1. Visual Models in Math
Connecting Concepts with Procedures for Fraction Addition and Subtraction
Tuesday, March 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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6. Visual Models in Math: Connecting Concepts with Procedures
March 3, 2015: Fraction
Addition and Subtraction
Sara Delano Moore, Ph.D.
Director of Mathematics & Science
ETA hand2mind

7. 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

8. 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

9. 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

10. 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

11. Key Ideas for Fraction Addition & Subtraction
Reminder: procedural focus in this series
Equivalence
Changing units
Regrouping
Composing & decomposing
Strategies & Methods
Moving from concrete to abstract

12. Equivalence A number can be named/described in many different ways.
Depending on the situation, it can be helpful to name/describe a number differently
Equivalent fractions can be created by representing the same value using a different unit fraction

13. Regrouping Fractions
A whole is created by a complete set of unit fractions
A fractional number can be composed or decomposed by regrouping the unit fractions from which it is built.

14. Strategies and Methods
Making a whole
Representing with the same unit
Partial sums for mixed numbers
Estimation is still helpful!

15. Moving from Concrete to Abstract: Common Denominators

16. Moving from Concrete to Abstract: Common Denominators1 2 3 4 5

17. Moving from Concrete to Abstract: Common Denominators

18. Moving from Concrete to Abstract: Uncommon Denominators
What do I call it?

19. Moving from Concrete to Abstract: Uncommon Denominators

20. Should one strategy come first?
Same unit first means we can use our other strategies to find a solution
Hence, the standard algorithm typically finds same unit first.
It doesn’t matter what the same unit is, except from an efficiency perspective.

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

22. 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

23. 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

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

25. Visual Models in Math: Join us for the next webinar
Tuesday, April 7th – 4 PM Eastern Time
Visual Models in Math:
Connecting Concepts with Procedures for Whole Number & Decimal Multiplication and Division
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Join Building Understanding in Mathematics

26. Thank you!