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

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 www.edweb.net/math

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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

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

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

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

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

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

Place Value System Digits vs value

Expanded Notation Shows connection between value & digits

+

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

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)

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

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

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

How can I subtract 8?

23 -8 15 1 1

Special Strategies & General Methods 398 + 17 Special strategy – useful in particular situations 398 + (2 + 15) = (398 + 2) + 15 = 415 General method – useful in all cases (39 tens + 1 ten) + (8 ones + 7 ones) = 415 …. ….. ..

Decimal Addition Example 123 + 450 123 + 450 573

Decimal Addition Example 1.23 + 4.5 1.23 + 4.5 5.73

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

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

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 www.edweb.net/math

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

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

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