## Table of Contents

**1. An Introduction to Problem Solving**

1-1 Mathematics and Problem Solving

1-2 Explorations with Patterns

1-3 Reasoning and Logic: An Introduction

**2. Numeration Systems and Sets**

2-1 Numeration Systems

2-2 Describing Sets

2-3 Other Set Operations and Their Properties

**3. Whole Numbers and Their Operations**

3-1 Addition and Subtraction of Whole Numbers

3-2 Algorithms for Whole-Number Addition and Subtraction

3-3 Multiplication and Division of Whole Numbers

3-4 Algorithms for Whole-Number Multiplication and Division

3-5 Mental Mathematics and Estimation for Whole-Number Operations

**4. Number Theory**

4-1 Divisibility

4-2 Prime and Composite Numbers

4-3 Greatest Common Divisor and Least Common Multiple

Online Module: Clock & Modular Arithmetic

**5. Integers**

5-1 Integers and the Operations of Addition and Subtraction

5-2 Multiplication and Division of Integers

**6. Rational Numbers and Proportional Reasoning**

6-1 The Set of Rational Numbers

6-2 Addition, Subtraction, and Estimation with Rational Numbers

6-3 Multiplication and Division of Rational Numbers

6-4 Ratios, Proportions, and Proportional Reasoning

**7. Decimals: Rational Numbers and Percent**

7-1 Introduction to Decimals

7-2 Operations on Decimals

7-3 Nonterminating Decimals

7-4 Percents and Interest

**8. Real Numbers and Algebraic Thinking**

8-1 Real Numbers

8-2 Variables

8-3 Equations

8-4 Functions

8-5 Equations in a Cartesian Coordinate System

Online Module: Using Real Numbers in Equations

**9. Probability**

9-1 How Probabilities Are Determined

9-2 Multistage Experiments with Tree Diagrams and Geometric Probabilities

9-3 Using Simulations in Probability

9-4 Odds, Conditional Probability, and Expected Value

9-5 Using Permutations and Combinations in Probability

**10. Data Analysis/Statistics: An Introduction**

10-1 Designing Experiments/Collecting Data

10-2 Displaying Data: Part I

10-3 Displaying Data: Part II

10-4 Measures of Central Tendency and Variation

10-5 Abuses of Statistics

**11. Introductory Geometry**

11-1 Basic Notions

11-2 Linear Measure

11-3 Curves, Polygons, and Symmetry

11-4 More About Angles

Online Module: Networks

**12. Congruence and Similarity with Constructions**

12-1 Congruence through Constructions

12-2 Other Congruence Properties

12-3 Other Constructions

12-4 Similar Triangles and Similar Figures

Online Module: Trigonometry Ratios via Similarity

**13. Congruence and Similarity with Transformations**

13-1 Translations and Rotations

13-2 Reflections and Glide Reflections

13-3 Dilations

13-4 Tessellations of the Plane

**14. Area, Pythagorean Theorem, and Volume**

14-1 Areas of Polygons and Circles

14-2 The Pythagorean Theorem, Distance Formula, and Equation of a Circle

14-3 Geometry in Three Dimensions

14-4 Surface Areas

14-5 Volume, Mass, and Temperature

Online Appendices

Spreadsheets

Graphing calculators

Geometer’s Sketchpad

GeoGebra