Contents: 1. Thinking Critically 1.1 An Introduction to Problem Solving 1.2 Polya's Problem-Solving Principles 1.3 More Problem-Solving Strategies 1.4 Additional Problem-Solving Strategies 1.5 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 Addition and Subtraction of Whole Numbers 3.4 Algorithms for Multiplication and Division of Whole Numbers 3.5 Mental Arithmetic and Estimation 3.5 3.6 Getting the most out of your calculator 4. Number Theory 4.1 Divisibility of Natural Numbers 4.2 Tests for Divisibility 4.3 Greatest Common Divisors and Least Common Multiples 4.4 Codes and credit card numbers 5. Integers 5.1 Representations of Integers 5.2 Addition and Subtraction of Integers 5.3 Multiplication and Division of Integers 5.4 Clock arithmetic 6. Fractions and Rational Numbers 6.1 The Basic Concepts of Fractions and Rational Numbers 6.2 The Arithmetic of rational numbers 6.3 The Rational Number System 7. Decimals, Real Numbers, and Proportional Reasoning 7.1 Decimals 7.2 Computations with Decimals 7.3 Ratio and Proportion 7.4 Percent 8. Algebraic Reasoning and representation 8.1 Variables, Algebraic Expressions, and equations 8.2 Functions 8.3 Graphing functions 9. Statistics: the interpretation of data 9.1 Graphical representation of data 9.2 Measures of central tendency and variability 9.3 Statistical Inference 10. Probability 10.1 Empirical probability 10.2 Principles of counting 10.3 Theoretical probability 11. Geometric figures 11.1 Figures in the plane 11.2 Curves and polygons in the plane 11.3 Figures in space 11.4 Networks 12. Measurement 12.1 The measurement process 12.2 Area and perimeter 12.3 The Pythagorean Theorem 12.4 Surface Area and volume 13. Transformations, Symmetries, and Tilings 13.1 Rigid Motions and Similarity Transformations 13.2 Patterns and Symmetries 13.3 Tilings and Escher-like Designs 14. Congruence, Constructions, and Similarity 14.1 Congruent Triangles 14.2 Constructing Geometric Figures 14.3 Similar Triangles Appendices- A. Manipulatives in the Mathematics Classroom B. Spreadsheets C. Graphing calculators. D. A Brief Guide to The Geometer's Sketchpad E. Resources