Good Questions

“A must for any educator who is serious about reaching more students more often and achieving more positive results.” —Resources for the Mathematics Educator (for previous edition)

Now in its fourth edition—with more than 50 new questions and a new chapter on financial literacy—this bestselling resource helps experienced and novice teachers effectively and efficiently differentiate mathematics instruction in grades K–8.

Math education expert Marian Small shows teachers how to get started and become expert at using two powerful and universal strategies: Open Questions and Parallel Tasks. This edition is even easier for teachers to use in all quality state standards environments, including direct links to content standards and standards for mathematical practice. Parallel tasks and question examples are provided at each grade band: K–2, 3–5, and 6–8. Along with each example, the text describes how teachers can evoke productive conversations that meet the needs of a broad range of learners.

Book Features:

• New tasks and questions to develop financial literacy.
• Connection of tasks and questions to standards and mathematical big ideas.
• About 500 tasks and questions that teachers can adapt or use as-is.
• Teaching tips and task variations.
• A template to help teachers build new tasks.
• “Look-fors” to see student thinking and diagnose difficulties.
• Guidance for using follow-up questions and math conversations to create a rich math classroom.

Marian Small is an international professional developer and conference speaker. A former dean of education and professor of mathematics education, she is widely known for her bestselling books and her in-district work with educators. Visit her website at www.onetwoinfinity.ca for in-person and online professional development.

“When I read Marian Small’s work, I see the power of math revealed, but I also see her work opening that power to so many students who might never otherwise experience it…I am a disciple of her approach to differentiating math!”
—From the Foreword by Carol Ann Tomlinson, University of Virginia

“Successful instruction causes students to wonder, conjecture, investigate, collaborate, and talk math. Good questioning is central to all the above, and for ‘knowing what students know.’ Small’s book focuses on the big ideas of mathematics, with questions, examples, and parallel tasks that assess student understanding and promote learning. This book is a must-read for every preservice and inservice teacher.”
—Carole Greenes, professor emerita, mathematics education, Arizona State University

“In a classroom full of students, it can be hard to meet the needs of all learners. That is where this book has your back. Marian Small provides meaningful tasks while modeling how simple tweaks and intentional number choice can unlock students’ mathematical potential.”
—Graham Fletcher, math specialist

“Throughout her career, Marian Small has shown that ‘differentiation’ in math class does not mean ‘ability grouping’ or breaking mathematics down into tiny, digestible subskills. Marian’s kind of differentiation means focusing on big ideas, offering students choice, and being curious about students’ thinking. In the 4th edition of this essential book, Marian teaches us powerful questioning techniques with her trademark clarity and provides plenty of specific examples across the content strands and grade bands. We can use these questions with our students immediately and internalize Marian’s teaching strategies through practice. How lucky for us that she has crafted these questions that will encourage student thinking, build our curiosity, and teach us to craft good questions of our own.”
—Tracy Johnston Zager, math coach

“I just finished teaching an elementary math methods course to teacher candidates in a graduate program. I wish I had had Marian Small’s Good Questions: Great Ways to Differentiate Mathematics Instruction in the Standards-Based Classroom to use with these preservice teachers. Small covers all the key content in the Common Core PreK–8 math curriculum, and she addresses the topic of open questions in a very accessible way. She walks the reader step-by-step through how to teach the big ideas in the CCSS PreK–8 math curriculum using specified open questions. At the same time, she provides a menu of choices so teachers can draw from their own expertise to select the open questions that they see fit. Each chapter explains math content in an easy-to-reference manner. It is like having a reference book and a teaching coach all in one book. This semester, I watched teacher candidates struggle with how to lead a Number Talk, because they were not sure which open questions to ask to facilitate learning. Small’s book provides the guidance that they need. I look forward to using Small’s book the next time I teach Elementary Math Methods to teacher candidates. Inservice teachers will also benefit from the practical ideas about how to promote higher-order math thinking by asking the open questions outlined in Good Questions.”
—Felicia Darling, math instructor at Santa Rosa Junior College

Contents

Foreword ix
by Carol Ann Tomlinson

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 & 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

Download appendix in PDF format.

Copublished with and available in Canada exclusively from Nelson Education Ltd.