Q&A #4319

Teachers' Lounge Discussion: Estimation: Order of Magnitude, Compensation

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From: Anonymous

To: Teacher2Teacher Public Discussion
Date: 2001110216:36:44
Subject: Order of Magnitude, compensation

After months of researching and begging for information about what the
ITBS meant by Order of magnitude and compensation, I finally found a
web site in Technology and Learning for Riverside Publishing. They
would not send the information directly to me, but only to the head of
testing in my district. They, however, relayed the information on to
me at my request. How I wish Riverside would simply make this
available to everyone!
   At the middle school level,if they have an estimation problem where
they use patterns, for instance 7166 divided by 9, they want the
student to make 7166 into 7200, for 9 will divide easily into it. By
evaluating order of magnitude, they want to see if the student will
decide to mark 8, 80, 800, or 8000 for their answer. In other words,
do they know thier powers of 10 and what will be a reasonable answer.
This seems so easy once it is explained to us.....so why don't they
tell teachers up front what they expect?
   Another thing they emphasised was that they always want the CLOSEST
ESTIMATE, so for compensation, if they have a problem like this:      
$63.99 sneakers
                            Sale   1/3 off
Give the closest estimate of how much you would save on the sneakers:
A) $10-$20
D) $40-50

They expected the student to round $63.99 to 60, since it is easily
divided mentally by 3. That would give you $20. But that would make
you decide between A & B. They then expected the student to think,"But
the sneakers really were a little more than $60, so how much I save
will really be a little more than $20 (this is what they mean by
"compensating" for the difference). Thus , they expected the student
to choose B, since you really save a little more than $21. Notice that
if the student failed to read the problem well (that they were trying
to find the savings, NOT what they spent), they have the other wrong
answers that they would have gotten.

              Please pass this along......after several years of
frustration, we finally have a definitive answer!

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