . . . . . .101Lesson 52 3.NBT.3 Problem Solving • Use the Distributive Property . . . .103Lesson 53 3.NBT.3 Multiplication Strategies with Multiples of 10 . . . . . .105Lesson 54 3.NBT.3 Multiply Multiples of 10 by 1-Digit Numbers . . . . . . .107

Number and Operations–FractionsDevelop understanding of fractions as numbers.

Lesson 55 3.NF.1 Equal Parts of a Whole . . . . . . . . . . . . . . . . . .109Lesson 56 3.NF.1 Equal Shares . . . . . . . . . . . . . . . . . . . . . . .111Lesson 57 3.NF.1 Unit Fractions of a Whole . . . . . . . . . . . . . . . .113Lesson 58 3.NF.1 Fractions of a Whole . . . . . . . . . . . . . . . . . . .115Lesson 59 3.NF.1 Fractions of a Group . . . . . . . . . . . . . . . . . . .117Lesson 60 3.NF.1 Find Part of a Group Using Unit Fractions. . . . . . . . .119Lesson 61 3.NF.1 Problem Solving • Find the Whole Group Using

Unit Fractions . . . . . . . . . . . . . . . . . . . . . .121Lesson 62 3.NF.2a Fractions on a Number Line . . . . . . . . . . . . . . .123

3.NF.2bLesson 63 3.NF.3a Investigate • Model Equivalent Fractions . . . . . . . .125Lesson 64 3.NF.3b Equivalent Fractions . . . . . . . . . . . . . . . . . . .127Lesson 65 3.NF.3c Relate Fractions and Whole Numbers. . . . . . . . . . .129Lesson 66 3.NF.3d Problem Solving • Compare Fractions . . . . . . . . .131Lesson 67 3.NF.3d Compare Fractions with the Same Denominator . . . . .133Lesson 68 3.NF.3d Compare Fractions with the Same Numerator . . . . . .135Lesson 69 3.NF.3d Compare Fractions . . . . . . . . . . . . . . . . . . . .137Lesson 70 3.NF.3d Compare and Order Fractions . . . . . . . . . . . . . .139

→

→

3_MNLAESEXXXXXX_TOC.indd v 12/8/10 5:20:27 AM

4vi

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny

Measurement and DataSolve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

Lesson 71 3.MD.1 Time to the Minute. . . . . . . . . . . . . . . . . . . .141Lesson 72 3.MD.1 A.M. and P.M. . . . . . . . . . . . . . . . . . . . . . .143Lesson 73 3.MD.1 Measure Time Intervals . . . . . . . . . . . . . . . . . .145Lesson 74 3.MD.1 Use Time Intervals . . . . . . . . . . . . . . . . . . . .147Lesson 75 3.MD.1 Problem Solving • Time Intervals . . . . . . . . . . . .149Lesson 76 3.MD.2 Estimate and Measure Liquid Volume. . . . . . . . . . .151Lesson 77 3.MD.2 Estimate and Measure Mass . . . . . . . . . . . . . . .153Lesson 78 3.MD.2 Solve Problems About Liquid Volume and Mass . . . . .155

Represent and interpret data.

Lesson 79 3.MD.3 Problem Solving • Organize Data . . . . . . . . . . . .157Lesson 80 3.MD.3 Use Picture Graphs . . . . . . . . . . . . . . . . . . . .159Lesson 81 3.MD.3 Make Picture Graphs . . . . . . . . . . . . . . . . . . .161Lesson 82 3.MD.3 Use Bar Graphs. . . . . . . . . . . . . . . . . . . . . .163Lesson 83 3.MD.3 Make Bar Graphs. . . . . . . . . . . . . . . . . . . . .165Lesson 84 3.MD.3 Solve Problems Using Data . . . . . . . . . . . . . . . .167Lesson 85 3.MD.4 Use and Make Line Plots . . . . . . . . . . . . . . . . .169Lesson 86 3.MD.4 Measure Length . . . . . . . . . . . . . . . . . . . . .171

Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

Lesson 87 3.MD.5 Understand Area . . . . . . . . . . . . . . . . . . . . .173 3.MD.5aLesson 88 3.MD.5b Investigate • Measure Area . . . . . . . . . . . . . . .175 3.MD.6Lesson 89 3.MD.7a Use Area Models . . . . . . . . . . . . . . . . . . . . .177Lesson 90 3.MD.7b Problem Solving • Area of Rectangles . . . . . . . . .179Lesson 91 3.MD.7c Area of Combined Rectangles . . . . . . . . . . . . . .181 3.MD.7d

Geometric measurement: recognize perimeter as an attribute of plane fi gures and distinguish between linear and area measures.

Lesson 92 3.MD.8 Investigate • Model Perimeter . . . . . . . . . . . . .183Lesson 93 3.MD.8 Find Perimeter . . . . . . . . . . . . . . . . . . . . . .185Lesson 94 3.MD.8 Algebra • Find Unknown Side Lengths . . . . . . . . .187Lesson 95 3.MD.8 Same Perimeter, Different Areas . . . . . . . . . . . . .189Lesson 96 3.MD.8 Same Area, Different Perimeters . . . . . . . . . . . . .191

→

→

→

→

3_MNLAESEXXXXXX_TOC.indd vi 12/8/10 5:20:27 AM

vii

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny

GeometryReason with shapes and their attributes.

Lesson 97 3.G.1 Describe Plane Shapes . . . . . . . . . . . . . . . . . .193Lesson 98 3.G.1 Describe Angles in Plane Shapes . . . . . . . . . . . . .195Lesson 99 3.G.1 Identify Polygons . . . . . . . . . . . . . . . . . . . . .197Lesson 100 3.G.1 Describe Sides of Polygons . . . . . . . . . . . . . . . .199Lesson 101 3.G.1 Classify Quadrilaterals . . . . . . . . . . . . . . . . . .201Lesson 102 3.G.1 Draw Quadrilaterals . . . . . . . . . . . . . . . . . . .203Lesson 103 3.G.1 Describe Triangles . . . . . . . . . . . . . . . . . . . .205Lesson 104 3.G.1 Problem Solving • Classify Plane Shapes . . . . . . . .207Lesson 105 3.G.2 Investigate • Relate Shapes, Fractions, and Area . . . .209

→

3_MNLAESEXXXXXX_TOC.indd vii 12/8/10 5:20:27 AM

5vii

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

nyGeometryReason with shapes and their attributes.

Lesson 97 3.G.1 Describe Plane Shapes . . . . . . . . . . . . . . . . . .193Lesson 98 3.G.1 Describe Angles in Plane Shapes . . . . . . . . . . . . .195Lesson 99 3.G.1 Identify Polygons . . . . . . . . . . . . . . . . . . . . .197Lesson 100 3.G.1 Describe Sides of Polygons . . . . . . . . . . . . . . . .199Lesson 101 3.G.1 Classify Quadrilaterals . . . . . . . . . . . . . . . . . .201Lesson 102 3.G.1 Draw Quadrilaterals . . . . . . . . . . . . . . . . . . .203Lesson 103 3.G.1 Describe Triangles . . . . . . . . . . . . . . . . . . . .205Lesson 104 3.G.1 Problem Solving • Classify Plane Shapes . . . . . . . .207Lesson 105 3.G.2 Investigate • Relate Shapes, Fractions, and Area . . . .209

→

3_MNLAESEXXXXXX_TOC.indd vii 12/8/10 5:20:27 AM

7

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny

Operations and Algebraic Thinking 37

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny

Name

72

Lesson 4.10Problem Solving • Multiplication

Solve.

1. Henry has a new album for his baseball cards. Some of the pages hold 6 cards and the other pages hold 3 cards. If Henry has 36 cards, how many different ways can he put them in his album?

Henry can put the cards in his album _ ways.

2. Ms. Hernandez has 17 tomato plants that she wants to plant in rows. She will put 2 plants in some rows and 1 plant in the others. How many different ways can she plant the tomato plants? Make a table to solve.

Ms. Hernandez can plant the tomato plants _ ways.

3. Bianca has a total of 25¢. She has some nickels and pennies. How many different combinations of nickels and pennies could Bianca have? Make a table to solve.

Bianca could have _ combinations of 25¢.

8

4

COMMON CORE STANDARD 3.OA.8

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Pages with 6 Cards 1 2 3 4 5 6


Total Cards 36 36 36 36 36 36

Rows with 2 Plants 8 7 6 5 4 3 2 1

Rows with 1 Plant 1 3 5 7 9 11 13 15

Total Plants 17 17 17 17 17 17 17 17

Number of Nickels 1 2 3 4

Number of Pennies 20 15 10 5

Total Value 25¢ 25¢ 25¢ 25¢

Possible table is shown.


6

Lesson 36CC.3.OA.8

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny

Name


Lesson 36COMMON CORE STANDARD CC.3.OA.8

Lesson Objective: Solve multiplication problems by using the strategy make a table.Problem Solving • Multiplication

1

1

1

6

2

2 5

2

12

4 5

4

4 5

3024

Number of Pitchers

Cans of Fruit Juice

Bottles of Ginger Ale

Scoops of Sherbet

3

3

3

18

Lucy’s mother is making punch for the students. For eachpitcher, she uses 1 can of fruit juice, 1 bottle of ginger ale,and 6 scoops of sherbet. How much of each ingredient will she need to make 5 pitchers of punch?

Read the Problem Solve the ProblemWhat do I need to fi nd? First, make a table with the information.

Next, look for information in the table that will help you solve the problem.

Look for a pattern. The cans of fruit juice and the bottles of ginger ale increase by 1. The scoops of sherbet increase by 6. Complete the table.

So, Lucy’s mother will need 5 cans of fruit juice, 5 bottles of ginger ale, and30 scoops of sherbet.

What information do I need to use?Lucy’s mother uses can of fruit juice, bottle of ginger ale, and scoops of sherbet for each pitcher.

How will I use the information?I will make a to show the total amounts for the ingredients Lucy’s mother uses.

1. Suppose Lucy’s mother decides to make 2 more pitchers of punch. How many scoops of sherbet would she need for 7 pitchers of punch? Explain your answer.

2. Jake gives his dog 4 chew bones and 1 dog toy each month. Howmany chew bones and toys will Jake give his dog in 5 months?

table

42 scoops; Possible answer: The table shows that 6 scoops are needed for 1 pitcher. I can multiply 7 3 6 to fi nd the number of scoops needed for 7 pitchers.

20 chew bones and 5 toys

11

I need to fi nd how much of each ingredient is needed for the 5 pitchers of punch.

6

About the MathIn many problems the given information is not a set of data, but instead is a statement of one or more relationships between quantities. One strategy for solving these problems is to use the given relationships and appropriate operations to generate a set of data. Using tables to organize the data that is generated in this way can help students make sense of problems and persevere in solving them.

The LessonIntroduce Remind students that in some problems they were given a set of data, and they organized the data in a table. Explain that they will learn how to use multiplication and other operations to create their own set of data for a problem, and they will use patterns to organize their data in a table.

Teach Have students read the problem at the top of the page. Guide students through the Read the Problem questions. Lead students to see that a table will help them create and organize data about the amount of each ingredient needed for different amounts of punch. Then lead the students through the solution of the problem. Stress the importance of looking for patterns in the table.

Practice Have students complete page 72. Encourage students to use patterns when organizing the data in each table in order to account for all possible combinations.

Problem Solving • Multiplication

COMMON CORE STANDARDCC.3.OA.8

OBJECTIVESolve multiplication problems by using the strategy make a table.

ESSENTIAL QUESTIONHow can you use the strategy make a table to solve multiplication problems?

VOCABULARY

MATERIALS

PREREQUISITESMultiply two one-digit numbers.

Solve problems involving two operations.

LESSON 36Pages 71–72Page 36, Assessment Guide

3_MNLAEWB591087_TE_L036.indd 37 12/16/10 2:57:33 AM

8

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

nyName




1

1

1

6

2

2 5

2

12

4 5

4

4 5

3024

Number of Pitchers

Cans of Fruit Juice


Scoops of Sherbet

3

3

3

18










table



11


6

3_MNLAEWB575230_SE_L036R.indd 71 12/9/10 10:55:05 PM

9

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny

Name




1

1

1

6

2

2 5

2

12

4 5

4

4 5

3024

Number of Pitchers

Cans of Fruit Juice


Scoops of Sherbet

3

3

3

18










table



11


6


© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny

Name

72

Lesson 4.10Problem Solving • Multiplication

Solve.

1. Henry has a new album for his baseball cards. Some of the pages hold 6 cards and the other pages hold 3 cards. If Henry has 36 cards, how many different ways can he put them in his album?

Henry can put the cards in his album _ ways.

2. Ms. Hernandez has 17 tomato plants that she wants to plant in rows. She will put 2 plants in some rows and 1 plant in the others. How many different ways can she plant the tomato plants? Make a table to solve.

Ms. Hernandez can plant the tomato plants _ ways.

3. Bianca has a total of 25¢. She has some nickels and pennies. How many different combinations of nickels and pennies could Bianca have? Make a table to solve.

Bianca could have _ combinations of 25¢.

8

4

COMMON CORE STANDARD 3.OA.8

Solve problems involving the four operations, and identify and explain patterns in arithmetic.



Total Cards 36 36 36 36 36 36

Rows with 2 Plants 8 7 6 5 4 3 2 1

Rows with 1 Plant 1 3 5 7 9 11 13 15

Total Plants 17 17 17 17 17 17 17 17

Number of Nickels 1 2 3 4

Number of Pennies 20 15 10 5

Total Value 25¢ 25¢ 25¢ 25¢



6

Lesson 36CC.3.OA.8

3_MNLAEWB575230_SE_L036P.indd 72 12/16/10 2:33:59 AM

10 Number and Operations–Fractions 71

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny

136

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny

Name

18

1818

18

18

1 81 8

18

12

12

Compare. Write , or ..

CC.3.NF.3d

Lesson 68

10. Javier is buying food in the lunch line. The tray of salad plates is 3 __ 8 full. The tray of fruit plates is 3 __ 6 full. Which tray is more full?

11. Rachel bought some buttons. Of the buttons, 2 __ 6 are yellow and 2 __ 8 are red. Rachel bought more of which color buttons?

4. 2 __ 8 2 __ 3

7. 5 __ 6 5 __ 8

5. 1 __ 8 1 __ 6

8. 4 __ 6 4 __ 8

6. 1 __ 4 1 __ 6

9. 3 __ 6 3 __ 4

Compare Fractions with the Same Numerator

1. 1 __ 8 1 __ 2 2. 3 __ 8 3 __

6 3. 2 __ 3 2 __

4 ,

,

,

,

.

.

. .

,

yellowthe fruit plate tray

Name

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny

Number and Operations–Fractions 135

Dog Owners Cat Owners

16

1 6

16

16

16

16

,

Lesson Objective: Compare fractions with the same numerator by using models and reasoning strategies.

COMMON CORE STANDARD CC.3.NF.3d

Lesson 68


1. 3 __ 4 3 __ 6 2. 1 __ 6 1 __ 3 3. 3 __ 4 3 __ 8

4. 2 __ 4 2 __ 8 5. 4 __ 6 4 __ 8 6. 2 __ 6 2 __ 4

7. 5 __ 6 5 __ 8 8. 1 __ 2 1 __ 4 9. 1 __ 6 1 __ 4

10. 1 __ 4 1 __ 8 11. 1 __ 4 1 __ 8 12. 2 __ 8 2 __ 6


Ryan takes a survey of his class. 1 _ 8

of the class has dogs,

and 1 _ 6

of the class has cats. Are there more dog owners or cat

owners in Ryan’s class?

Compare the fractions. 1 _ 8

1 _ 6

Step 1 Divide the fi rst circle into 8 equal parts. Shade 1 _

8 of the circle to show dog owners.

Step 2 Divide the second circle into 6 equal parts. Shade 1 _

6 of the circle to

show cat owners.

Step 3 Compare the shaded parts of the circles. Which shaded part is larger?

1 _ 6

is larger than 1 _ 8

. 1 _ 8

1 _ 6

So, there are more cat owners than dog owners in Ryan’s class.

. , .

. . ,

. .

. .

,

,


Compare Fractions with the Same NumeratorAbout the MathIt is often possible to compare fractions with different denominators without finding a common denominator. Reasoning about the size of the pieces is one strategy to compare fractions. When two fractions have the same numerator, students can think about the size of the pieces. When the whole is divided into a greater number of pieces, the size of the pieces is smaller. Using strategies to compare fractions develops the ability to reason abstractly and quantititatively.

The LessonIntroduce Remind students that a unit fraction describes one piece of a whole divided into equal-sized pieces. Read the problem on the page and ask students which fraction is divided into smaller pieces. Then discuss how the number of pieces a whole is divided into affects the size of the pieces. Students should reach the conclusion that the greater number of pieces a whole is divided into, the smaller the pieces are.

Teach Remind students that the numerator tells the number of equal-sized pieces that are being considered. When they think about the size of the pieces as determined by the denominator, they know that the same number of pieces will be a smaller part of the whole when the pieces are smaller. When the pieces are larger, the part of the whole will be larger.

Practice Have students complete page 136. Encourage students to use fraction circles or drawings to help them make sense of the comparisons.

COMMON CORE STANDARDCC.3.NF.3d

OBJECTIVECompare fractions with the same numerator by using models and reasoning strategies.

ESSENTIAL QUESTIONHow can you compare fractions with the same numerator?

VOCABULARY

MATERIALSfraction circles

PREREQUISITESUnderstand unit fractions and partitioning a whole into equal-sized pieces.

Use < and > to compare numbers.

3_MNLAEWB591087_TE_L068.indd 71 12/16/10 4:11:03 PM

11Number and Operations–Fractions 71

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny

136

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny

Name

18

1818

18

18

1 81 8

18

12

12


CC.3.NF.3d

Lesson 68



4. 2 __ 8 2 __ 3

7. 5 __ 6 5 __ 8

5. 1 __ 8 1 __ 6

8. 4 __ 6 4 __ 8

6. 1 __ 4 1 __ 6

9. 3 __ 6 3 __ 4


1. 1 __ 8 1 __ 2 2. 3 __ 8 3 __

6 3. 2 __ 3 2 __

4 ,

,

,

,

.

.

. .

,


Name

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny



16

1 6

16

16

16

16

,



Lesson 68


1. 3 __ 4 3 __ 6 2. 1 __ 6 1 __ 3 3. 3 __ 4 3 __ 8

4. 2 __ 4 2 __ 8 5. 4 __ 6 4 __ 8 6. 2 __ 6 2 __ 4

7. 5 __ 6 5 __ 8 8. 1 __ 2 1 __ 4 9. 1 __ 6 1 __ 4

10. 1 __ 4 1 __ 8 11. 1 __ 4 1 __ 8 12. 2 __ 8 2 __ 6


Ryan takes a survey of his class. 1 _ 8

of the class has dogs,

and 1 _ 6

of the class has cats. Are there more dog owners or cat


Compare the fractions. 1 _ 8

1 _ 6




6 of the circle to

show cat owners.


1 _ 6

is larger than 1 _ 8

. 1 _ 8

1 _ 6


. , .

. . ,

. .

. .

,

,


Compare Fractions with the Same NumeratorAbout the MathIt is often possible to compare fractions with different denominators without finding a common denominator. Reasoning about the size of the pieces is one strategy to compare fractions. When two fractions have the same numerator, students can think about the size of the pieces. When the whole is divided into a greater number of pieces, the size of the pieces is smaller. Using strategies to compare fractions develops the ability to reason abstractly and quantititatively.

The LessonIntroduce Remind students that a unit fraction describes one piece of a whole divided into equal-sized pieces. Read the problem on the page and ask students which fraction is divided into smaller pieces. Then discuss how the number of pieces a whole is divided into affects the size of the pieces. Students should reach the conclusion that the greater number of pieces a whole is divided into, the smaller the pieces are.

Teach Remind students that the numerator tells the number of equal-sized pieces that are being considered. When they think about the size of the pieces as determined by the denominator, they know that the same number of pieces will be a smaller part of the whole when the pieces are smaller. When the pieces are larger, the part of the whole will be larger.

Practice Have students complete page 136. Encourage students to use fraction circles or drawings to help them make sense of the comparisons.

COMMON CORE STANDARDCC.3.NF.3d

OBJECTIVECompare fractions with the same numerator by using models and reasoning strategies.

ESSENTIAL QUESTIONHow can you compare fractions with the same numerator?

VOCABULARY

MATERIALSfraction circles

PREREQUISITESUnderstand unit fractions and partitioning a whole into equal-sized pieces.

Use < and > to compare numbers.

3_MNLAEWB591087_TE_L068.indd 71 12/16/10 4:11:03 PM

12

Name©

Hou

ghto

n M

ifflin

Har

cour

t P

ublis

hing

Com

pany



16

1 61

616

16

16

,



Lesson 68


1. 3 __ 4 3 __ 6 2. 1 __ 6 1 __ 3 3. 3 __ 4 3 __ 8

4. 2 __ 4 2 __ 8 5. 4 __ 6 4 __ 8 6. 2 __ 6 2 __ 4

7. 5 __ 6 5 __ 8 8. 1 __ 2 1 __ 4 9. 1 __ 6 1 __ 4

10. 1 __ 4 1 __ 8 11. 1 __ 4 1 __ 8 12. 2 __ 8 2 __ 6


Ryan takes a survey of his class. 1 _ 8 of the class has dogs,

and 1 _ 6 of the class has cats. Are there more dog owners or cat


Compare the fractions. 1 _ 8 1 _

6




6 of the circle to

show cat owners.


1 _ 6 is larger than 1 _

8 . 1 _

8 1 _

6


. , .

. . ,

. .

. .

,

,


136

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny

Name

18

1818

18

18

1 81 8

18

12

12


CC.3.NF.3d

Lesson 68



4. 2 __ 8 2 __ 3

7. 5 __ 6 5 __ 8

5. 1 __ 8 1 __ 6

8. 4 __ 6 4 __ 8

6. 1 __ 4 1 __ 6

9. 3 __ 6 3 __ 4


1. 1 __ 8 1 __ 2 2. 3 __ 8 3 __

6 3. 2 __ 3 2 __

4 ,

,

,

,

.

.

. .

,


3_MNLAEWB575230_SE_L068P.indd 136 12/9/10 10:52:29 PM

13136

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny

Name

18

1818

18

18

1 81 8

18

12

12


CC.3.NF.3d

Lesson 68



4. 2 __ 8 2 __ 3

7. 5 __ 6 5 __ 8

5. 1 __ 8 1 __ 6

8. 4 __ 6 4 __ 8

6. 1 __ 4 1 __ 6

9. 3 __ 6 3 __ 4


1. 1 __ 8 1 __ 2 2. 3 __ 8 3 __

6 3. 2 __ 3 2 __

4 ,

,

,

,

.

.

. .

,


3_MNLAEWB575230_SE_L068P.indd 136 12/9/10 10:52:29 PM

15

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny

88 Measurement and Data

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny

Name

168

Solve Problems Using Data

Use the Favorite Hot Lunch bar graph for 1–3.

6. Is the number of students who get to school by car and bus greater than or less than the number of students who get to school by walking and biking? Explain.

7. What if 5 more students were asked and they get to school by walking? Do more students walk or ride a bike to school? Explain.

1. How many more students chose pizza than chose grilled cheese?

Think: Subtract the number of students who chose grilled cheese, 2, from the number of students who chose pizza, 11. 11 2 2 5 9

more students

2. How many students did not choose chicken patty?

students

3. How many fewer students chose grilled cheese than chose hot dog?

fewer students

Use the Ways to Get to School bar graph for 4–7.

4. How many more students walk than ride in a car to get to school?

more students

5. How many students walk and ride a bike combined?

students


9

21

6

3

10

greater than; Possible explanation: 4 1 12 5 16; 7 1 3 5 10; 14 . 10

12 students walk, 12 students ride. Possible explanation: the same number walk and ride.

2468

1012

HotDog

ChickenPatty

Pizza GrilledCheese

Nu

mb

er o

f Vo

tes

0

Lunch

Favorite Hot Lunch

2

4

6

8

10

14

12

Nu

mb

er o

f S

tud

ents

0

Transportation

Ways to Get to School

Car Bus Walk Bike

Lesson 84CC.3.MD.3

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny

Name

Measurement and Data 167

Lesson 84COMMON CORE STANDARD CC.3.MD.3

Lesson Objective: Solve one- and two-step compare problems using data represented in scaled bar graphs.Solve Problems Using Data

Use the Computer Center bar graph for 1–3.

1. How many more students use the computer center for homework

than for email? more students

2. How many students use the computer center for projects

and homework combined? students

3. Do more students use the computer center for projects or for email and games combined?

students

Projects Homework Email Games

Nu

mb

er o

f S

tud

ents

Activity

Computer Center

1416

1210

86420

You can use a model or write a number sentence to help you answer questions about data.

The bar graph shows the different ways students use the computer center after school. How many more students use the computer center for projects than for games?

One Way Find the bar for projects. The bar ends at 12. So, 12 students use the computer center for projects.

Find the bar for games. The bar ends halfway between 4 and 6. So, 5 students use the computer center for games. Count back along the scale to fi nd the difference.

Another Way Subtract to compare the number of students.

Think: There are 12 students who work on projects. There are 5 students who play games. Write a number sentence.

12 2 5 5 7

So, 7 more students use the computer center for projects than for games.

5

26

14for email and games;

About the MathA bar graph uses bars to represent categories of data. By applying the numerical scale on the graph, it is possible to identify the data value for each category. These values can then be used to solve problems about relationships among the categories. Using a bar graph to solve problems develops the ability to model with mathematics and to draw conclusions by analyzing relationships mathematically.

The LessonIntroduce Remind students that the bars on a bar graph represent data. Ask students to explain how to use the scale of a bar graph to find the data value that each bar represents. Tell students that they will learn how to use these data values to solve problems.

Teach Direct students’ attention to the Computer Center graph. Have students make general observations about the graph by asking questions about the heights of the bars, such as which bar is tallest and which bars are shorter than the Projects bar. Discuss that a problem can be solved in more than one way. Guide students through both solutions to the problem, showing them how to use the graph to count back along the scale and how to write a number sentence to solve the problem.

Practice Have students complete page 168. Point out to students that they must read each problem carefully and decide if they need to add or subtract the data values in order to solve the problem. Remind students that there is more than one way to solve each problem.


COMMON CORE STANDARDCC.3.MD.3

OBJECTIVESolve one- and two-step compare problems using data represented in scaled bar graphs.

ESSENTIAL QUESTIONHow can you solve problems using data represented in bar graphs?

VOCABULARY

MATERIALS

PREREQUISITESRead bar graphs.

Choose the appropriate operation to solve a problem.


3_MNLAEWB591087_TE_L084.indd 88 12/15/10 4:56:38 AM

16

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

nyName










students


Nu

mb

er o

f S

tud

ents

Activity

Computer Center

1416

121086420







12 2 5 5 7


5

26


3_MNLAEWB575230_SE_L084R.indd 167 12/15/10 4:27:39 AM

17

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny

Name










students


Nu

mb

er o

f S

tud

ents

Activity

Computer Center

1416

121086420







12 2 5 5 7


5

26


3_MNLAEWB575230_SE_L084R.indd 167 12/15/10 4:27:39 AM

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny

Name

168


Use the Favorite Hot Lunch bar graph for 1–3.

6. Is the number of students who get to school by car and bus greater than or less than the number of students who get to school by walking and biking? Explain.

7. What if 5 more students were asked and they get to school by walking? Do more students walk or ride a bike to school? Explain.

1. How many more students chose pizza than chose grilled cheese?

Think: Subtract the number of students who chose grilled cheese, 2, from the number of students who chose pizza, 11. 11 2 2 5 9

more students

2. How many students did not choose chicken patty?

students

3. How many fewer students chose grilled cheese than chose hot dog?

fewer students

Use the Ways to Get to School bar graph for 4–7.

4. How many more students walk than ride in a car to get to school?

more students

5. How many students walk and ride a bike combined?

students


9

21

6

3

10

greater than; Possible explanation: 4 1 12 5 16; 7 1 3 5 10; 14 . 10

12 students walk, 12 students ride. Possible explanation: the same number walk and ride.

2468

1012

HotDog

ChickenPatty

Pizza GrilledCheese

Nu

mb

er o

f Vo

tes

0

Lunch

Favorite Hot Lunch

2

4

6

8

10

14

12N

um

ber

of

Stu

den

ts

0

Transportation

Ways to Get to School

Car Bus Walk Bike

Lesson 84CC.3.MD.3

3_MNLAEWB575230_SE_L084P.indd 168 12/15/10 4:26:53 AM

18

The following pages from the On Core Assessment Guide support the student lessons presented earlier in this sampler:

Lesson 36: Problem Solving • Multiplication

Lesson 68: Compare Fractions with the Same Numerator

lesson 84: solve problems using data

Assessment Guide Sample Pages

19

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny

Name

36 Operations and Algebraic Thinking

Lesson 36CC.3.OA.8

5. Erin wants to plant seeds in pots. Each pot can have 4 or 6 seeds planted. She has a total of 22 seeds and wants to know how many different ways she can plant them. Explain how Erin could make and use a table to find the answer.

Bella makes game sets. Each game set has 3 decks of cards, 2 pairs of number cubes, and 4 notepads for keeping score.

Game Sets 1 2 3 4 5 6 n n

Decks of Cards 3 6 9 n n n n n

Pairs of Number Cubes 2 4 6 n n n n n

Notepads 4 8 12 n n n 28 32

1. How many decks of cards will Bella need if she makes 6 game sets?

A 18 C 6

B 9 D 3

2. Bella has 32 notepads. How many game sets can she make?

A 4 C 16

B 8 D 32

Todd has a photo album. Some pages can hold 1 photo, and some pages can hold 2 photos. In the table, Todd recorded all the ways he could place his photos in the album.

Pages with 1 Photo 0 2 4 6 8 10 12

Pages with 2 Photos 6 5 4 3 n 1 0

Total Photos n n n n n n n

3. How many total photos did Todd place in his album?

A 2 C 10

B 6 D 12

4. If Todd has 8 pages that hold 1 photo, how many pages that hold 2 photos does he need?

A 12 C 4

B 8 D 2

Erin could make a table with three rows. The top row would

show pots with 4 seeds. The second row would show pots with

6 seeds. The bottom row would show the total number of seeds,

which is 22. Erin could fi ll in the table with all the different

combinations to fi nd the different ways she can plant the seeds.

3_MNLAEAS590486_CC_L036T.indd 36 12/15/10 11:00:44 AM

20

Name

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny

68 Number and Operations–Fractions

CC.3.NF.3dLesson 68

1. Ted ran 1 __ 2 mile and Steve ran 1 __ 3 mile. Which of these compares the fractions correctly?

A 1 __ 2 , 1 __ 3

B 1 __ 3 . 1 __ 2

C 1 __ 3 , 1 __ 2

D 1 __ 2 5 1 __ 3

2. Martin had 2 bottles of water. One bottle was 3 __ 8 full. The other bottle was 3 __ 4 full. Which of these compares the fractions correctly?

A 3 __ 8 , 3 __ 4

B 3 __ 4 5 3 __

8

C 3 __ 4 , 3 __

8

D 3 __ 8 . 3 __

4

3. Sami read 2 __ 6 of her book. Danny read 2 __ 4 of the same book. Which of these compares the fractions correctly?

A 2 __ 4 5 2 __ 6

B 2 __ 6 . 2 __ 4

C 2 __ 4 , 2 __ 6

D 2 __ 6 , 2 __ 4

4. Emily ate 2 __ 8 of the pizza. Andy ate 2 __ 4 of the pizza. Which of these compares the fractions correctly?

A 2 __ 4 , 2 __

8

B 2 __ 8 , 2 __

4

C 2 __ 8 5 2 __

4

D 2 __ 8 . 2 __

4

5. Molly decorated 2 __ 3 of the cookies she baked. Abby decorated 2 __ 8 of the cookies. Who decorated the greater fraction of the cookies? Explain how you know.Molly decorated more cookies because 2 _ 3 is greater than 2 _ 8 .

If you divide a whole into 3 equal parts, the parts are larger than

if you divide it into 8 equal parts. Since both girls decorated

2 parts, the girl who decorated larger parts decorated more

cookies. Thirds are larger than eighths so Molly decorated more.

3_MNLAEAS590486_CC_L068T.indd Sec1:68 12/15/10 10:16:59 AM

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny

Name CC.3.MD.3Lesson 84


A biologist made a bar graph to show how many samples of each type of marine life she saw on a dive.

43210

Num

ber

ofM

arin

e Li

fe

Marine Life

Type of Marine Life

PufferFish

CowFish

Seahorse Seaweed

1. Of which type of marine life did the marine biologist see the fewest?

A Cow Fish C Seahorse

B Puffer Fish D Seaweed

2. How many more Cow Fish did the biologist see than Seahorses?

A 1 B 2 C 3 D 4

Nigel made a bar graph to show how many bushels of each type of orange are for sale at a fruit stand.

Type

of O

rang

e

Oranges for Sale

Number of Bushels

Navel

Pineapple

Temple

Valencia

0 2 4 6 8 10 12 14 16

3. How many more bushels of Pineapple oranges and Navel oranges are there than Temple oranges and Valencia oranges?

A 1 bushel

B 3 bushels

C 7 bushels

D 24 bushels

4. How would you use the graph to find out if there were more Navel and Pineapple oranges for sale or more Temple and Valencia oranges for sale?I would use the data in the graph and add the total

number of bushels of Navel and Pineapple oranges

for sale and then the number of Temple and Valencia

oranges for sale. By comparing the sums, I could tell

which groups of oranges there were more of.


21

© H

ough

ton

Miff

lin H

arco

urt

Pub

lishi

ng C

ompa

ny

Name CC.3.MD.3Lesson 84


A biologist made a bar graph to show how many samples of each type of marine life she saw on a dive.

43210

Num

ber

ofM

arin

e Li

fe

Marine Life

Type of Marine Life

PufferFish

CowFish

Seahorse Seaweed

1. Of which type of marine life did the marine biologist see the fewest?

A Cow Fish C Seahorse

B Puffer Fish D Seaweed

2. How many more Cow Fish did the biologist see than Seahorses?

A 1 B 2 C 3 D 4

Nigel made a bar graph to show how many bushels of each type of orange are for sale at a fruit stand.

Type

of O

rang

e

Oranges for Sale

Number of Bushels

Navel

Pineapple

Temple

Valencia

0 2 4 6 8 10 12 14 16

3. How many more bushels of Pineapple oranges and Navel oranges are there than Temple oranges and Valencia oranges?

A 1 bushel

B 3 bushels

C 7 bushels

D 24 bushels

4. How would you use the graph to find out if there were more Navel and Pineapple oranges for sale or more Temple and Valencia oranges for sale?I would use the data in the graph and add the total

number of bushels of Navel and Pineapple oranges

for sale and then the number of Temple and Valencia

oranges for sale. By comparing the sums, I could tell

which groups of oranges there were more of.


ExamView® is a registered trademark of eInstruction Corporation. © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Printed in the U.S.A. 03/11 MS15330 F-1480583

On Core MathematicsKindergarten–Grade 6

For more information, contact your sales representative at

800.462.6595

Houghton Mifflin Harcourt Alliance InitiativeComprehensive support for all your Common Core needs!

Professional Services and Training · Content

Curriculum Management · Data Systems

hmheducation.com/commoncore

Teacher ediTion and assessmenT Guide sampler On...

Documents

Transcript of Teacher ediTion and assessmenT Guide sampler On...