AboutLongDivision

(I actually wrote this post a couple of days ago, when my internet connection was down!).

Ben's half-brother is visiting for Memorial Day Weekend. It's always wonderful when Colin comes; in spite of their size difference (Colin, who is 16 and about 6'2", is more than a foot taller than Ben) there is a lot that they can do together; watch movies, play Nintendo, play basketball.

But, of course, learning still has to go on, and last night I insisted that Ben had to get some long division practice in. He knows the long division algorithm, and a few months ago I taught him how to divide by decimals. So now I am trying to get Ben to overlearn decimal long division, and the best way to do that is to get him to practice it.

So I handed him a sheet of paper with some long division problems on it and asked him to do them. He did them too fast -- too eager to get back to Colin and the Nintendo game -- and got most of them wrong. Not surprising, perhaps, but I'm looking for his long division skills to be so automatic that he can do them when most of his conscious attention is elsewhere.

I want long division to be a no-brainer for him, literally. It should be in his fingers.

He did the problems over again this morning; I stood looking over his shoulder to try to figure out what had gone wrong the night before. I was surprised at how good he actually is at the long division algorithm. He is, in fact, working out the few bugs left before he achieves mastery, and the distraction of Colin's presence had driven them out into the light.

If your kid is at or near the mastery point in long division, here are a few problems to look out for, and some sample problems that might help diagnose them.

• Uncertainty about what to do if the divisor does not divide the current number, after you bring the next digit down. For example, this occurs in the second step of dividing 92.0 by 9. The answer to this problem is 10.2222... a child who does not have this down cold will typically get 12.222222 for an answer, skipping over that lone zero.

• Uncertainty about what to do with a problem where the dividend has fewer decimal places than the divisor. One example of this is the problem 34/.21. In setting up this long division algorithm, the divisor and dividend should both be multiplied by 100: i.e., the decimal should move to the right by two places for both values, and the division problem should become 3400/21. A kid who does not completely have this nailed may get confused about what to do with the 34.

• Uncertainty about where to stop the long division process. Division problems that do not terminate should read, in general, something like "find the value of 213/14 to the nearest tenth (or hundredth, or whole number) ". A kid needs to be taught explicitly how to handle answering these questions. For example, suppose a problem reads: find 92.17 divided by 13 to the nearest tenth. Then the child should actually calculate the quotient out to the hundredth place, and round the answer to the nearest tenth. In the case of this problem, the child will get 7.09 as an answer through long division, and should round this answer to 7.1.

I would strongly advise against doing what I did last night -- that is, handing him ten juicy long division problems to do in a chunk. When faced with a lot of problems like that, my kid tends to lose hope of ever finishing, and despair makes him careless. Better to give him only three or four at a time, which I plan to do from now until he has long division down cold.


StrugglesWithLongDivision
MathInTheBlood
ForgivingDivision
ForgivingDivisionPart2
TryThisWithForgivingDivision
TeacherGuideEverydayMath
EverydayMathEpilogue
ThirteenQuartersInTerc
HowNotToTeachMath
WhoSaysLongDivisionIsHard

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