**1. Thinking Critically**

1.1 An Introduction to Problem Solving

1.2 Pólya's Problem-Solving Principles

1.3 More Problem-Solving Strategies

1.4 Algebra as a Problem-Solving Strategy

1.5 Additional Problem-Solving Strategies

1.6 Reasoning Mathematically

**2. Sets and Whole Numbers**

2.1 Sets and Operations on Sets

2.2 Sets, Counting, and the Whole Numbers

2.3 Addition and Subtraction of Whole Numbers

2.4 Multiplication and Division of Whole Numbers

**3. Numeration and Computation**

3.1 Numeration Systems Past and Present

3.2 Nondecimal Positional Systems

3.3 Algorithms for Adding and Subtracting Whole Numbers

3.4 Algorithms for Multiplication and Division of Whole Numbers

3.5 Mental Arithmetic and Estimation

**4. Number Theory**

4.1 Divisibility of Natural Numbers

4.2 Tests for Divisibility

4.3 Greatest Common Divisors and Least Common Multiples

**5. Integers**

5.1 Representations of Integers

5.2 Addition and Subtraction of Integers

5.3 Multiplication and Division of Integers

**6. Fractions and Rational Numbers**

6.1 The Basic Concepts of Fractions and Rational Numbers

6.2 Addition and Subtraction of Fractions

6.3 Multiplication and Division of Fractions

6.4 The Rational Number System

**7. Decimals, Real Numbers, and Proportional Reasoning**

7.1 Decimals and Real Numbers

7.2 Computations with Decimals

7.3 Proportional Reasoning

7.4 Percent

**8. Algebraic Reasoning and Connections with Geometry**

8.1 Algebraic Expressions, Functions, and Equations

8.2 Graphing Points, Lines, and Elementary Functions

8.3 Connections Between Algebra and Geometry

**9. Geometric Figures**

9.1 Figures in the Plane

9.2 Curves and Polygons in the Plane

9.3 Figures in Space

9.4 Networks

**10. Measurement: Length, Area, and Volume**

10.1 The Measurement Process

10.2 Area and Perimeter

10.3 The Pythagorean Theorem

10.4 Surface Area and Volume

**11. Transformations, Symmetries, and Tilings**

11.1 Rigid Motions and Similarity Transformations

11.2 Patterns and Symmetries

11.3 Tilings and Escher-like Designs

**12. Congruence, Constructions, and Similarity**

12.1 Congruent Triangles

12.2 Constructing Geometric Figures

12.3 Similar Triangles

**13. Statistics: The Interpretation of Data**

13.1 Organizing and Representing Data

13.2 Measuring the Center and Variation of Data

13.3 Statistical Inference

**14. Probability**

14.1 Experimental Probability

14.2 Principles of Counting

14.3 Permutations and Combinations

14.4 Theoretical Probability

Appendices

A. Manipulatives in the Mathematics Classroom

B. Getting the Most out of Your Calculator

C. A Brief Guide to the Geometer's Sketchpad

D. Resources