Check Your Readiness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2

1-1 Comparing and Ordering Integers 7.NS.1.b . . . . . . . . . . . . . . . . . . . . . .4

1-2a Activity Lab Hands On: Modeling Integer Addition and Subtraction 7.NS.1.a, 7.NS.1.b . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8

1-2 Adding and Subtracting Integers 7.NS.1.a, 7.NS.1.b, 7.NS.1.c, 7.NS.1.d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10

1-3a Activity Lab Hands On: Modeling Integer Multiplication 7.NS.2, 7.NS.2.a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15

1-3 Multiplying and Dividing Integers 7.NS.2, 7.NS.2.a, 7.NS.2.b . . . . . . . . .16• Vocabulary Builder: Learning New Math Terms, 20

Checkpoint Quiz 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20

1-4 Fractions and Decimals 7.NS.2.d, 7.EE.3 . . . . . . . . . . . . . . . . . . . . . . . . .21

1-5 Rational Numbers 7.NS.2.b, 7.NS.2.d . . . . . . . . . . . . . . . . . . . . . . . . . . . .26

1-6a Activity Lab Hands On: Modeling Addition and Subtraction of Rational Numbers 7.NS.1 . . . . . . . . . . . . . . . . . .30

1-6 Adding and Subtracting Rational Numbers 7.NS.1, 7.NS.1.b, 7.NS.1.c, 7.NS.1.d, 7.NS.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32

1-6b Activity Lab Data Analysis: Using Tables to Compare Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .36

Checkpoint Quiz 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .36

1-7 Multiplying Rational Numbers 7.NS.2, 7.NS.2.a, 7.NS.2.c, 7.NS.3 . . . . . . .37

1-8 Dividing Rational Numbers 7.NS.2, 7.NS.2.b, 7.NS.2.c, 7.NS.3 . . . . . . . . . .42• Guided Problem Solving: Choosing Operations, 47

Assessment and Test Prep

• Test-Taking Strategies: Writing Gridded Responses, 49• Chapter Review, 50• Chapter Test, 52• Test Prep: Reading Comprehension, 53

Integers and Rational Numbers

CHAPTER

1

x Contents

In this chapter, you will apply and

extend previous understandings of

operations with fractions to add,

subtract, multiply, and divide rational

numbers. You will also solve multistep

real-world and mathematical

problems with positive and negative

rational numbers.

The Number System7.NS.17.NS.1.a7.NS.1.b7.NS.1.c7.NS.1.d7.NS.27.NS.2.a7.NS.2.b7.NS.2.c7.NS.2.d7.NS.3

Expressions & Equations7.EE.3

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Check Your Readiness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54

2-1a Activity Lab Describing Patterns 7.EE.4 . . . . . . . . . . . . . . . . . . .56

2-1 Evaluating and Writing Algebraic Expressions 7.EE.4 . . . . . . . . . . . . .57

2-1b Activity Lab Technology: Using Spreadsheets 7.EE.4 . . . . . . . .61

2-2 Simplifying Expressions 7.EE.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .62

Checkpoint Quiz 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .66

2-3a Activity Lab Hands On: Modeling Equations 7.EE.4 . . . . . . . . .67

2-3 Solving One-Step Equations 7.EE.4 . . . . . . . . . . . . . . . . . . . . . . . . . . .68

2-3b Activity Lab Algebra Thinking: Keeping the Balance . . . . . . .73

2-4 Exploring Two-Step Equations 7.EE.4.a . . . . . . . . . . . . . . . . . . . . . . . .74

2-5a Activity Lab Hands On: Modeling Two-Step Equations 7.EE.4.a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .79

2-5 Solving Two-Step Equations (7.EE.3, 7.EE.4.a) . . . . . . . . . . . . . . . . . .80

Checkpoint Quiz 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .85• Guided Problem Solving: Practice Solving Problems, 86• Vocabulary Builder: High-Use Academic Words, 88

2-6 Solving Equations Involving the Distributive Property 7.EE.3, 7.EE.4.a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .89

Assessment and Test Prep

• Test-Taking Strategies: Writing Short Responses, 93• Chapter Review, 94• Chapter Test, 96• Test Prep: Cumulative Review, 97

EquationsCHAPTER

2

In this chapter, you will apply

properties of operations as strategies

to add, subtract, factor, and expand

linear expressions with rational

coeffi cients. You will also use variables

to represent quantities and construct

simple equations to solve problems.

Expressions & Equations7.EE.17.EE.37.EE.47.EE.4.a

Contents xi

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Check Your Readiness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .98

3-1 Graphing and Writing Inequalities 7.EE.4.b . . . . . . . . . . . . . . . . . . . .100

3-2 Solving Inequalities by Adding or Subtracting 7.EE.4.b . . . . . . . . . .104

Checkpoint Quiz 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .108

3-2b Activity Lab Data Analysis: Inequalities in Bar Graphs . . . . .108

3-3 Solving Inequalities by Multiplying or Dividing 7.EE.4.b . . . . . . . . .109• Guided Problem Solving: Writing Inequalities, 114

3-4 Solving Two-Step Inequalities 7.EE.4.b . . . . . . . . . . . . . . . . . . . . . . . .116

Assessment and Test Prep

• Test-Taking Strategies: Reading for Understanding, 121• Chapter Review, 122• Chapter Test, 124• Test Prep: Cumulative Review, 125

InequalitiesCHAPTER

3

xii Contents

In this chapter, you will extend

your understanding of the inverse

relationship of operations to solve

inequalities. You will use variables to

write expressions and solve real-

world and mathematical problems

by graphing, writing, and solving

inequalities. You will also develop

a more complete understanding of

variables and expressions as you

begin to see patterns in the structure

of inequalities.

Expressions & Equations7.EE.4.b

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4-1 Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .128

4-2 Unit Rates and Proportional Reasoning 7.RP.1 . . . . . . . . . . . . . . . . .132

4-2b Activity Lab Algebra Thinking: Using Conversion Factors 7.RP.1 . . . . . . . . . . . . . . . . . . . . . . . . . . .136

4-3 Proportions 7.RP.2, 7.RP.2.a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .137

Checkpoint Quiz 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .141

4-4a Activity Lab Data Collection: Using Proportions with Data 7.RP.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .142

4-4 Solving Proportions 7.RP.1, 7.RP.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . .143• Guided Problem Solving: Proportions and Equations, 148

4-5a Activity Lab Hands On: Exploring Similar Figures 7.G.1 . . . . .150

4-5 Similar Figures 7.RP.1, 7.RP.2, 7.G.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . .151

4-5b Activity Lab Technology: Drawing Similar Figures 7.RP.2 . . .155

4-6a Activity Lab Hands On: Scale Drawings and Models 7.G.1 . .156

4-6 Maps and Scale Drawings 7.G.1, 7.RP.1 . . . . . . . . . . . . . . . . . . . . . . . .157

4-6b Activity Lab: Plan a Trip 7.G.1 . . . . . . . . . . . . . . . . . . . . . . . . .162

Checkpoint Quiz 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .163• Vocabulary Builder: Learning Vocabulary, 163

4-7a Activity Lab Graphs and Proportional Relationships 7.RP.2.a, 7.RP.2.d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .164

4-7 Proportional Relationships 7.RP.2.a, 7.RP.2.b, 7.RP.2.c, 7.RP.2.d . . . . . . .165

Assessment and Test Prep

• Test-Taking Strategies: Using a Variable, 169• Chapter Review, 170• Chapter Test, 172• Test Prep: Reading Comprehension, 173

Ratios, Rates, and Proportions

CHAPTER

4

In this chapter, you will compute

unit rates associated with ratios of

fractions. You will also recognize and

represent proportional relationships

between quantities and solve

problems involving scale drawings of

geometric fi gures.

Ratios & Proportional Relationships

7.RP.17.RP.27.RP.2.a7.RP.2.b7.RP.2.c7.RP.2.d

Geometry7.G.1

Contents xiiiContents xiii

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5-1 Percents, Fractions, and Decimals 7.EE.3 . . . . . . . . . . . . . . . . . . . . . .176

5-2 Solving Percent Problems Using Proportions 7.RP.3 . . . . . . . . . . . . .181

5-3 Solving Percent Problems Using Equations 7.RP.3 . . . . . . . . . . . . . . .185

Checkpoint Quiz 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .189• Guided Problem Solving: Solving Percent Problems, 190

5-4 Applications of Percents 7.RP.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .192

5-4b Activity Lab Algebra Thinking: Percent Equations 7.RP.3 . . .197

5-5 Simple Interest 7.RP.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .198

Checkpoint Quiz 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .201

5-6a Activity Lab Data Analysis: Exploring Percent of Change 7.RP.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .201

5-6 Finding Percent of Change 7.RP.3, 7.EE.2 . . . . . . . . . . . . . . . . . . . . . . .202

Assessment and Test Prep

• Test-Taking Strategies: Working Backward, 207• Chapter Review, 208• Chapter Test, 210• Test Prep: Cumulative Review, 211

PercentsCHAPTER

5

xiv Contents

In this chapter, you will convert

between forms of rational numbers

and use proportional relationships

to solve multistep ratio and percent

problems (e.g., simple interest, tax,

markups and markdowns, gratuities

and commissions, fees, percent

increase and decrease, percent error).

Ratios & Proportional Relationships

7.RP.3

Expressions & Equations7.EE.27.EE.3

Contents

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6-1a Activity Lab Hands On: Drawing Geometric Figures 7.G.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .214

6-1 Angle Measures 7.G.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .215

6-1b Activity Lab Hands On: Drawing Triangles 7.G.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .220

6-2a Activity Lab Hands On: Generating Formulas for Area 7.G.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .222

6-2 Area of a Parallelogram 7.G.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .223

Checkpoint Quiz 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .227

6-3 Area of a Triangle 7.G.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .228

6-4 Areas of Other Figures 7.G.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .232

Checkpoint Quiz 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .237

6-5a Activity Lab Hands On: Modeling a Circle 7.G.4 . . . . . . . . . . .237

6-5 Circumference and Area of a Circle 7.G.4 . . . . . . . . . . . . . . . . . . . . . .238• Guided Problem Solving: Areas of Irregular Figures, 243

Assessment and Test Prep

• Test-Taking Strategies: Measuring to Solve, 245• Chapter Review, 246• Chapter Test, 248• Test Prep: Cumulative Review, 249

Geometry and AreaCHAPTER

6

In this chapter, you will draw,

construct, and describe geometrical

fi gures and describe the relationships

between them. You will also solve

real-life and mathematical problems

involving angle measure and area.

Geometry7.G.27.G.47.G.57.G.6

Contents xv

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Check Your Readiness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .250

7-1 Three-Dimensional Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .252

7-2 Surface Areas of Prisms and Cylinders 7.G.6 . . . . . . . . . . . . . . . . . . .256

7-2b Activity Lab Algebra Thinking: Patterns in 3-Dimensional Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .261

Checkpoint Quiz 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .262

7-3 Volumes of Prisms and Cylinders 7.G.6 . . . . . . . . . . . . . . . . . . . . . . .263

7-3b Activity Lab Hands On: Generating Formulas for Volume 7.G.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .268

• Guided Problem Solving: Practice Solving Problems, 269

7-4 Cross Sections 7.G.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .271

Assessment and Test Prep

• Test-Taking Strategies: Drawing a Picture, 275• Chapter Review, 276• Chapter Test, 278• Test Prep: Cumulative Review, 279

Surface Area and VolumeCHAPTER

7

xvi Contents

In this chapter, you will solve real-

world and mathematical problems

involving volume and surface area of

three-dimensional objects. You will

also describe the two-dimensional

fi gures that result from slicing three-

dimensional fi gures.

Geometry7.G.37.G.6

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8-1 Random Samples and Surveys 7.SP.1 . . . . . . . . . . . . . . . . . . . . . . . . .282

8-2 Estimating Population Size 7.SP.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . .286

Checkpoint Quiz 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .289• Guided Problem Solving: Describing Data, 290

8-3 Inferences 7.SP.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .292• Vocabulary Builder: High-Use Academic Words, 296

8-4 Data Variability 7.SP.3, 7.SP.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .297

Assessment and Test Prep

• Test-Taking Strategies: Interpreting Data, 301• Chapter Review, 302• Chapter Test, 304• Test Prep: Reading Comprehension, 305

Analyzing DataCHAPTER

8

In this chapter, you will use random

sampling to draw inferences about

a population. You will also draw

informal comparative inferences

about two populations and

understand the effect sampling has

on data collection.

Statistics & Probability7.SP.17.SP.27.SP.37.SP.4

Contents xvii

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Check Your Readiness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .306

9-1 Probability 7.SP.5, 7.SP.7.a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .308

9-2a Activity Lab Hands On: Exploring Probability 7.SP.7, 7.SP.7.b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .312

9-2 Experimental Probability 7.SP.6, 7.SP.7, 7.SP.7.b . . . . . . . . . . . . . . . . . .313

9-2b Activity Lab Technology: Random Numbers 7.SP.7, 7.SP.7.b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .317

Checkpoint Quiz 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .318

9-3 Sample Spaces 7.SP.8, 7.SP.8.b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .319

9-3b Activity Lab Data Analysis: Using Data to Predict 7.SP.8, 7.SP.8.b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .324

9-4a Activity Lab: Exploring Multiple Events 7.SP.8, 7.SP.8.a, 7.SP.8.b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .325

9-4 Compound Events 7.SP.8, 7.SP.8.a, 7.SP.8.b . . . . . . . . . . . . . . . . . . . . . .326

Checkpoint Quiz 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .331• Vocabulary Builder: High-Use Academic Words, 332• Guided Problem Solving: Practice With Probability, 333

9-5 Simulating Compound Events 7.SP.8.c . . . . . . . . . . . . . . . . . . . . . . . .335

Assessment and Test Prep

• Test-Taking Strategies: Eliminating Answers, 339• Chapter Review, 340• Chapter Test, 342• Test Prep: Cumulative Review, 343

ProbabilityCHAPTER

9

xviii Contents

In this chapter, you will investigate

chance processes and develop, use,

and evaluate probability models.

You will also compare theoretical

probabilities of simple and compound

events to observed frequencies.

Statistics & Probability7.SP.57.SP.67.SP.77.SP.7.a7.SP.7.b7.SP.87.SP.8.a7.SP.8.b7.SP.8.c

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