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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