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Bestseller!

Mine the Gap for Mathematical Understanding, Grades 3-5

Common Holes and Misconceptions and What To Do About Them
It’s hard to find the time to figure out the ”why” behind students’ math mistakes, so here is a bank of 180 downloadable, standards-aligned math tasks, the common misunderstandings, and next instructional steps.

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A copy:
How good are you at exploiting students’ mathematical mistakes? In this remarkable book, John SanGiovanni reminds us that mistakes are not random, and when we take the time to “mine the gap,” we can dispel misunderstandings before they take root. Included are 180 downloadable high-quality tasks, aligned to the standards and big ideas grades 3-5 mathematics. Each task includes sample student work, commentary on strengths and gaps, and next instructional steps. Whether you use this bank of tasks for instruction or assessment, you will love how it helps you easily identify students’ thinking and then follow-up with instruction that brings clear, complete understanding.

Full description


Product Details
  • Grade Level: PreK-12
  • ISBN: 9781506337678
  • Published By: Corwin
  • Series: Corwin Mathematics Series
  • Year: 2016
  • Page Count: 384
  • Publication date: October 10, 2016
Price: $37.95
Volume Discounts applied in Shopping Cart

Review Copies

This book is not available as a review copy.
Description

Description

Being an effective math educator is one part based on the quality of the tasks we give, one part how we diagnose what we see, and one part what we do with what we find. Yet with so many students and big concepts to cover, it can be hard to slow down enough to look for those moments when students’ responses tell us what we need to know about next best steps. In this remarkable book, John SanGiovanni helps us value our students’ misconceptions and incomplete understandings as much as their correct ones—because it’s the gap in their understanding today that holds the secrets to planning tomorrow’s best teaching.

SanGiovanni lays out 180 high-quality tasks aligned to the standards and big ideas of Grades 3-5 mathematics, including addition and subtraction of multi-digit whole numbers, multiplication and division of single and multi-digit whole numbers, foundational fraction concepts, foundational decimal concepts, and operations with fractions and decimals. The tasks are all downloadable so you can use or modify them for instruction and assessment. Each big idea offers a starting task followed by:

  • what makes it a high-quality task
  • what you might anticipate before students work with the task
  • 4 student examples of the completed task showcasing a distinct “gap”
  • commentary on what precisely counts for mathematical understanding and the next instructional steps
  • commentary on the misconception or incomplete understanding so you learn why the student veered off course
  • three additional tasks aligned to the mathematics topic and ideas about what students might do with these additional tasks.

It’s time to break our habit of rushing into re-teaching for correctness and instead get curious about the space between right and wrong answers. Mine the Gap for Mathematical Understanding is a book you will return to again and again to get better at selecting tasks that will uncover students’ reasoning—better at discerning the quality and clarity of students’ understanding—and better at planning teaching based on the gaps you see.

Author(s)

Author(s)

John J. SanGiovanni photo

John J. SanGiovanni

John J. SanGiovanni is a mathematics coordinator in Howard County, Maryland. There, he leads mathematics curriculum development, digital learning, assessment, and professional development. John is an adjunct professor and coordinator of the Elementary Mathematics Instructional Leadership graduate program at McDaniel College. In addition to this Figuring Out Fluency series, some of his many Corwin books include Daily Routines to Jump-Start Problem Solving, Grades K-8, Answers to Your Biggest Questions about Teaching Elementary Math, the Daily Routines to Jump-Start Math series, and Productive Math Struggle: A 6-Point Action Plan for Fostering Perseverance. John is a national mathematics curriculum and professional learning consultant who also speaks frequently at national conferences and institutes. He is active in state and national professional organizations, recently serving on the board of directors for the National Council of Teachers of Mathematics (NCTM) and currently on the board of directors for the National Council of Supervisors of Mathematics (NCSM).

Table of Contents

Table of Contents

Big Ideas & Tasks at a Glance


Acknowledgments


Publisher’s Acknowledgments


About the Author


Introduction


CHAPTER 1: RICH MATHEMATICS TASKS, STUDENT MISCONCEPTIONS, USING TASKS

CHAPTER 2: ADDITION AND SUBTRACTION WITHIN 1,000

BIG IDEAS

1: Adding Within 1,000

2: Reasoning About Addition Within 1,000

3: Subtraction Within 1,000

4: Reasoning About Subtraction Within 1,000

5: Problem Solving With Addition and Subtraction

CHAPTER 3: MULTIPLICATION AND DIVISION

BIG IDEAS

6: Representing Multiplication

7: Reasoning About Multiplication

8: Properties of Multiplication

9: Representing Division

10: Reasoning About Division

11: Problem Solving With Multiplication and Division

12: Connecting Multiplication and Division

13: Representing Multi-Digit Multiplication

14: Reasoning About Multi-Digit Multiplication

15: Representing Multi-Digit Division

16: Reasoning About Multi-Digit Division

CHAPTER 4: FOUNDATIONAL FRACTION CONCEPTS

BIG IDEAS

17: Representing Fractions

18: Connecting Representations of Fractions

19: Fractions on a Number Line

20: Fractions Greater Than 1 on a Number Line

21: Decomposing Fractions

22: Equivalent Fractions on a Number Line

23: Comparing Fractions

24: Reasoning About Fractions

25: More Reasoning About Fractions

CHAPTER 5: DECIMAL CONCEPTS

BIG IDEAS

26: Representing Decimals

27: Representing Decimals as Numbers

28: Estimating and Rounding Decimals

29: Decomposing Decimals

30: Comparing Decimals

31: Addition With Decimals

32: Subtracting With Decimals

33: Problem Solving With Decimals

CHAPTER 6: ADDITION AND SUBTRACTION WITH FRACTIONS

BIG IDEAS

34: Addition With Fractions on Number Lines

35: Reasoning About Addition With Fractions

36: Subtraction With Fractions

37: Reasoning About Subtraction With Fractions

38: Problem Solving With Addition and Subtraction of Fractions

39: Addition and Subtraction With Mixed Numbers

CHAPTER 7: MULTIPLICATION AND DIVISION WITH FRACTIONS AND DECIMALS

BIG IDEAS

40: Multiplication of Fractions

41: More With Multiplication of Fractions

42: Division With Fractions

43: Problem Solving With Multiplication and Division of Fractions

44: Multiplication With Decimals

45: Division With Decimals

CHAPTER 8: WHAT DO WE DO NEXT?

References and Additional Resources


Reviews

Reviews

Price: $37.95
Volume Discounts applied in Shopping Cart

Review Copies

This book is not available as a review copy.

Related Resources

  • Access to companion resources is available with the purchase of this book.
  • Big Idea 12:  [Lessons and Strategies]
  • Big Idea 43:  [Lessons and Strategies]