Pet peeve #253 (actually, let’s just call it #300): Estimation

Quick: How many seconds are in an hour?

(Pause to let you come up with the answer.)

Okay, you probably quickly recalled that there are 60 seconds in a minute, and 60 minutes in an hour. Therefore, the number of seconds in an hour is determined by multiplying 60 x 60, which equals 3,600. That’s the correct answer, right?

Well, hold on. Remember that I said “Quick.” I would suggest there is another way to come up with an answer, and it is theoretically quicker. I do it by estimating. Let me explain. I make a mental note that there are 60 seconds in a minute, and 60 minutes in an hour. But to make it easier to calculate, I round each 60 to the nearest hundred, which in this case would be 100. Thus my quick estimate of how many seconds are in an hour is 100 x 100 = 10,000.

So even though the actual answer is 3,600, I was able to come up with a reasonable guess of 10,000 by doing some simple, quick rounding. Surely you can begin to see the power of estimation.

Does this strike you as ridiculous?

Well, stay with me for a moment. Here is an actual question from an actual math worksheet assigned to my fourth-grader a few weeks ago. They were studying estimation.

846,543 – 587,018 =

I will spare you the need to do the calculations and tell you that the real answer to this subtraction problem is 259,525. But to find the answer by estimating, the “proper procedure” is to round to the nearest 100,000. So the first number rounds down to 800,000 and the second number rounds up to 600,000. So, the correct estimate of the answer is 200,000.

Now, I don’t know about you, but this astounds me. What good is estimating if your estimate is almost 60,000 off from the real answer? I’ll say it again. The real answer is 259,525, but the “correct” estimate is 200,000. Really, what’s the point? It’s like me “estimating” that there are 10,000 seconds in an hour. It’s meaningless. Not to put too fine a point on it, but according to Webster, an estimate is “an approximate calculation,” and approximate means “nearly correct or exact.” An estimate is supposed to be close to the real answer!

Sarcastic parent that I am, I tried to remember learning estimation when I was in grade school. And for the life of me, I can’t remember it. I might just be forgetting it. Or perhaps I thought it was so stupid that I’ve blocked it out of my memory. But what I do remember is this . . . brace yourself . . . I remember learning how to add and subtract really big numbers rather quickly so WE COULD GET THE RIGHT ANSWER THE FIRST TIME AND NOT HAVE TO MAKE BOGUS ESTIMATIONS!

Nevertheless, maybe I can briefly offer a more plausible alternative. Look once again at the problem I posed above. Maybe instead of teaching kids to round off to the nearest 100,000 in a situation like this, they can be taught to round off to the nearest 10,000. This would make the estimate look like this:

850,000 – 590,000 = 260,000

Now that’s a lot closer of an estimate! Of course, one might object that this would not be fast because a child would have to subtract 85 – 59 in his or her head rather quickly. That seems difficult. All I would say to that is I disagree. Instead of trying to subtract 59, just subtract 60 then add 1 back on to it. That makes it quick, and kids are capable of learning a trick like that.

Well, I’m going to estimate that a few people will not agree with my flow of thought on this matter, or wonder why it bugs me. But hey, that’s why they call them “pet peeves.”