Dad, Mother, Sister, Brother, Dog (Divide, Multiply, Subtract, Bring Down) Is this the only way to divide? National Council of Teachers of Mathematics Annual Meeting April 29, 2006 Sharonda Harris, Milwaukee Public Schools Melissa Hedges, Milwaukee Public Schools Meghan Steinmeyer, University of Wisconsin - Milwaukee

Session Overview Explore several number oriented strategies for multi-digit division of whole numbers Investigate the role these strategies play when developing computational fluency for division Analyze student work samples

Our guiding questions… Can elementary students compute fluently using a variety of number oriented strategies for the division of whole numbers? What mathematical knowledge and skills would they need to know in order to be successful?

169 ÷ 14 =  Individually: Estimate a solution Solve using two different strategies (Use something other than the traditional algorithm for both strategies, if possible.) Small group discussion Share: Estimate strategy Computation strategy

Fundamental Understandings… What are some mathematical skills and concepts you need to successfully approach problems in this way?

Principles and Standards for School Mathematics Computational fluency refers to having efficient and accurate methods for computing. Students exhibit computational fluency when they demonstrate flexibility in the computational methods they choose, understand and can explain these methods, and produce accurate answers efficiently. (p. 152)

Principles and Standards for School Mathematics Having access to more than one method for each operation allows students to choose an approach that best fits the numbers in a particular problem. (p. 155)

About the students… Fourth graders, March and April, ’05 – ‘06 Primary curriculum: reform curricula since four-year old kindergarten Dual language immersion program – students are dominant in either Spanish or English Previously explored division with single digit divisors but not double-digit divisors

The teaching context… Open-ended problem solving using word problems. Began with double-digit divided by single-digit and moved into triple-digit divided by double-digit division. Each class session was followed by sharing of strategies that lead into the next problem. Highlighted problems:  Tyrone has a collection of 169 Yu-Gi-Oh cards. He shares them equally among his 14 friends. How many cards will each friend get?  Tyrone has a collection of 169 Yu-Gi-Oh cards. He wants to give each friend 14 cards. How many friends can he share his cards with?

Viewing student work Organize into groups of 5 Select one of the 5 strategies.  Understand the thinking by studying both the student work and the accompanying transcript. Which context would best fit this problem?  Highlight mathematical skills/concepts that are embedded in your strategy. Apply your strategy to 279 ÷ 24. Be prepared to explain the student work sample and your application of the strategy to 279 ÷ 24.

The strategies… Direct modeling a measurement strategy Repeated subtraction (measurement division) Dealing out in groups (partitive division) Using multiplication Partitioning the dividend

Whole-class Sharing of Student Strategies It is not just show and tell…. but rather a crucial time for teaching and learning.

“As students develop methods to solve multidigit computation problems they should be encouraged to record and share their methods. As they do so, they can learn from one another, analyze efficiency and generalizability, and try one another’s methods.” PSSM p. 153

What is the role of the teacher as students are sharing strategies?

Reflections on this experience The critical role context plays when supporting children as they “invent” meaningful multidigit division strategies. The importance of a problem solving environment. The insights gained while sharing strategies whole group.

Contact Information Milwaukee Mathematics Partnership Sharonda Harris Melissa Hedges Meghan Steinmeyer