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Visual Models in Math: Connecting Concepts with Procedures

Learn how to build fluency with procedures in math by connecting them with conceptual understanding through visual models. Join us for this webinar on Whole Number & Decimal Multiplication and Division.

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Visual Models in Math: Connecting Concepts with Procedures

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  1. Visual Models in Math Connecting Concepts with Procedures for Whole Number & Decimal Multiplication and Division Tuesday, April 7, 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 April 7, 2015: Base Ten Multiplication & Division 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 Base Ten Multiplication & Division • Reminder: procedural focus in this series • Models for Multiplication • Repeated addition • Area model • Models for Division • How many groups? • How many in each group?

  11. Strategies and Methods: Multiplication • Repeated Addition • Opportunity to show young learners about efficiency – “there has to be a better way” • Good transition from addition to multiplication • See Spring 2014 series for more information • This method becomes inefficient with larger numbers and numbers which are not whole numbers. • Arrays serve as a transition to area model.

  12. Repeated Addition Example • Susan gets 10₵ per day allowance. How much allowance does she receive in one week? • 10₵ + 10₵ + 10₵ + 10₵ + 10₵ + 10₵ + 10₵ = 70₵ • For 7 days, she receives 10₵ each day. • 7 × 10₵ = 70₵ • What happens over two weeks?

  13. Strategies and Methods: Multiplication • Area Model • Connects the operation to one of its applications • Translates more easily to a wider range of factor types • e.g., fractions or algebraic expressions • Most effective for one or two terms/digits in each factor

  14. Area Model Examples • 7 × 10 = 70

  15. Area Model Examples • 7 × 10 = 70 • 12 × 14 = 168 • 12 × (10 + 4) = • (12 × 10) + (12 × 4) = • 120 + 48 = 168

  16. Moving from Concrete to Abstract:Partial Products Multiplication 12 × 14 20 8 2 + 10 8 40 20 + 100 100 40 168 10 + 4

  17. Strategies and Methods: Division • Repeated subtraction • Inverse of repeated addition • Find the missing factor • Inverse of area model • Both models are appropriate for both forms of division • How many groups? • How many in each group? • As with multiplication, each model has situations where it is a better fit.

  18. Repeated Subtraction Example • 30 ÷ 6 = 5 • How many times can I subtract 6 from 30? 1 2 3 4 5

  19. Missing Factor Example • 30 ÷ 6 = 5 6 × = 30

  20. Moving from Concrete to Abstract:Partial Quotients Division 21 12)252 10 -120 10 132 -120 1 12 - 12 0

  21. Working with Decimals • Multiplication • Extend the models we have to more decimal places.

  22. Multiplying Decimals 1.2 × 32.4 = 30 + 2 + 1 + 30 2 6 38 + + = 38.88

  23. Working with Decimals • Multiplication • Extend the models we have to more decimal places. • Division • Understand the fraction bar as a representation of division. • Use knowledge of equivalent fractions & multiplicative identity.

  24. Dividing Decimals • 25.2 ÷ 1.2 = . . 12 × =

  25. 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

  26. 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

  27. 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

  28. Join us for the next webinar Tuesday, May 5th – 4 PM Eastern Time Visual Models in Math: Connecting Concepts with Procedures for Fraction Multiplication and Division For an invitation to the next webinar Join Building Understanding in Mathematicswww.edweb.net/math

  29. Thank you! www.hand2mind.com

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