Get Them Into the Ball Park! Using Estimation As A Means To Help Students Determine Reasonableness Melissa Hedges, Math Teaching Specialist, Beth Schefelker, Mathematics Teaching Specialist, The Milwaukee Mathematics Partnership (MMP) is supported with funding from the National Science Foundation.

Session Goals  To investigate connections between estimation and mental computation.  To explore estimation strategies that support fluent and flexible thinking.  Deepen the understanding of the language of estimation.

What Was Your Method? 139 x 43  Make an estimate. Keep track of how you got your estimate.  Share your strategy.  Note the mathematical understandings you needed to make this estimate?

A Different Approach… What is happening here? 139 x 43 What if the estimate was 6000? Where did this estimate come from? Was it a good approach? How should it be adjusted? Why might someone select 150 instead of 140?

Estimation What does it take to make a good one? Estimation requires good mental arithmetic skills which come from an understanding of the nature of the operations, a firm understanding of place value, and the ability to use various properties. Bassarear, T. Mathematics for Elementary School Teachers. 2nd Edition. Houghton Mifflin Company.

National Research Council’s Strands of Proficiency Adding It Up, 2001  Adaptive Reasoning  Strategic Competence  Conceptual Understanding  Productive Disposition  Procedural Fluency

Nearest Answer Ten Minute Math, Dale Seymour Publications 5, ≈ 5,400 5,500 7,000 8, x 11≈ , ÷ 9.9 ≈ ,500

Reasonableness: What does it mean? 87 x 52  Estimate an answer  Share with a neighbor  What did you know to feel comfortable with your estimate?

Estimation Ideas To Support Division Strategies 3,482 ÷ 7  Think multiplication In which place value would your answer land?

Looking At Student Work Solve 259 ÷ 24  What do the students know about division?  How does the estimation strategy support their number sense?

Effective Use of Estimation Adding It Up, 2001  Takes advantage of important properties of numbers and notational systems, including powers of ten, place value, and relations among different operations.  Requires recognizing that the appropriateness of an estimate is related to a problem and its context.

Why Practice Estimation Strategies? “When there is an over emphasis on routine paper and pencil calculation it is difficult for students to move from calculating answers to estimating wisely. (pg. 216) Adding It Up, 2001

Is the Answer Over or Under? ProblemOver/Under    349 ÷  17 x

Estimation Game Ten Minute Math, Dale Seymour Publications ____ ____ x ____  Make a template  Use a set of number cards  Fill the template with the numbers as they are flipped.  Make an estimate (approx. 30 seconds)

What do the researchers suggest?  Long term goal of computational estimation is to be able to quickly produce an approximate result that’s adequate for the situation. (Van de Walle, 2009)

Principles and Standards, 2000  Teachers should help students learn how to decide when an exact answer or an estimate would be more appropriate, how to choose the computational methods that would be best to use, and how to evaluate the reasonable ness of computations.  Most calculations should arise as students solve computations in context.

References  Van de Walle,J. (2007) Elementary and Middle School Mathematics, Teaching Developmentally.  Tierney, C. Russell, S.(2001) Ten Minute Math. Dale Seymour  Adding It Up. (2001) National Research Council.  Principles and Standards for School Mathematics, 2000  Milwaukee Mathematics Partnership (MMP)