Get Them Into the Ball Park!Using Estimation As A Means To Help Students

Determine Reasonableness

Melissa Hedges, Math Teaching Specialist,

hoganme@milwaukee.k12.wi.us

Beth Schefelker, Mathematics Teaching Specialist, schefeba@milwaukee.k12.wi.us

www.mmp.uwm.eduThe 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’sStrands of ProficiencyAdding It Up, 2001

Adaptive Reasoning Strategic Competence Conceptual

Understanding Productive Disposition Procedural Fluency

Nearest AnswerTen Minute Math, Dale Seymour Publications

5,210 + 298 ≈ 5,400 5,500 7,000 8,000

59 x 11≈ 60 500 600 6,000

268 ÷ 9.9 ≈ 25 250 2.5 2,500

Reasonableness: What does it mean?

87 x 52

Estimate an answerShare with a neighborWhat 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?

0.1 1 10 100 1000

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 EstimationAdding 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?

Problem Over/Under 37 + 75 100

476 - 117 300

349 ÷ 45 10

17 x 38 800

Estimation GameTen 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)

www.mmp.uwm.edu