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

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

• Melissa Hedges, Math Teaching Specialist,
• hoganme_at_milwaukee.k12.wi.us
• Beth Schefelker, Mathematics Teaching Specialist,
  schefeba_at_milwaukee.k12.wi.us

www.mmp.uwm.edu
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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.

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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?

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A Different ApproachWhat 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?

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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.

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National Research CouncilsStrands of
ProficiencyAdding It Up, 2001

• Adaptive Reasoning
• Strategic Competence
• Conceptual Understanding
• Productive Disposition
• Procedural Fluency

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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

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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?

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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

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Looking At Student Work

• Solve 259 24
• What do the students know
• about division?
• How does the estimation strategy support their
  number sense?

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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.

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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
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Is the Answer Over or Under?

• Problem Over/Under
• 37 75 100
• 476 - 117 300
• 349 45 10
• 17 x 38 800

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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)

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What do the researchers suggest?

• Long term goal of computational estimation is to
  be able to quickly produce an approximate result
  thats adequate for the situation. (Van de Walle,
  2009)

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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.

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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