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

## Common Holes and Misconceptions and What To Do About Them

Tap to preview

#### About the eBook

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.

#### About the Author

• Publisher:
• Published: ; Copyright:
• ISBN:
• Edition:
• Title:
• Series:
• Author:
• Imprint:
• Language:
• Number of Pages:  [disclaimer] Page count shown is an approximation provided by the publisher. The actual page count will vary based on various factors such your device's screen size and font-size.

#### Read online

You can read this ebook online in a web browser, without downloading anything or installing software.

#### Download file formats

This ebook is available in file types:

This ebook is available in:

After you've bought this ebook, you can choose to download either the PDF version or the ePub, or both.

#### DRM Free

The publisher has supplied this book in DRM Free form with digital watermarking.

##### Required software

You can read this eBook on any device that supports DRM-free EPUB or DRM-free PDF format.

#### Digital Rights Management (DRM)

The publisher has supplied this book in encrypted form, which means that you need to install free software in order to unlock and read it.

##### Required software

To read this ebook on a mobile device (phone or tablet) you'll need to install one of these free apps:

To download and read this eBook on a PC or Mac:

• Adobe Digital Editions (This is a free app specially developed for eBooks. It's not the same as Adobe Reader, which you probably already have on your computer.)

#### Limits on printing and copying

The publisher has set limits on how much of this ebook you may print or copy. See details.

• {{ format_drm_information.format_name }} unrestricted {{ format_drm_information.format_name }} {{format_drm_information.page_percent}}% pages every day{{format_drm_information.interval}} days {{ format_drm_information.format_name }} off
##### Read Aloud
• {{ read_aloud_information.format_name }} on {{ read_aloud_information.format_name }} off
•  >