This best-selling text emphasizes solid mathematics content, problem-solving skills, and analytical techniques. The seventh edition focuses on the National Council of Teachers of Mathematics (NCTM) Principles and Standards 2000. The text allows for a variety of approaches to teaching, encourages discussion and collaboration among students and with their instructors, allows for the integration of projects into the curriculum, and promotes discovery and active learning. Students using this text will receive solid preparation in mathematics, develop confidence in their math skills and benefit from teaching and learning techniques that really work. For mathematics teachers.
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Table of Contents
(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.