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.edu
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?
 Make an estimate.
Keep track of how you
got your estimate.
139 x 43
 Share your strategy.
 Note the mathematical
understandings you
needed to make this
estimate?
A Different Approach…
What is happening here?
What if the estimate was
6000?
139 x 43
 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
5,210 + 298 ≈
5,400
5,500
7,000
59 x 11≈
60
500
600
6,000
268 ÷ 9.9 ≈
25
250
2.5
2,500
8,000
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?
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 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?
Problem
 37 + 75
Over/Under
100
 476 - 117
300
 349 ÷ 45
10
 17 x 38
800
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)
 www.mmp.uwm.edu