Table of Contents
Foreword Carol Ann Tomlinson ix
Preface xi
Organization of the Book xi
Mathematical Practice Standards xii
Changes in the Fourth Edition xiii
Acknowledgments xiv
Introduction: Why and How to Differentiate Math Instruction 1
The Challenge in Math Classrooms 1
What It Means to Meet Student Needs 3
Assessing Students' Needs 4
Principles and Approaches to Differentiating Instruction 4
Two Core Strategies for Differentiating Mathematics Instruction: Open Questions and Parallel Tasks 6
Creating a Math Talk Community 13
1 Counting & Cardinality and Number & Operations in Base Ten 17
Topics 17
The Big Ideas for Counting & Cardinality and for Number & Operations in Base Ten 18
Open Questions for Prekindergarten-Grade 2 19
Open Questions for Grades 3-5 28
Parallel Tasks for Prekindergarten-Grade 2 36
Parallel Tasks for Grades 3-5 43
Summing Up 48
2 Number & Operations-Fractions 49
Topics 49
The Big Ideas for Number & Operations-Fractions 50
Open Questions for Grades 3-5 51
Parallel Tasks for Grades 3-5 57
Summing Up 64
3 The Number System 65
Topics 65
The Big Ideas for The Number System 65
Open Questions for Grades 6-8 66
Parallel Tasks for Grades 6-8 70
Summing Up 74
4 Ratios & Proportional Relationships 75
Topics 75
The Big Ideas for Ratios & Proportional Relationships 76
Open Questions for Grades 6-8 76
Parallel Tasks for Grades 6-8 84
Summing Up 90
5 Operations & Algebraic Thinking 91
Topics 91
The Big Ideas for Operations & Algebraic Thinking 92
Open Questions for Prekindergarten-Grade 2 93
Open Questions for Grades 3-5 98
Parallel Tasks for Prekindergarten-Grade 2 108
Parallel Tasks for Grades 3-5 111
Summing Up 116
6 Expressions 8r Equations and Functions 117
Topics 117
The Big Ideas for Expressions & Equations and for Functions 118
Open Questions for Grades 6-8 118
Parallel Tasks for Grades 6-8 128
Summing Up 134
7 Financial Literacy 135
Topics 135
The Big Ideas for Financial Literacy 136
Open Questions for Prekindergarten-Grade 2 137
Open Questions for Grades 3-5 139
Open Questions for Grades 6-8 143
Parallel Tasks for Prekindergarten-Grade 2 147
Parallel Tasks for Grades 3-5 149
Parallel Tasks for Grades 6-8 151
Summing Up 156
8 Measurement & Data 157
Topics 157
The Big Ideas for Measurement & Data 158
Open Questions for Prekindergarten-Grade 2 159
Open Questions for Grades 3-5 169
Parallel Tasks for Prekindergarten-Grade 2 181
Parallel Tasks for Grades 3-5 187
Summing Up 196
9 Geometry 197
Topics 197
The Big Ideas for Geometry 198
Open Questions for Prekindergarten-Grade 2 199
Open Questions for Grades 3-5 205
Open Questions for Grades 6-8 211
Parallel Tasks for Prekindergarten-Grade 2 224
Parallel Tasks for Grades 3-5 227
Parallel Tasks for Grades 6-8 231
Summing Up 240
10 Statistics & Probability 241
Topics 241
The Big Ideas for Statistics & Probability 242
Open Questions for Grades 6-8 243
Parallel Tasks for Grades 6-8 252
Summing Up 262
Conclusions 263
The Need for Manageable Strategies 263
Developing Open Questions and Parallel Tasks 264
The Benefits of These Strategies 266
Appendix A Mathematical Practices Addressed in This Resource 267
Appendix B Worksheet for Open Questions and Parallel Tasks 268
Glossary 270
Bibliography 280
Index 283
Index of Subjects and Cited Authors 283
Index of Big Ideas 286
About the Author 290