1. Introduction to Problem Solving.

1.1 The Problem Solving Process and Strategies.

1.2 Three Additional Strategies.

2. Sets, Whole Numbers, and Numeration.

2.1 Sets as a Basis for Whole Numbers.

2.2 Whole Numbers and Numeration.

2.3 The Hindu-Arabic System.

2.4 Relations and Functions.

3. Whole Numbers: Operations and Properties.

3.1 Addition and Subtraction.

3.2 Multiplication and Division.

3.3 Ordering and Exponents.

4. Whole Number Computation: Mental, Electronic, and Written.

4.1 Mental Math, Estimation, and Calculators.

4.2 Written Algorithms for Whole-Number Operations.

4.3 Algorithms in Other Bases.

5. Number Theory.

5.1 Primes, Composites, and Tests for Divisibility.

5.2 Counting Factors, Greatest common Factor, and Least Common Multiple.

6. Fractions.

6.1 The Sets of Fractions.

6.2 Fractions: Addition and Subtraction.

6.3 Fractions: Multiplication and Division.

7. Decimals, Ratio, Proport ion, and Percent.

7.1 Decimals.

7.2 Operations with decimals.

7.3 Ratios and Proportion.

7.4 Percent.

8. Integers.

8.1 Addition and Subtraction.

8.2 Multiplication, Division and Order.

9. Rational Numbers, Real Numbers and Algebra

9.1 The Rational Numbers.

9.2 The Real Numbers.

9.3 Functions and Their Graphs.

10. Statistics.

10.1 Organizing and Picturing Information.

10.2 Analyzing Data.

10.3 Misleading Graphs and Statistics.

11. Probability.

11.1 Probability and Simple Experiments.

11.2 Probability and Complex Experiments.

11.3 Additional Counting Techniques.

11.4 Simulation, Expected Value, Odds, and Conditional Probability.

12. Geometric Shapes.

12.1 Recognizing Geometric Shapes.

12.2 Analyzing Shapes.

12.3 Properties of Geometric Shapes: Lines and Angles.

12.4 Regular Polygons and Tessellations.

12.5 Describing Three-Dimensional Shapes.

13. Measurement.

13.1 Measurement with Nonstandard and Standard Units.

13.2 Length and Area.

13.3 Surface Area.

13.4 Volume.

14. Geometry Using Triangle Congruence and Similarity.

14.1 Congruence of Triangles.

14.2 Similarity of Triangles.

14.3 Basic Euclidean Constructions.

14.4 Additional Euclidean Constructions.

14.5 Geometric Problem Solving Using Triangle Congruence and Similarity.

15. Geometry Using Coordinates.

15.1 Distance and Slope in the Coordinate Plane.

15.2 Equations and Coordinates.

15.3 Geometric Problem Solving Using Coordinates.

16. Geometry Using Transformations.

16.1 Transformations.

16.2 Congruence and Similarity Using Transformations.

16.3 Geometric Problem Solving Using Transformations.

Epilogue: An Eclectic Approach to Geometry.

Topic 1. Elementary Logic.

Topic 2. Clock Arithmetic: A Mathematical System.

Topic 3. Introduction to Graph Theory.

References.

Answers to Exercise/Problem Sets-Part A, Chapter Tests, and Topics.

Photograph Credits.

Index.