Good Questions

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

• ContentsForeword ixby Carol Ann TomlinsonPreface xiOrganization of the Book xiMathematical Practice Standards xiiChanges in the Fourth Edition xiiiAcknowledgments xivIntroduction: Why and How to Differentiate Math Instruction 1The Challenge in Math Classrooms 1What It Means to Meet Student Needs 3Assessing Students’ Needs 4Principles and Approaches to Differentiating Instruction 4Two Core Strategies for Differentiating Mathematics Instruction: Open Questions and Parallel Tasks 6Creating a Math Talk Community 131  Counting & Cardinality and Number & Operations in Base Ten 17Topics 17The Big Ideas for Counting & Cardinality and for Number & Operations in Base Ten 18Open Questions for Prekindergarten–Grade 2 19Open Questions for Grades 3–5 28Parallel Tasks for Prekindergarten–Grade 2 36Parallel Tasks for Grades 3–5 43Summing Up 482  Number & Operations—Fractions 49Topics 49The Big Ideas for Number & Operations—Fractions 50Open Questions for Grades 3–5 51Parallel Tasks for Grades 3–5 57Summing Up 643  The Number System 65Topics 65The Big Ideas for The Number System 65Open Questions for Grades 6–8 66Parallel Tasks for Grades 6–8 70Summing Up 744  Ratios & Proportional Relationships 75Topics 75The Big Ideas for Ratios & Proportional Relationships 76Open Questions for Grades 6–8 76Parallel Tasks for Grades 6–8 84Summing Up 905  Operations & Algebraic Thinking 91Topics 91The Big Ideas for Operations & Algebraic Thinking 92Open Questions for Prekindergarten–Grade 2 93Open Questions for Grades 3–5 98Parallel Tasks for Prekindergarten–Grade 2 108Parallel Tasks for Grades 3–5 111Summing Up 1166  Expressions & Equations and Functions 117Topics 117The Big Ideas for Expressions & Equations and for Functions 118Open Questions for Grades 6–8 118Parallel Tasks for Grades 6–8 128Summing Up 1347  Financial Literacy 135Topics 135The Big Ideas for Financial Literacy 136Open Questions for Prekindergarten–Grade 2 137Open Questions for Grades 3–5 139Open Questions for Grades 6–8 143Parallel Tasks for Prekindergarten–Grade 2 147Parallel Tasks for Grades 3–5 149Parallel Tasks for Grades 6–8 151Summing Up 1568  Measurement & Data 157Topics 157The Big Ideas for Measurement & Data 158Open Questions for Prekindergarten–Grade 2 159Open Questions for Grades 3–5 169Parallel Tasks for Prekindergarten–Grade 2 181Parallel Tasks for Grades 3–5 187Summing Up 1969  Geometry 197Topics 197The Big Ideas for Geometry 198Open Questions for Prekindergarten–Grade 2 199Open Questions for Grades 3–5 205Open Questions for Grades 6–8 211Parallel Tasks for Prekindergarten–Grade 2 224Parallel Tasks for Grades 3–5 227Parallel Tasks for Grades 6–8 231Summing Up 24010  Statistics & Probability 241Topics 241The Big Ideas for Statistics & Probability 242Open Questions for Grades 6–8 243Parallel Tasks for Grades 6–8 252Summing Up 262Conclusions 263The Need for Manageable Strategies 263Developing Open Questions and Parallel Tasks 264The Benefits of These Strategies 266Appendix A: Mathematical Practices Addressed in This Resource 267Appendix B: Worksheet for Open Questions and Parallel Tasks 268Glossary 270Bibliography 280Index 283Index of Subjects and Cited Authors 283Index of Big Ideas 286About the Author 290