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
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