Table of Contents

Introduction: Math and the Real World 1

1 Mathematics Helps Us Make Sense of the World 2

2 How to Think Like a Mathematician 5

3 A Mathematician's Tools 8

4 Equipment for Learning 10

Chapter 1 Ratio Relationships: Part 1 13

1 Ratio Basics 14

2 Ratios vs. Rates 23

2 Putting Rates and Ratios to Work 33

Chapter 2 Ratio Relationships: Part 1 53

1 Properties of Proportionality 54

2 The Constant of Proportionality 55

3 Simple Interest 74

Chapter 3 Operations and Rational Numbers: Part 1 85

1 Division: Going Beyond Whole Numbers 86

2 Dividing a Fraction by a Fraction 90

3 Operations with Decimals 98

4 Terminating and Repeating Decimals 103

5 Greatest Common Factor of Whole Numbers 100 or Less 105

6 Least Common Multiples of Whole Numbers 12 or Less 111

Chapter 4 Operations and Rational Numbers: Part 2 121

1 Positive and Negative Integers 122

2 Absolute Value 129

3 Positive and Negative Numbers on the Coordinate Plans 135

Chapter 5 Operations and Rational Numbers: Part 3 151

1 Adding and Subtracting Rational Numbers 152

2 Multiplying and Dividing Rational Numbers 163

3 Simplifying with Order of Operations 174

Chapter 6 Expressions and Equations: Part 1 183

1 Exponents 184

2 Writing Algebraic Expressions 192

3 Expressions: Algebraic Language 197

Chapter 7 Expressions and Equations: Part 2 207

1 Writing and Interpreting One-Step Equations 208

2 Solving One-Step Equations 212

3 Solving Two-Step Equations 221

4 Understanding and Solving Inequalities 227

Chapter 8 Expressions and Equations: Part 3 241

1 Professional Relationships 242

2 Linear Relationships 249

3 Solving and Graphing Systems of Linear Equations 256

4 Solutions to Systems of Linear Equations Types 265

5 Defining and Identifying Functions 270

Chapter 9 Area, Volume, and Surface Area 283

1 Area 284

2 Polygons in the Coordinate Plane 300

3 Volume 305

4 Surface Area of Right Rectangular Prisms 312

Chapter 10 Cross Sections, Circles, Volume, and Angles 323

1 Cross Sections of Solids 324

2 Circles: Finding Circumference and Area 328

3 Problem Solving: Standard Shapes 334

4 Volume: Cylinders, Cones, and Spheres 336

5 Angles 340

Chapter 11 Similarity, Congruence, and Angle Relationships 353

1 Scale Factor, Sides, and Area 354

2 Congruence 359

3 Angle Relationships 369

4 The Pythagorean Theorem 376

Chapter 12 Statistics 397

1 Statistical Variability 398

2 Random Sampling 402

3 Using Data to make Inference and Generalizations about a Population 408

4 More Data Displays 415

5 Comparing Populations 437

Chapter 13 Probability 453

1 Probability 454

2 Theoretical vs. Experimental Probability 459

3 Probability of Compounds Events 467

Chapter 14 Bivariate Data 491

1 Constructing, Examining, and Interpreting Scatterplots 492

2 Line of Best Fit 505

3 Two-Way Frequency Tables 510