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Visual Models in Math: Connecting Concepts with Procedures for Fraction Addition and Subtraction

Learn effective strategies and methods for teaching fraction addition and subtraction using visual models. Develop conceptual understanding and fluency in procedures.

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Visual Models in Math: Connecting Concepts with Procedures for Fraction Addition and Subtraction

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  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 Join our community on edWeb.net Building Understanding in Mathematics www.edweb.net/math

  2. 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 www.edweb.net/math

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

  4. Webinar Tips • For better audio/video, close other applications (like Skype) that use bandwidth. • If you are having any audio or video issues, try refreshing your browser. • Maximize your screen for a larger view by using the link in the upper right corner. Tweet with #edwebchat

  5. 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

  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 Abstract

  10. 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

  11. 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

  12. 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.

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

  14. Moving from Concrete to Abstract:Common Denominators

  15. Moving from Concrete to Abstract:Common Denominators 0 2 3 4 1 5

  16. Moving from Concrete to Abstract:Common Denominators

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

  18. Moving from Concrete to Abstract:Uncommon Denominators

  19. 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.

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

  21. 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

  22. 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 www.edweb.net/math

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

  24. 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 For an invitation to the next webinar Join Building Understanding in Mathematicswww.edweb.net/math

  25. Thank you! www.hand2mind.com

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