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CHAPTER 1 Integers
1-1 A Plan for Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . 24
1-2 Variables, Expressions, and Properties . . . . . . . . . . . . . . . 29
1-3 Integers and Absolute Value . . . . . . . . . . . . . . . . . . . . . . . 35
Extend 1-3 Algebra Lab: Graphing Data . . . . . . . . . . . . . . . . . 40
1-4 Adding Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
1-5 Subtracting Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
1-6 Multiplying and Dividing Integers . . . . . . . . . . . . . . . . . . . 51
1-7 Writing Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
1-8 Problem-Solving Investigation:
Work Backward . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Reading Word Problems: Simplify the Problem. . . . . . . 64
1-9 Solving Addition and Subtraction Equations . . . . . . . . . . 65
1-10 Solving Multiplication and Division Equations . . . . . . . . . 70
ASSESSMENT
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . 74
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
California Standards Practice . . . . . . . . . . . . . . . . . . . 80
CHAPTER 2 Algebra: Rational Numbers
2-1 Rational Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Reading Word Problems: New Vocabulary . . . . . . . . . . 90
2-2 Comparing and Ordering Rational Numbers . . . . . . . . . . 91
2-3 Multiplying Positive and Negative Fractions . . . . . . . . . . . 96
2-4 Dividing Positive and Negative Fractions . . . . . . . . . . . . 102
2-5 Adding and Subtracting Like Fractions . . . . . . . . . . . . . . 108
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
2-6 Adding and Subtracting Unlike Fractions . . . . . . . . . . . . 114
2-7 Solving Equations with Rational Numbers . . . . . . . . . . . 119
2-8 Problem-Solving Investigation:
Look for a Pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
2-9 Powers and Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
2-10 Scientific Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
ASSESSMENT
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . 134
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
California Standards Practice . . . . . . . . . . . . . . . . . . 140
CHAPTER 3 Real Numbers and the Pythagorean Theorem
3-1 Square Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
3-2 Estimating Square Roots . . . . . . . . . . . . . . . . . . . . . . . . . 148
3-3 Problem–Solving Investigation:
Use a Venn Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
Reading Word Problems: The Language
of Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
3-4 The Real Number System . . . . . . . . . . . . . . . . . . . . . . . . 155
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
Explore 3-5 Geometry Lab: The Pythagorean Theorem . . . . 161
3-5 The Pythagorean Theorem . . . . . . . . . . . . . . . . . . . . . . . 162
3-6 Using the Pythagorean Theorem . . . . . . . . . . . . . . . . . . 167
Extend 3-6 Geometry Lab: Graphing Irrational Numbers . . 172
3-7 Geometry: Distance on the Coordinate Plane . . . . . . . . 173
ASSESSMENT
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . 179
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
California Standards Practice . . . . . . . . . . . . . . . . . . 184
CHAPTER 4 Proportions and Similarity
4-1 Ratios and Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
4-2 Proportional and Nonproportional Relationships . . . . . 194
4-3 Solving Proportions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
Extend 4-3 Geometry Lab: The Golden Rectangle . . . . . . . .203
4-4 Problem–Solving Investigation:
Draw a Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .204
4-5 Similar Polygons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .206
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
4-6 Measurement: Converting Length, Weight/Mass,
Capacity, and Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
Extend 4-6 Spreadsheet Lab: Converting Measures . . . . . . 219
4-7 Measurement: Converting Square Units and
Cubic Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .220
4-8 Scale Drawings and Models . . . . . . . . . . . . . . . . . . . . . .224
4-9 Rate of Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .230
4-10 Constant Rate of Change . . . . . . . . . . . . . . . . . . . . . . . . .236
ASSESSMENT
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . .242
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
California Standards Practice . . . . . . . . . . . . . . . . . .248
CHAPTER 5 Percent
5-1 Ratios and Percents . . . . . . . . . . . . . . . . . . . . . . . . . . . . .252
5-2 Comparing Fractions, Decimals, and Percents . . . . . . . .256
Reading Word Problems: Comparing Data . . . . . . . .262
5-3 Algebra: The Percent Proportion . . . . . . . . . . . . . . . . . . .263
5-4 Finding Percents Mentally . . . . . . . . . . . . . . . . . . . . . . . .268
5-5 Problem-Solving Investigation:
Reasonable Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
5-6 Percent and Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 275
5-7 Algebra: The Percent Equation . . . . . . . . . . . . . . . . . . . . 279
5-8 Percent of Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .284
5-9 Simple Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .290
Extend 5-9 Spreadsheet Lab:
Compound Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . .294
ASSESSMENT
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . .295
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .299
California Standards Practice . . . . . . . . . . . . . . . . . .300
CHAPTER 6 Geometry and Spatial Reasoning
6-1 Line and Angle Relationships . . . . . . . . . . . . . . . . . . . . .306
Extend 6-1 Geometry Lab: Constructions . . . . . . . . . . . . . . . 311
6-2 Problem-Solving Investigation:
Use Logical Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . . . 314
6-3 Polygons and Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316
6-4 Congruent Polygons . . . . . . . . . . . . . . . . . . . . . . . . . . . . .320
Extend 6-4 Geometry Lab: Investigating
Congruent Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . .324
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . .326
6-5 Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .327
6-6 Reflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .332
6-7 Translations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337
ASSESSMENT
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . .342
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
California Standards Practice . . . . . . . . . . . . . . . . . .348
CHAPTER 7 Measurement: Area and Volume
7-1 Circumference and Area of Circles . . . . . . . . . . . . . . . . .352
Extend 7-1 Geometry Lab: Investigating Arcs and Angles . .358
7-2 Problem-Solving Investigation:
Solve a Simpler Problem . . . . . . . . . . . . . . . . . . . . . . . . .360
Explore 7-3 Measurement Lab: Area of Irregular Figures . .362
7-3 Area of Complex Figures . . . . . . . . . . . . . . . . . . . . . . . . .363
7-4 Three-Dimensional Figures . . . . . . . . . . . . . . . . . . . . . . .368
7-5 Volume of Prisms and Cylinders . . . . . . . . . . . . . . . . . . . 373
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379
7-6 Volume of Pyramids and Cones . . . . . . . . . . . . . . . . . . .380
Explore 7-7 Measurement Lab:
Surface Area of Cylinders . . . . . . . . . . . . . . . . . . . . . . . . .385
7-7 Surface Area of Prisms and Cylinders . . . . . . . . . . . . . . .386
Extend 7-7 Measurement Lab:
Net of a Cone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .392
7-8 Surface Area of Pyramids . . . . . . . . . . . . . . . . . . . . . . . .393
Explore 7-9 Spreadsheet Lab: Similar Solids . . . . . . . . . . . . . 397
7-9 Similar Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .399
ASSESSMENT
Study Guide and Review . . . . . . . . . . . . . . . .405
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . .409
California Standards Practice . . . . . . . . 410
CHAPTER 8 Algebra: More Equations and Inequalities
8-1 Simplifying Algebraic Expressions . . . . . . . . . . . . . . . . . . 416
8-2 Solving Two-Step Equations . . . . . . . . . . . . . . . . . . . . . . .422
8-3 Writing Two-Step Equations . . . . . . . . . . . . . . . . . . . . . . .427
Explore 8-4 Algebra Lab: Equations with
Variables on Each Side . . . . . . . . . . . . . . . . . . . . . . . . . . .432
8-4 Solving Equations with Variables on Each Side . . . . . . .434
8-5 Problem-Solving Investigation:
Guess and Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .438
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . .440
8-6 Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441
8-7 Solving Inequalities by Adding or Subtracting . . . . . . . .445
8-8 Solving Inequalities by Multiplying or Dividing . . . . . . .449
ASSESSMENT
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . .454
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .459
California Standards Practice . . . . . . . . . . . . . . . . . .460
CHAPTER 9 Algebra: Linear Functions
Explore 9-1 Algebra Lab: Functions . . . . . . . . . . . . . . . . . . . .464
9-1 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .465
Explore 9-2 Algebra Lab:
Graphing Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . 470
9-2 Representing Linear Functions . . . . . . . . . . . . . . . . . . . . 471
9-3 Slope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477
9-4 Direct Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .483
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . .489
Explore 9-5 Algebra Lab: Proportional and
Nonproportional Functions . . . . . . . . . . . . . . . . . . . . . . .490
9-5 Slope-Intercept Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491
Extend 9-5 Graphing Calculator Lab:
Modeling Linear Behavior . . . . . . . . . . . . . . . . . . . . . . . .496
9-6 Writing Systems of Equations and Inequalities . . . . . . .498
9-7 Problem-Solving Investigation:
Use a Graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .502
9-8 Scatter Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .504
Extend 9-8 Graphing Calculator Lab: Scatter Plots . . . . . . . 510
ASSESSMENT
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . 512
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517
California Standards Practice . . . . . . . . . . . . . . . . . . 518
CHAPTER 10 Algebra: Nonlinear Functions and Polynomials
10-1 Linear and Nonlinear Functions . . . . . . . . . . . . . . . . . . .522
10-2 Graphing Quadratic Functions . . . . . . . . . . . . . . . . . . . . .528
10-3 Problem-Solving Investigation:
Make a Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .532
10-4 Graphing Cubic Functions . . . . . . . . . . . . . . . . . . . . . . . .534
Extend 10-4 Graphing Calculator Lab: Families of
Nonlinear Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .538
10-5 Multiplying Monomials . . . . . . . . . . . . . . . . . . . . . . . . . .539
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . .543
10-6 Dividing Monomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . .544
10-7 Powers of Monomials . . . . . . . . . . . . . . . . . . . . . . . . . . . .549
10-8 Roots of Monomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . .553
ASSESSMENT
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . 557
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 561
California Standards Practice . . . . . . . . . . . . . . . . . .562
CHAPTER 11 Statistics
11-1 Problem-Solving Investigation:
Make a Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .568
11-2 Histograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570
Extend 11-2 Graphing Calculator Lab: Histograms . . . . . . . . 575
11-3 Circle Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576
Extend 11-3 Spreadsheet Lab:
Line, Bar, and Circle Graphs . . . . . . . . . . . . . . . . . . . . . .583
11-4 Measures of Central Tendency and Range . . . . . . . . . . .585
Extend 11-4 Spreadsheet Lab:
Mean, Median, and Mode . . . . . . . . . . . . . . . . . . . . . . . . 591
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . .592
11-5 Measures of Variation . . . . . . . . . . . . . . . . . . . . . . . . . . .593
11-6 Box-and-Whisker Plots . . . . . . . . . . . . . . . . . . . . . . . . . . .599
Extend 11-6 Graphing Calculator Lab:
Box-and-Whisker Plots . . . . . . . . . . . . . . . . . . . . . . . . . . .605
11-7 Stem-and-Leaf Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . .606
11-8 Select an Appropriate Display . . . . . . . . . . . . . . . . . . . . . 611
ASSESSMENT
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . 616
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 621
California Standards Practice . . . . . . . . . . . . . . . . . .622
CHAPTER 12 Looking Ahead to Grade 8: Probability
12-1 Counting Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . .626
12-2 Probability of Compound Events . . . . . . . . . . . . . . . . . . 631
12-3 Experimental and Theoretical Probability . . . . . . . . . . . .637
Extend 12-3 Probability Lab: Fair Games . . . . . . . . . . . . . . . .642
12-4 Problem-Solving Investigation:
Act it Out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .644
Mid-Chapter Quiz . . . . . . . . . . . . . . . . . . . . . . . . . . . . .646
12-5 Using Sampling to Predict . . . . . . . . . . . . . . . . . . . . . . . . 647
ASSESSMENT
Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . .653
Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .657
California Standards Practice . . . . . . . . . . . . . . . . . .658
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