1. Visual Models in Math: Connecting Concepts with Procedures for Whole Number & Decimal Addition and Subtraction
Tuesday, February 3, 2015
Presented by Sara Delano Moore, Ph.D.
Director of Mathematics and Science at ETA hand2mind
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Building Understanding in Mathematics

2. Building Understanding in Mathematics
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5. Visual Models in Math: Connecting Concepts with Procedures
February 3, 2014: Whole Number & Decimal
Addition and Subtraction
Sara Delano Moore, Ph.D.
Director of Mathematics & Science
ETA hand2mind

6. Visual Models in Math: Series Overview
January 6: Connecting Concepts with Procedures Overview
February 3: Connecting Concepts with Procedures for Whole Number & Decimal Addition & Subtraction
March 3: Connecting Concepts with Procedures for Fraction Addition & Subtraction
April 7: Connecting Concepts with Procedures for Whole Number & Decimal Multiplication & Division
May 5: Connecting Concepts with Procedures for Fraction Multiplication & Division

7. Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems.
PtA, page 42

8. Being fluent means that students are able to choose flexibly among methods and strategies to solve contextual and mathematical problems, they understand and are able to explain their approaches, and they are able to produce accurate answers efficiently.
PtA, page 42

9. Hands-On Learning Instructional Cycle
Concrete
Representational
This instructional cycle is how we make the connections between work with manipulatives (the Concrete gear in the graphic) and abstract mathematics (the A gear in the graphic). If you remove the representations gear, the concrete and abstract ones don’t connect. When we use this instructional method with fidelity, what do we see in terms of student learning?
[Research supporting this CRA cycle appears in Appendix D of the RTI report.]
Abstract

10. Key Ideas for Base Ten Addition & Subtraction
Reminder: procedural focus in this series
Spring 2014 conceptual focus series
Place Value System
Expanded Notation
Regrouping
Strategies & Methods

11. Place Value System
Digits vs value

13. Expanded Notation
Shows connection between value & digits

15. +

17. Expanded Notation Shows connection between value & digits
400 as four hundreds vs 400 units
(4 x 100) = (400 x 1)

18. Regrouping
Ten of one item make a single item of the next column to the left.
This is true for whole numbers and for decimals.
This works in both directions (moving left to right or right to left)

20. Regrouping
Ten of one item make a single item of the next column to the left.
This is true for whole numbers and for decimals.
This works in both directions (moving left to right or right to left)
Iteration – process repeats across the place value columns
In general, multi-digit computation is reduced to single digit computation by use of properties

22. Regrouping
Ten of one item make a single item of the next column to the left.
This is true for whole numbers and for decimals.
This works in both directions (moving left to right or right to left)
Iteration – process repeats across the place value columns
In general, multi-digit computation is reduced to single digit computation by use of properties
Scale – factor of 10 with each place moved
Saving this conversation for multiplication session in April

23. Moving from Concrete to Abstract
23 – 8
How many ways can you build 23 with base ten materials?

24. How can I subtract 8?

25. 23 -8 15 1 1

26. Special Strategies & General Methods
Special strategy – useful in particular situations
398 + (2 + 15) = ( ) + 15 = 415
General method – useful in all cases
(39 tens + 1 ten) + (8 ones + 7 ones) = 415 ….
….. ..

27. Decimal Addition Example
123
+ 450
573

28. Decimal Addition Example
1.23
+ 4.5
5.73

29. The operation doesn’t change; the way we record it does.

30. Visual Models in Math: Series Overview
January 6: Connecting Concepts with Procedures Overview
February 3: Connecting Concepts with Procedures for Whole Number & Decimal Addition & Subtraction
March 3: Connecting Concepts with Procedures for Fraction Addition & Subtraction
April 7: Connecting Concepts with Procedures for Whole Number & Decimal Multiplication & Division
May 5: Connecting Concepts with Procedures for Fraction Multiplication & Division

32. Building Understanding in Mathematics
Join our community on edWeb.net
Building Understanding in Mathematics
Invitations to upcoming webinars
Webinar recordings and resources
CE quizzes
Online discussions
Join the community

33. Recognition for your participation today!
Attending Live?
Your CE Certificate will be
ed to you within 24 hours.
Viewing the Recording?
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Go to the Webinar Archives folder
Take the CE Quiz to get a personalized CE Certificate
CE Certificate provided by

34. Join us for the next webinar
Tuesday, March 3rd - 4PM Eastern Time
Visual Models in Math:
Connecting Concepts with Procedures for Fraction Addition and Subtraction
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Join Building Understanding in Mathematics

35. Thank you!