You are here

Mine the Gap for Mathematical Understanding, Grades 3-5
Share

Mine the Gap for Mathematical Understanding, Grades 3-5
Common Holes and Misconceptions and What To Do About Them



© 2017 | 384 pages | Corwin

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. 

 
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

Purchasing options

Volume Discounts Available

contact corwin

Please select a format:

ISBN: 9781506337678
*Includes a 20% everyday educator discount!

For instructors