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Thursday, September 5, 2013

Estimating Subtraction Problems

Today I will teach my fourth grade students how to estimate when subtracting. Some of them already understand how to estimate, but most have no clue (as their pretests have shown). And most of those who know to round then compute clearly don't understand the purpose of estimation.

Here's what I've been getting:

Now what's wrong with this picture? (After all, it's the way our textbook teaches it. Shhh! Don't tell, but haven't opened that text yet this year.) The trouble is that the problem is no easier to solve, and that, my friends, is why we estimate. Estimation should make the problem easy enough to do in your head, which will allow you to check if an actual answer is correct or make some other decision in everyday life.

There's no best way to estimate, but some strategies are better than others.  Here are the steps I will take with my students:
  1. When estimating with whole numbers, always round each number to the biggest digit possible then compute. This way we can estimate using mental math. (This is today's lesson, which we will practice, practice, practice.)
  2. When estimating numbers that include decimals, do the same.
  3. Think! If a problem is easy to compute in your head, why estimate? (For example, the answer to 2060 - 1060 is clearly 1000.) If both numbers round to the same number, go to a lower digit. (For example, if we round the problem 7132 - 6854 to the highest digit, we would come up with 7000 - 7000, and our estimate would be zero. That clearly does not make sense, so in this case, we could round to 7100 - 6900 and see that the answer will be around 200.)
  4. Continue building strategies, such as using compatible numbers. I found this set of activities online to use with students who already have a decent grasp of estimating.
Good mathematicians can and do estimate every day. It's a skill worth teaching and honing throughout the year.