(Each chapter begins with a "Preliminary Problem" and concludes with a "Hint for Solution to the Preliminary Problem," "Questions from the Classroom," "Chapter Outline," "Chapter Review," and a "Selected Biography.")
(*indicates optional section.)
1. An Introduction to Problem Solving.
Mathematics and Problem Solving.
*Logic: An Introduction.
2. Sets, Whole Numbers and Functions.
Other Set Operations and Their Properties.
Addition and Subtraction of Whole-Numbers.
Multiplication and Division of Whole-Numbers.
3. Whole Number Computation.
Algorithms for Whole-Number Addition and Subtraction.
Algorithms for Whole-Number Multiplication and Division.
Mental Mathematics and Estimation for Whole-Number Operations.
4. Integers and Number Theory.
Multiplication and Division of Integers.
Prime and Composite Numbers.
Greatest Common Divisor and Least Common Multiple.
*Clock and Modular Arithmetic.
5. Rational Numbers as Fractions.
Addition and Subtraction of Rational Numbers.
Multiplication and Division of Rational Numbers.
6. Decimals, Percents, and Real Numbers.
Operations on Decimals.
Multistage Experiments with Tree Diagrams and Geometric Probabilities.
Using Simulations in Probability.
Odds and Expected Value.
Methods of Counting.
8. Statistics: An Introduction.
Measures of Central Tendency and Variation.
Abuses of Statistics.
9. Introductory Geometry.
More About Angles.
Geometry in Three Dimensions.
10. Constructions, Congruence and Similarity.
Other Congruence Properties.
Similar Triangles and Similar Figures.
Lines in a Cartesian Coordinate System.
11. Concepts of Measurement.
Areas of Polygons and Circles.
The Pythagorean Theorem.
Volume, Mass, and Temperature.
12. Motion Geometry and Tessellations.
Reflections and Glide Reflections.
*Tessellations of the Plane.
Appendix I. Logo Turtle Graphics.
Appendix II. Graphing Calculators.
Appendix III. Using a Geometry Drawing Utility.
Appendix IV. Using a Spreadsheet.
Answers to Selected Problems.