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Q&A #340


Compensation as a form of estimation

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From: Gail (for Teacher2Teacher Service)
Date: Jun 20, 1998 at 10:59:20
Subject: Re: Compensation

Dear Bettie,

I teach fourth grade math, and have shared compensation with my students
for the past five years.  It is in our textbook in the estimation section,
but I don't think it is really an estimaiton activity, because it involves
finding the exact answer.  What you do is adjust the numbers being added or
subtracted to make the problem easier to do mentally...   for example,
if the problem is 198 + 217, you could take 2 from the 217 and add it to the
198.  Now you would have 200 + 215, an easier mental math problem.  If the
problem was 217 - 198, you could add 2 to BOTH numbers to get 219 - 200,
again, easier to solve mentally.

To help my students understand why this works, I give them a set of problems,
for example, 191 + 225,  192 + 224, 193 + 223, 194 + 222, 195 + 221, 196 +
220, 197 + 219, 198 + 218, 199 + 217, etc.  But I don't arrange the problems
in that order.  I give them a few minutes to solve the problems, and then we
discuss what we found.  It doesn't take long for them to realize that all the
sums are going to be the same...   then I guide them to figure out why it is
happening. From there it is a small step to applying it to other problems.
Every student won't want to use this method, but it really helps those who
are still having trouble regrouping when they subtract.  I have students who
will use it every once in a while, long after we have left the topic, and the
others will recall the lessons.  I think it is a valuable tool for students
who are having difficulty regrouping, and it can liven up a computational
practice lesson.

 -Gail, for the Teacher2Teacher service

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