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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 14. Probability 14.1 Experimental Probability 14.2 Principles of Counting 14.3 Permutations and Combinations 14.4 Theoretical Probability 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 Table of Contents
Get Mathematical Reasoning for Elementary School Teachers plus MyLab Math with Pearson eText Package, 6th Edition by Calvin T. Long, Washington State University Duane W. DeTemple, Washington State University Richard S. Millman, Georgia Institute of Technology
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