Edition Course 3 MATHEMATICS - Pearson Education

Prentice Hall

2013

Edition

Course 3

MATHEMATICS Common Core

Charles Illingworth McNemar

Mills Ramirez Reeves

Taken from: Prentice Hall Mathematics, Course 3, Global Edition by Randall I. Charles, Mark Illingworth, Bonnie McNemar,

Darwin Mills, Alma Ramirez, and Andy Reeves Prentice Hall Mathematics, Common Core, Course 3, Student Edition

CHAPTER

1

Real Numbers and the Coordinate Plane

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 System 8.NS.1 8.NS.2

Expressions & Equations 8.EE.2

Geometry 8.G.6 8.G.7 8.G.8

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

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CHAPTER

2

Solving Linear Equations

In this chapter, you will solve linear equations with rational number coefficients. You will also simplify equations to identify the different types of solutions of linear equations, such as having no solutions, one solution, or infinitely many solutions.

Expressions & Equations 8.EE.7 8.EE.7.a 8.EE.7.b

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

Assessment and Test Prep

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

Contents xi

CHAPTER

3

Introduction to Functions

In this chapter, you will define 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.

Expressions & Equations 8.EE.5

Functions 8.F.1 8.F.3 8.F.5

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

Assessment and Test Prep

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

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CHAPTER

4

Graphing Functions

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 & Equations 8.EE.5 8.EE.6

Functions 8.F.1 8.F.2 8.F.3 8.F.4

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

Assessment and Test Prep

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

Contents xiii

CHAPTER

5

Systems of Linear Equations

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 & Equations 8.EE.8.a 8.EE.8.b 8.EE.8.c

Check Your Readiness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .146 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 Infinitely 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

Assessment and Test Prep

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

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CHAPTER

6

Exponents

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 scientific notation.

Expressions & Equations 8.EE.1 8.EE.3 8.EE.4

Check Your Readiness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .176 6-1 Scientific 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 Scientific Notation 8.EE.4. . . . . . . . . . . . . . . . . . . .188 6-3b Activity Lab Technology: Calculations with

Scientific 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 Scientific Notation 8.EE.3, 8.EE.4 . . . . . . . . . . . . . . . . .202

Assessment and Test Prep

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

Contents xv

CHAPTER

7

An Introduction to Geometry

In this chapter, you will develop an understanding of the congruence and similarity of two-dimensional figures. 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.

Expressions & Equations 8.EE.6

Geometry 8.G.2 8.G.4 8.G.5

Check Your Readiness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .212 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

Assessment and Test Prep

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

xvi Contents

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