Algebra and Integers -...

Table of Contents

Algebra and IntegersChapter The Tools of Algebra 4

Getting Started ...................................................................5

1-1 Using a Problem-Solving Plan.........................................6

Reading Mathematics: Translating Expressions Into Words....................................................................11

1-2 Numbers and Expressions .............................................12

1-3 Variables and Expressions..............................................17

Practice Quiz 1: Lessons 1-1 through 1-3 ....................21

Spreadsheet Investigation: Expressions and Spreadsheets.........................................................22

1-4 Properties ..........................................................................23

1-5 Variables and Equations .................................................28

Practice Quiz 2: Lessons 1-4 and 1-5............................32

1-6 Ordered Pairs and Relations..........................................33

Algebra Activity: Scatter Plots ......................................39

1-7 Scatter Plots ......................................................................40

Graphing Calculator Investigation: Scatter Plots .....45

Study Guide and Review ..............................................47

Practice Test.....................................................................51

Standardized Test Practice...........................................52

• Introduction 3

• Follow-Ups 43, 79, 135

• Culmination 136

Snapshots 3, 8, 16

Standardized Test Practice• Multiple Choice 10, 16, 21, 27, 29, 30, 32, 38, 44,

51, 52

• Short Response/Grid In 53

• Extended Response 53Study Organizer 5

Reading and Writing Mathematics• Translating Expressions into Words 11

• Reading Math Tips 17, 23, 24

• Writing in Math 10, 16, 21, 27, 32, 37, 44

Prerequisite Skills• Getting Started 5

• Getting Ready for the Next Lesson 10, 16, 21, 27, 32, 38

Lesson 1-2, page 15

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Unit 1Unit 1

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Chapter Integers 54

Getting Started .................................................................55

2-1 Integers and Absolute Value..........................................56

Algebra Activity: Adding Integers ...............................62

2-2 Adding Integers...............................................................64

Reading Mathematics: Learning MathematicsVocabulary....................................................................69

2-3 Subtracting Integers ........................................................70

Practice Quiz 1: Lessons 2-1 through 2-3 ....................74

2-4 Multiplying Integers .......................................................75

2-5 Dividing Integers.............................................................80

Practice Quiz 2: Lessons 2-4 and 2-5............................84

2-6 The Coordinate System ..................................................85

Study Guide and Review ..............................................90

Practice Test.....................................................................93

Standardized Test Practice...........................................94


• Getting Ready for the Next Lesson61, 68, 74, 79, 84

Study Organizer 55

Reading and WritingMathematics• Learning Mathematics Vocabulary 69

• Reading Math Tips 56, 57, 64, 75,80, 88

• Writing in Math 61, 68, 74, 79,84, 89

Standardized Test Practice• Multiple Choice 61, 68, 74, 76, 77,

79, 84, 89, 93, 94


• Extended Response 95

Lesson 2-4, page 78Snapshots 60

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Unit 1Unit 1

Chapter Equations 96

Getting Started .................................................................97

3-1 The Distributive Property ..............................................98

3-2 Simplifying Algebraic Expressions.............................103

Practice Quiz 1: Lessons 3-1 and 3-2 .........................107

Algebra Activity: Solving Equations Using Algebra Tiles ..............................................................108

3-3 Solving Equations by Adding or Subtracting...........110

3-4 Solving Equations by Multiplying or Dividing........115

3-5 Solving Two-Step Equations........................................120

Reading Mathematics: Translating Verbal Problems into Equations..........................................125

3-6 Writing Two-Step Equations........................................126

Practice Quiz 2: Lessons 3-3 through 3-6 ..................130

3-7 Using Formulas .............................................................131

Spreadsheet Investigation: Perimeter and Area....137

Study Guide and Review ............................................138

Practice Test ..................................................................141

Standardized Test Practice ........................................142

Snapshots 101

Standardized Test Practice• Multiple Choice 102, 107, 112, 113, 114, 119, 124,

130, 136, 141, 142

• Short Response/Grid In 124, 143


Study Organizer 97

Reading and Writing Mathematics• Translating Verbal Problems into Equations 125

• Reading Math Tips 98, 103

• Writing in Math 101, 106, 114, 119, 123, 130, 136


• Getting Ready for the Next Lesson 102, 107, 114, 119,124, 130

Lesson 3-6, page 127

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Algebra and Rational Numbers

Chapter Factors and Fractions 146

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• Introduction 145

• Follow-Ups 173, 242, 301

• Culmination 314


• Getting Ready for the Next Lesson152, 157, 163, 168, 173, 179, 185

Study Organizer 147

Reading and WritingMathematics• Powers 174

• Reading Math Tips 148, 149, 150,159, 177

• Writing in Math 152, 157, 162,168, 173, 179, 184, 190

Standardized Test Practice• Multiple Choice 152, 157, 163,

168, 171, 173, 179, 184, 190,195, 196



Snapshots 145, 156


Getting Started...............................................................147

4-1 Factors and Monomials ................................................148

4-2 Powers and Exponents .................................................153

Algebra Activity: Base 2...............................................158

4-3 Prime Factorization.......................................................159


4-4 Greatest Common Factor (GCF) .................................164

4-5 Simplifying Algebraic Fractions..................................169

Reading Mathematics: Powers..................................174

4-6 Multiplying and Dividing Monomials.......................175

Algebra Activity: A Half-Life Simulation..................180

4-7 Negative Exponents......................................................181


4-8 Scientific Notation.........................................................186


Practice Test ..................................................................195


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Unit 2Unit 2

Chapter Rational Numbers 198

Getting Started...............................................................199

5-1 Writing Fractions as Decimals.....................................200

5-2 Rational Numbers .........................................................205

5-3 Multiplying Rational Numbers...................................210

5-4 Dividing Rational Numbers ........................................215

5-5 Adding and Subtracting Like Fractions ....................220


Reading Mathematics: Factors and Multiples ........225

5-6 Least Common Multiple ..............................................226

Algebra Activity: Juniper Green.................................231

5-7 Adding and Subtracting Unlike Fractions ................232

Algebra Activity: Analyzing Data ..............................237

5-8 Measures of Central Tendency....................................238

Graphing Calculator Investigation: Mean and Median................................................................243

5-9 Solving Equations with Rational Numbers...............244


5-10 Arithmetic and Geometric Sequences........................249

Algebra Activity: Fibonacci Sequence .......................253


Practice Test ..................................................................259


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Snapshots 203, 213


240, 241, 242, 247, 252, 259, 260



Study Organizer 199

Reading and Writing Mathematics• Factors and Multiples 225

• Reading Math Tips 200, 205, 206, 215

• Writing in Math 204, 209, 214, 219, 223, 230, 236,242, 247, 251


• Getting Ready for the Next Lesson 204, 209, 214, 219,224, 230, 236, 242,248

Algebra Activity, page 253

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Unit 2Unit 2

Chapter Ratio, Proportion, and Percent 262

Getting Started...............................................................263

6-1 Ratios and Rates ............................................................264

Reading Mathematics: Making Comparisons ........269

6-2 Using Proportions .........................................................270

Algebra Activity: Capture-Recapture ........................275

6-3 Scale Drawings and Models ........................................276

6-4 Fractions, Decimals, and Percents ..............................281

Algebra Activity: Using a Percent Model .................286

6-5 Using the Percent Proportion ......................................288


6-6 Finding Percents Mentally ...........................................293

6-7 Using Percent Equations ..............................................298

Spreadsheet Investigation: Compound Interest....303

6-8 Percent of Change .........................................................304


Algebra Activity: Taking a Survey .............................309

6-9 Probability and Predictions .........................................310

Graphing Calculator Activity: Probability Simulation ..................................................................315


Practice Test ..................................................................321


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Snapshots 289, 290, 312, 314


305, 306, 308, 314, 321, 322



Study Organizer 263

Reading and Writing Mathematics• Making Comparisons 269


• Writing in Math 268, 274, 280, 285, 292, 297, 302,307, 314


• Getting Ready for the Next Lesson 268, 274, 280, 285,292, 297, 302, 308


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Linear Equations,Inequalities, and Functions

Chapter Equations and Inequalities 326

Getting Started...............................................................327

Algebra Activity: Equations with Variables on Each Side ....................................................................328

7-1 Solving Equations with Variables on Each Side.......330

7-2 Solving Equations with Grouping Symbols..............334

Practice Quiz 1: Lessons 7-1 and 7-2 .........................338

Reading Mathematics: Meanings of At Mostand At Least................................................................339

7-3 Inequalities .....................................................................340

7-4 Solving Inequalities by Adding or Subtracting ........345

7-5 Solving Inequalities by Multiplying or Dividing.....350


7-6 Solving Multi-Step Inequalities...................................355


Practice Test ..................................................................363




Study Organizer 327

Reading and WritingMathematics• Meanings of At Most and At Least

339

• Reading Math Tips 341

• Writing in Math 333, 338, 344,349, 354, 359


349, 351, 353, 354, 359, 363, 364



Snapshots 325, 343


• Follow-Ups 333, 411

• Culmination 422


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Unit 3Unit 3

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Chapter Functions and Graphing 366

Getting Started...............................................................367

Algebra Activity: Input and Output ..........................368

8-1 Functions ........................................................................369

Graphing Calculator Investigation: Function Tables ..........................................................................374

8-2 Linear Equations in Two Variables.............................375

Reading Mathematics: Language of Functions ......380

8-3 Graphing Linear Equations Using Intercepts ...........381

Algebra Activity: It’s All Downhill ............................386

8-4 Slope ................................................................................387

Algebra Activity: Slope and Rate of Change............392

8-5 Rate of Change...............................................................393


8-6 Slope-Intercept Form ....................................................398

Graphing Calculator Investigation: Families of Graphs....................................................................402

8-7 Writing Linear Equations.............................................404

8-8 Best-Fit Lines..................................................................409

8-9 Solving Systems of Equations .....................................414


8-10 Graphing Inequalities ...................................................419

Graphing Calculator Investigation: GraphingInequalities.................................................................423


Practice Test ..................................................................429



• Getting Ready for the Next Lesson373, 379, 385, 391, 397, 401,408, 413, 418

Study Organizer 367

Reading and WritingMathematics• Language of Functions 380


• Writing in Math 373, 379, 385,391, 397, 401, 408, 412, 418, 422


389, 390, 391, 397, 401, 408,413, 418, 422, 429, 430




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Applying Algebra to Geometry

Chapter Real Numbers and Right Triangles 434

Getting Started...............................................................435

9-1 Squares and Square Roots............................................436

9-2 The Real Number System ............................................441

Reading Mathematics: Learning Geometry Vocabulary .................................................................446

9-3 Angles .............................................................................447


Spreadsheet Investigation: Circle Graphs andSpreadsheets ............................................................. 452

9-4 Triangles..........................................................................453

Algebra Activity: The Pythagorean Theorem...........458

9-5 The Pythagorean Theorem...........................................460

Algebra Activity: Graphing Irrational Numbers .....465

9-6 The Distance and Midpoint Formulas .......................466


9-7 Similar Triangles and Indirect Measurement............471

Algebra Activity: Ratios in Right Triangles ..............476

9-8 Sine, Cosine, and Tangent Ratios................................477

Graphing Calculator Investigation: Finding Angles of a Right Triangle.......................................482


Practice Test ..................................................................487



• Follow-Ups 481, 542, 571

• Culmination 594

Snapshots 433, 450


470, 475, 481, 487, 488



Study Organizer 435

Reading and Writing Mathematics• Learning Geometry Vocabulary 446

• Reading Math Tips 437, 448, 453, 455, 471, 472, 477

• Writing in Math 440, 445, 451, 457, 464, 469,475, 481


• Getting Ready for the Next Lesson 440, 445, 451, 457,464, 470, 475

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Unit 4Unit 4

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Chapter Two-Dimensional Figures 490

Getting Started...............................................................491

10-1 Line and Angle Relationships .................................... 492

Algebra Activity: Constructions .................................498

10-2 Congruent Triangles .....................................................500

Algebra Activity: Symmetry .......................................505

10-3 Transformations on the Coordinate Plane.................506

Algebra Activity: Dilations..........................................512

10-4 Quadrilaterals ................................................................513

Practice Quiz 1: Lessons 10-1 through 10-4 ..............517

Algebra Activity: Area and Geoboards .....................518

10-5 Area: Parallelograms, Triangles, and Trapezoids.....520

Reading Mathematics: Learning Mathematics Prefixes .......................................................................526

10-6 Polygons .........................................................................527

Algebra Activity: Tessellations....................................532

10-7 Circumference and Area: Circles ................................533


10-8 Area: Irregular Figures .................................................539


Practice Test ..................................................................549




• Getting Ready for the Next Lesson497, 504, 511, 517, 525, 531, 538

Study Organizer 491

Reading and WritingMathematics• Learning Mathematics Prefixes 526


• Writing in Math 497, 504, 511,517, 525, 531, 537, 543


504, 511, 517, 525, 531, 537,543, 549, 550

• Short Response/Grid In 517, 531,537, 551


Snapshots 537

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Unit 4Unit 4

Chapter Three-Dimensional Figures 552

Getting Started...............................................................553

Geometry Activity: Building Three-Dimensional Figures ........................................................................554

11-1 Three-Dimensional Figures..........................................556

Geometry Activity: Volume ........................................562

11-2 Volume: Prisms and Cylinders....................................563

11-3 Volume: Pyramids and Cones .....................................568


11-4 Surface Area: Prisms and Cylinders...........................573

11-5 Surface Area: Pyramids and Cones ............................578

Geometry Activity: Similar Solids..............................583

11-6 Similar Solids .................................................................584


Reading Mathematics: Precision and Accuracy .....589

11-7 Precision and Significant Digits ..................................590


Practice Test ..................................................................599


Snapshots 593


588, 594, 599, 600



Study Organizer 553

Reading and Writing Mathematics• Precision and Accuracy 589

• Writing in Math 561, 567, 571, 577, 582, 588, 594


• Getting Ready for the Next Lesson 561, 567, 572, 577,582, 588


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Snapshots 603, 610, 649, 654


647, 648, 649, 655, 663, 664



Study Organizer 605

Reading and Writing Mathematics• Dealing with Bias 634

• Reading Math Tips 624, 641, 642, 643, 647, 650

• Writing in Math 610, 616, 621, 627, 633, 639, 645,649, 654


• Getting Ready for the Next Lesson 611, 616, 621, 628,633, 639, 645, 649

Extending Algebra toStatistics and Polynomials

Chapter More Statistics and Probability 604

Getting Started...............................................................605

12-1 Stem-and-Leaf Plots ......................................................606

12-2 Measures of Variation...................................................612

12-3 Box-and-Whisker Plots.................................................617

Graphing Calculator Investigation:Box-and-Whisker Plots.............................................622

12-4 Histograms .....................................................................623


Graphing Calculator Investigation: Histograms....629

12-5 Misleading Statistics .....................................................630

Reading Mathematics: Dealing with Bias ...............634

12-6 Counting Outcomes......................................................635

Algebra Activity: Probability and Pascal’s Triangle .......................................................................640

12-7 Permutations and Combinations ................................641


12-8 Odds ................................................................................646

12-9 Probability of Compound Events ...............................650

Algebra Activity: Simulations.....................................656


Practice Test ..................................................................663



• Follow-Ups 626, 690

• Culmination 696

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Unit 5Unit 5

Chapter Polynomials and Nonlinear Functions 666

Getting Started...............................................................667

Reading Mathematics: Prefixes and Polynomials ...............................................................668

13-1 Polynomials....................................................................669

Algebra Activity: Modeling Polynomials with Algebra Tiles.....................................................673

13-2 Adding Polynomials .....................................................674

13-3 Subtracting Polynomials ..............................................678


Algebra Activity: Modeling Multiplication ..............682

13-4 Multiplying a Polynomial by a Monomial................683

13-5 Linear and Nonlinear Functions.................................687

Practice Quiz 2: Lessons 13-4 and 13-5 .....................691

13-6 Graphing Quadratic and Cubic Functions................692

Graphing Calculator Investigation: Families of Quadratic Functions ............................................697


Practice Test ..................................................................701


Student Handbook

SkillsPrerequisite Skills..................................................................................706Extra Practice .........................................................................................724Mixed Problem Solving........................................................................758Preparing for Standardized Tests .......................................................771

ReferenceEnglish-Spanish Glossary...................................................R1

Selected Answers...........................................................R19Photo Credits ..................................................................R51

Index ..................................................................................R52



Study Organizer 667

Reading and WritingMathematics• Prefixes and Polynomials 668

• Reading Math Tips 678, 688

• Writing in Math 672, 677, 681,686, 691, 695


686, 689, 691, 695, 696, 701, 702



Snapshots 690

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