chapter real numbers and 1 the coordinate...

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

1-1 Rational Numbers 8.NS.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4

1-1b Activity Lab Repeating Decimals 8.NS.1 . . . . . . . . . . . . . . . . . . .8

1-2 Irrational Numbers and Square Roots 8.NS.1, 8.NS.2, 8.EE.2 . . . . . . . . . .9

1-3 Cube Roots 8.EE.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14

Checkpoint Quiz 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18

1-4a Activity Lab Hands On: Exploring the Pythagorean Theorem 8.G.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19

1-4 The Pythagorean Theorem 8.G.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20

1-4b Activity Lab Algebra Thinking: Proving the Pythagorean Theorem 8.G.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24

• Guided Problem Solving: Squares and Square Roots, 25

1-5 Using the Pythagorean Theorem 8.G.7 . . . . . . . . . . . . . . . . . . . . . . . .27

1-6 Converse of the Pythagorean Theorem 8.G.6 . . . . . . . . . . . . . . . . . . .31

1-6b Activity Lab Algebra Thinking: Proving the Converse of the Pythagorean Theorem 8.G.6 . . . . . . . . . . . . . . . . . . . . . . . . .35

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

1-7 Distance in the Coordinate Plane 8.G.7, 8.G.8 . . . . . . . . . . . . . . . . . . . .37

Assessment and Test Prep

• Test-Taking Strategies: Writing Gridded Responses, 41• Chapter Review, 42• Chapter Test, 44• Test Prep: Reading Comprehension, 45

Real Numbers and the Coordinate Plane

CHAPTER

1

x Contents

In this chapter, you will develop an

understanding of irrational numbers

and approximate them using rational

numbers. You will use square roots

and cube roots to express solutions

to equations. Additionally, you will

apply the Pythagorean Theorem and

its converse to solve real-world and

mathematical problems involving

unknown side lengths of right

triangles.

The Number System8.NS.18.NS.2

Expressions & Equations8.EE.2

Geometry8.G.68.G.78.G.8

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PEARSON LEARNING SOLUTIONS Not for resale or distribution

Check Your Readiness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .46

2-1a Activity Lab Hands On: Modeling Multi-Step Equations 8.EE.7, 8.EE.7.b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .48

2-1 Solving Two-Step Equations 8.EE.7, 8.EE.7.b . . . . . . . . . . . . . . . . . . . . .49

2-2a Activity Lab Hands On: Modeling Expressions 8.EE.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53

2-2 Simplifying Algebraic Expressions 8.EE.7.b . . . . . . . . . . . . . . . . . . . . .54

Checkpoint Quiz 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58

2-3 Solving Multi-Step Equations 8.EE.7, 8.EE.7.b . . . . . . . . . . . . . . . . . . . .59• Vocabulary Builder: High-Use Academic Words, 64

2-4 Solving Equations With Variables on Both Sides 8.EE.7, 8.EE.7.b . . . .65• Guided Problem Solving: Writing Equations, 68

Checkpoint Quiz 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .70

2-5 Types of Solutions of Linear Equations 8.EE.7, 8.EE.7.a, 8.EE.7.b . . . . . .71


• Test-Taking Strategies: Reading for Understanding, 75• Chapter Review, 76• Chapter Test, 78• Test Prep: Cumulative Review, 79

Solving Linear EquationsCHAPTER

2

In this chapter, you will solve linear

equations with rational number

coeffi cients. You will also simplify

equations to identify the different

types of solutions of linear equations,

such as having no solutions, one

solution, or infi nitely many solutions.

Expressions & Equations8.EE.78.EE.7.a8.EE.7.b

Contents xi

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Check Your Readiness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .80

3-1 Relating Graphs to Events 8.F.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .82

3-1b Activity Lab Data Collection: Changing Graphs 8.F.5 . . . . . . .86

3-2 Functions 8.F.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .87

Checkpoint Quiz 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .91

3-3 Proportional Relationships 8.EE.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .92

3-3b Activity Lab Proportional Relationships in Graphs . . . . . . . . .96• Guided Problem Solving: Using Data and Graphs, 97

3-4 Linear Functions 8.F.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .99• Vocabulary Builder: Making Word Cards, 103

3-5 Nonlinear Functions 8.F.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .104

3-5b Activity Lab Data Analysis: Using Linear and Nonlinear Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .108


• Test-Taking Strategies: Using a Variable, 109• Chapter Review, 110• Chapter Test, 112• Test Prep: Reading Comprehension, 113

Introduction to FunctionsCHAPTER

3

xii Contents

In this chapter, you will defi ne and

evaluate functions, and use functions

to model relationships between

quantities. You will also analyze

linear graphs to express qualitative

relationships between two quantities.

In addition, you will understand and

interpret linear functions, and give

examples of nonlinear functions.


Functions8.F.18.F.38.F.5

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Check Your Readiness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .114

4-1a Activity Lab Rate of Change 8.EE.5, 8.F.4 . . . . . . . . . . . . . . . . .116

4-1 Understanding Slope 8.EE.6, 8.F.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . .117

4-1b Activity Lab Slope of Parallel and Perpendicular Lines . . . . .121

4-2a Activity Lab Technology: Graphing Equations 8.F.1 . . . . . . . .122

4-2 Graphing Linear Functions 8.EE.6, 8.F.1, 8.F.3, 8.F.4 . . . . . . . . . . . . . . .123

4-3 Writing Rules for Linear Functions 8.F.4 . . . . . . . . . . . . . . . . . . . . . .128

4-3b Activity Lab Data Analysis: Changing Representations 8.F.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .132

Checkpoint Quiz 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .133

4-4 Comparing Functions 8.F.2, 8.EE.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . .134• Guided Problem Solving: Writing Rules for Linear

Functions, 139


• Test-Taking Strategies: Working Backwards, 141• Chapter Review, 142• Chapter Test, 144• Test Prep: Cumulative Review, 145

Graphing FunctionsCHAPTER

4

In this chapter, you will graph

proportional relationships and

interpret the unit rate as the slope

of the graph. You will also write

and graph functions to model linear

relationships and compare two

functions represented in different

ways.

Expressions & Equations8.EE.58.EE.6

Functions8.F.18.F.28.F.38.F.4

Contents xiii

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5-1 Solving Systems by Graphing 8.EE.8.a, 8.EE.8.b, 8.EE.8.c . . . . . . . . . . .148

5-1b Activity Lab Systems with Infi nitely Many Solutions or No Solution 8.EE.8.b . . . . . . . . . . . . . . . . . . . . .152

5-2 Solving Systems by Substitution 8.EE.8.b, 8.EE.8.c . . . . . . . . . . . . . . .153

5-3 Solving Systems by Elimination 8.EE.8.b, 8.EE.8.c . . . . . . . . . . . . . . . .158

5-3b Activity Lab Solving Systems by Inspection 8.EE.8.b . . . . . . . .162• Guided Problem Solving: Solving Systems of Equations, 163

Checkpoint Quiz 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .165• Vocabulary Builder: Learning Vocabulary, 165

5-4 Systems in the Real World 8.EE.8.b, 8.EE.8.c . . . . . . . . . . . . . . . . . . . .166


• Test-Taking Strategies: Writing Short Responses, 171• Chapter Review, 172• Chapter Test, 174• Test Prep: Reading Comprehension, 175

Systems of Linear Equations

CHAPTER

5

xiv Contents

In this chapter, you will analyze

and solve systems of linear equations

algebraically, and estimate solutions

by graphing the equations. You will

also model and solve real-world

problems using two linear equations.

Expressions & Equations8.EE.8.a8.EE.8.b8.EE.8.c

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6-1 Scientifi c Notation 8.EE.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .178

6-1b Activity Lab Data Analysis: Writing Measurements 8.EE.3 . .182

6-2a Activity Lab Exploring Exponents 8.EE.1 . . . . . . . . . . . . . . . . .183

6-2 Exponents and Multiplication 8.EE.1 . . . . . . . . . . . . . . . . . . . . . . . . .184

6-3 Multiplying with Scientifi c Notation 8.EE.4 . . . . . . . . . . . . . . . . . . . .188

6-3b Activity Lab Technology: Calculations with Scientifi c Notation 8.EE.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .192

Checkpoint Quiz 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .193

6-4 Exponents and Division 8.EE.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .194

6-4b Activity Lab Power Rules 8.EE.1 . . . . . . . . . . . . . . . . . . . . . . . .199• Guided Problem Solving: Solving Equations, 200

6-5 Dividing with Scientifi c Notation 8.EE.3, 8.EE.4 . . . . . . . . . . . . . . . . .202


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

ExponentsCHAPTER

6

In this chapter, you will develop and

apply properties of integer exponents,

and use numbers expressed as a

single digit times an integer power

of 10 to estimate very large or very

small quantities. You will also perform

operations with numbers expressed in

scientifi c notation.

Expressions & Equations8.EE.18.EE.38.EE.4

Contents xv

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7-1 Pairs of Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .214

7-2 Angles and Parallel Lines 8.G.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .218

7-3 Congruent Figures 8.G.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .222

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

7-4 Similar Figures 8.G.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .228

7-5 Proving Triangles Similar 8.G.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .232

7-5b Activity Lab Slope and Similar Triangles 8.EE.6 . . . . . . . . . . .236

Checkpoint Quiz 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .238

7-6a Activity Lab Angle Sums 8.G.5 . . . . . . . . . . . . . . . . . . . . . . . . .239

7-6 Angles and Polygons 8.G.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .240• Vocabulary Builder: Using Concept Maps, 244• Guided Problem Solving: Finding Angles, 245


• Test-Taking Strategies: Drawing a Picture, 247• Chapter Review, 248• Chapter Test, 250• Test Prep: Cumulative Review, 251

An Introduction to Geometry

CHAPTER

7

xvi Contents

In this chapter, you will develop an

understanding of the congruence and

similarity of two-dimensional fi gures.

You will also use informal arguments

to establish facts about the sum of

the angles of a triangle, the exterior

angle of triangles, and the angles

created when parallel lines are cut by

a transversal.


Geometry8.G.28.G.48.G.5

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8-1 Translations 8.G.1.a, 8.G.1.b, 8.G.1.c, 8.G.3 . . . . . . . . . . . . . . . . . . . . . . .254

8-2a Activity Lab Hands On: Exploring Refl ections 8.G.1.a, 8.G.1.b, 8.G.1.c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .258

8-2 Refl ections and Symmetry 8.G.1.a, 8.G.1.b, 8.G.1.c, 8.G.3 . . . . . . . . . . .259

Checkpoint Quiz 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .263

8-3a Activity Lab Hands On: Exploring Rotations 8.G.1.a, 8.G.1.b, 8.G.1.c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .264

8-3 Rotations 8.G.1.a, 8.G.1.b, 8.G.1.c, 8.G.3 . . . . . . . . . . . . . . . . . . . . . . . . .265

8-4 Transformations and Congruence 8.G.2 . . . . . . . . . . . . . . . . . . . . . . .269• Vocabulary Builder: High-Use Academic Words, 274

Checkpoint Quiz 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .275

8-5a Activity Lab Exploring Dilations 8.G.3, 8.G.4 . . . . . . . . . . . . . .276

8-5 Dilations 8.G.3, 8.G.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .277

8-5b Activity Lab Hands On: Technology: Geometry Software and Dilations 8.G.3, 8.G.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .281

8-6 Transformations and Similarity 8.G.4 . . . . . . . . . . . . . . . . . . . . . . . . .282• Guided Problem Solving: Transformations, 287


• Test-Taking Strategies: Answering the Question Asked, 289• Chapter Review, 290• Chapter Test, 292• Test Prep: Reading Comprehension, 293

TransformationsCHAPTER

8

In this chapter, you will explore

the behavior of two-dimensional

shapes under translations, rotations,

refl ections, and dilations. You will then

apply the understandings to concepts

of congruence and similarity and their

relationship to transformations.

Geometry8.G.1.a8.G.1.b8.G.1.c8.G.38.G.4

Reading Comprehension, 293

Contents xvii




9-1 Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .296

9-2a Activity Lab Hands On: Modeling Volume 8.G.9 . . . . . . . . . .300

9-2 Volumes of Prisms and Cylinders 8.G.7, 8.G.9 . . . . . . . . . . . . . . . . . . .301• Guided Problem Solving: Using Formulas, 306

Checkpoint Quiz 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .308

9-3a Activity Lab Finding Volume Using Models 8.G.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .308

9-3 Volumes of Pyramids and Cones 8.G.9 . . . . . . . . . . . . . . . . . . . . . . . .309

9-4 Spheres 8.G.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .313

Checkpoint Quiz 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .317

9-5a Activity Lab Changing Dimensions 8.G.9 . . . . . . . . . . . . . . . .318

9-5 Exploring Similar Solids 8.G.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .319


• Test-Taking Strategies: Eliminating Answers, 323• Chapter Review, 324• Chapter Test, 326• Test Prep: Reading Comprehension, 327

Geometry and Measurement

CHAPTER

9

xviii Contents

In this chapter, you will solve

real-world and mathematical

problems involving the volume of

cylinders, cones, and spheres. You

will also apply your understanding

of the Pythagorean Theorem to

fi nd unknown side lengths of right

triangles when determining the

volume of three-dimensional fi gures.

Geometry8.G.78.G.9




10-1a Activity Lab Data Collection: Scatter Plots 8.SP.1 . . . . . . . . .330

10-1 Scatter Plots 8.SP.1, 8.SP.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .331

10-2 Analyzing Scatter Plots 8.SP.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .335

Checkpoint Quiz 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .339

10-3 Modeling Data With Lines 8.SP.2, 8.SP.3 . . . . . . . . . . . . . . . . . . . . . . .340• Guided Problem Solving: Equations and Graphs, 345

10-4 Two-Way Tables 8.SP.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .347


• Test-Taking Strategies: Measuring to Solve, 351• Chapter Review, 352• Chapter Test, 354• Test Prep: Cumulative Review, 355

Data AnalysisCHAPTER

10

In this chapter, you will construct

and interpret scatter plots for

bivariate measurement data to

investigate patterns of association

between two quantitative variables.

You will also construct and interpret a

two-way table summarizing data on

two categorical variables collected on

the same subjects.

Statistics and Probability8.SP.18.SP.28.SP.38.SP.4

Contents xix

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chapter real numbers and 1 the coordinate...

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