PART I: REASONING ABOUT NUMBERS AND QUANTITIES Chapter 1: Reasoning About Quantities 1.1 Ways of Thinking About Solving Story Problems 1.2 Quantitative Analysis 1.3 Problem Solving 1.4 Issues for Learning: Ways of Illustrating Story Problems 1.5 Check Yourself Chapter 2: Numeration Systems 2.1 Ways of Expressing Values of Quantities 2.2 Place Value 2.

3 Bases Other Than Ten 2.4 Operations in Different Bases 2.5 Issues for Learning: Understanding Place Value 2.6 Check Yourself Chapter 3: Understanding Whole Number Operations 3.1 Ways of Thinking About Addition and Subtraction 3.2 Children''s Ways of Adding and Subtracting 3.3 Ways of Thinking About Multiplication 3.4 Ways of Thinking About Division 3.

5 Children Find Products and Quotients 3.6 Issues for Learning: Developing Number Sense 3.7 Check Yourself Chapter 4: Some Conventional Ways of Computing 4.1 Operating on Whole Numbers and Decimal Numbers 4.2 Issues for Learning: The Role of Algorithms 4.3 Check Yourself Chapter 5: Using Numbers in Sensible Ways 5.1 Mental Computation 5.2 Computational Estimation 5.

3 Estimating Values of Quantities 5.4 Using Scientific Notation for Estimating Values of Very Large and Very Small Quantities 5.5 Issues for Learning: Mental Computation 5.6 Check Yourself Chapter 6: Meanings for Fractions 6.1 Understanding the Meanings of a/b 6.2 Comparing Fractions 6.3 Equivalent (Equal) Fractions 6.4 Relating Fractions, Decimals, and Percents 6.

5 Issues for Learning: Understanding Fractions and Decimals 6.6 Check Yourself Chapter 7: Computing with Fractions 7.1 Adding and Subtracting Fractions 7.2 Multiplying by a Fraction 7.3 Dividing by a Fraction 7.4 Issues for Learning: Teaching Calculation with Fractions 7.5 Check Yourself Chapter 8: Multiplicative Comparisons and Multiplicative Reasoning 8.1 Quantitative Analysis of Multiplicative Situations 8.

2 Fractions in Multiplicative Comparisons 8.3 Issues for Learning: Standards for Learning 8.4 Check Yourself Chapter 9: Ratios, Rates, Proportions, and Percents 9.1 Ratio as a Measure 9.2 Comparing Ratios 9.3 Percents in Comparisons and Changes 9.4 Issues for Learning: Developing Proportional Reasoning 9.5 Check Yourself Chapter 10: Integers and Other Number Systems 10.

1 Big Ideas About Signed Numbers 10.2 Children''s Ways of Reasoning About Signed Numbers 10.3 Other Models for Signed Numbers 10.4 Operations with Signed Numbers 10.5 Multiplying and Dividing Signed Numbers 10.6 Number Systems 10.7 Issues for Learning: Open Number Sentences 10.8 Check Yourself Chapter 11: Number Theory 11.

1 Factors and Multiples, Primes and Composites 11.2 Prime Factorization 11.3 Divisibility Tests to Determine Whether a Number is Prime 11.4 Greatest Common Factor, Least Common Multiple 11.5 Issues for Learning: Understanding the Unique Factorization Theorem 11.6 Check Yourself PART II: REASONING ABOUT ALGEBRA AND CHANGE Chapter 12: What is Algebra? 12.1 Algebraic Reasoning in Elementary School 12.2 Numerical Patterns and Algebra 12.

3 Functions and Algebra 12.4 Algebra as Generalized Arithmetic 12.5 Algebraic Reasoning About Quantities 12.6 Issues for Learning: The National Assessment of Educational Progress and Achievement in Algebra 12.7 Check Yourself Chapter 13: A Quantitative Approach to Algebra and Graphing 13.1 Using Graphs and Algebra to Show Quantitative Relationships 13.2 Understanding Slope: Making Connections Across Quantitative Situations, Graphs, and Algebraic Equations 13.3 Linear Functions and Proportional Relationships 13.

4 Nonlinear Functions 13.5 Issues for Learning: Algebra in the Elementary Grades 13.6 Check Yourself Chapter 14: Understanding Change: Relationships Among Time, Distance, and Rate 14.1 Distance-Time and Position-Time Graphs 14.2 Using Motion Detectors 14.3 Graphs of Speed Against Time 14.4 Interpreting Graphs 14.5 Issues for Learning: Common Graphing Errors 14.

6 Check Yourself Chapter 15: Further Topics in Algebra and Change 15.1 Finding Linear Equations 15.2 Solving Two Linear Equations in Two Variables 15.3 Different Approaches to Problems 15.4 Average Speed and Weighted Averages 15.5 More About Functions 15.6 Issues for Learning: Topics in Algebra 15.7 Check Yourself PART III: REASONING ABOUT SHAPES AND MEASUREMENT Chapter 16: Polygons 16.

1 Review of Polygon Vocabulary 16.2 Organizing Shapes 16.3 Triangles and Quadrilaterals 16.4 A Focus on Problem-Solving Strategies 16.5 Issues for Learning: Some Research on Two-Dimensional Shapes 16.6 Check Yourself Chapter 17: Polyhedra 17.1 Shoeboxes Have Faces and Nets! 17.2 Introduction to Polyhedra 17.

3 Representing and Visualizing Polyhedra 17.4 Congruent Polyhedra 17.5 Some Special Polyhedra 17.6 Issues for Learning: Dealing with 3D Shapes 17.7 Check Yourself Chapter 18: Symmetry 18.1 Symmetry of Shapes in a Plane 18.2 Symmetry of Polyhedra 18.3 Issues for Learning: What Geometry Is in the Pre-K-8 Curriculum? 18.

4 Check Yourself Chapter 19: Tessellations 19.1 Tessellating the Plane 19.2 Tessellating Space 19.3 Check Yourself Chapter 20: Similarity 20.1 Similarity and Dilations in Planar Figures 20.2 More About Similar Figures 20.3 Similarity in Space Figures 20.4 Issues for Learning: Similarity and Proportional Reasoning 20.

5 Check Yourself Chapter 21: Curves, Constructions, and Curved Surfaces 21.1 Planar Curves and Constructions 21.2 Curved Surfaces 21.3 Issues for Learning: Standards for Mathematical Practice 21.4 Check Yourself Chapter 22: Transformation Geometry 22.1 Some Types of Rigid Motions 22.2 Finding Images for Rigid Motions 22.3 A Closer Look at Some Rigid Motions 22.

4 Composition of Rigid Motions 22.5 Transformations and Earlier Topics 22.6 Issues for Learning: Promoting Visualization in the Curriculum 22.7 Check Yourself Chapter 23: Measurement Basics 23.1 Key Ideas of Measurement 23.2 Length and Angle Size 23.3 Issues for Learning: Measurement of Length and Angle Size 23.4 Check Yourself Chapter 24: Area, Surface Area, and Volume 24.

1 Area and Surface Area 24.2 Volume 24.3 Issues for Learning: Measurement of Area and Volume 24.4 Check Yourself Chapter 25: Counting Units Fast: Measurement Formulas 25.1 Circumference, Area, and Surface Area Formulas 25.2 Volume Formulas 25.3 Issues for Learning: What Measurement is in the Curriculum? 25.4 Check Yourself Chapter 26: Special Topics in Measurement 26.

1 The Pythagorean Theorem 26.2 Some Other Kinds of Measurements 26.3 Check Yourself PART IV: REASONING ABOUT CHANCE AND DATA Chapter 27: Quantifying Uncertainty 27.1 Understanding Chance Events 27.2 Methods of Assigning Probabilities 27.3 Simulating Probabilistic Situations 27.4 Issues for Learning: Research on the Learning of Probability 27.5 Check Yourself Chapter 28: Determining More Complicated Probabilities 28.

1 Tree Diagrams and Lists for Multistep Experiments 28.2 Probability of One Event or Another Event 28.3 Probability of One Event and Another Event 28.4 Conditional Probability 28.5 Probability and Problem Solving 28.6 Check Yourself Chapter 29: Introduction to Statistics and Sampling 29.1 What Are Statistics? 29.2 Sampling: The Why and the How 29.

3 Simulating Random Sampling 29.4 Types of Data 29.5 Conducting a Survey 29.6 Issues for Learning: Sampling 29.7 Check Yourself Chapter 30: Representing and Interpreting Data with One Variable 30.1 Representing Categorical Data 30.2 Representing and Interpreting Measurement Data 30.3 Examining the Spread of Data 30.

4 Measures of Center 30.5 Deviations from the Mean as Measures of Spread 30.6 Examining Distributions 30.7 Issues for Learning: Understanding the Mean 30.8 Check Yourself Chapter 31: Dealing with Multiple Data Sets or with Multiple Variables 31.1 Comparing Data Sets 31.2 Lines of Best Fit and Correlation 31.3 Issues for Learning: More Than One Variable 31.

4 Check Yourself Chapter 32: Variability in Samples 32.1 Having Confidence in a Sample Statistic 32.2 Confidence Intervals 32.3 Issues for Learning: What Probability and Statistics Should Be in the Curriculum? 32.4 Check Yourself Chapter 33: Special Topics in Probability 33.1 Expected Value 33.2 Permutations and Combinations 33.3 Issues for Learning: Children Finding Permutations 33.

4 Check Yourself Appendix A: Video Clips Illustrating Children''s Mathematical Thinking Appendix B: Summ.