I love math – but man, do I hate long-division

by Seanba on December 9, 2009

I think math is pretty awesome. So when my wife told me about kids needing extra help on the subject at my daughter’s school then I quickly volunteered as a tutor there. As a game programmer I apply mathematics every day to accomplish something very cool – so I won’t hear of children being intimidated by the subject.

Long division image

Last week, while helping a 6th grader with a very boring math problem, I was reminded how much I hate long division and it’s unique ability to destroy any confidence a young student may have.

Here was the problem:

Kevin has access to as many cylindrical steel tanks as he needs. Each of the tanks has a radius of 19 feet and is 31 feet tall. If Kevin needs to transport 428,983 cubic feet of oil, how many steel tanks will he need?

When asked about the steps involved my little protégé suggested:

  1. Calculate the volume of oil in one cylinder (V = πhr² was provided).
  2. Divide it into the amount of oil we want to transport.

Awesome! You’ve got it! See? Math is easy!

But of course, because this is school – and not the real world – all the arithmetic must be done by hand. (And since I’m the tutor I’m going to have to do it too. Ugh, it’s too early in the morning for this.)

For the volume it wasn’t too bad:

r² = 19 * 19 = 361
hr² = 31 * 361 = 11,191
πhr² = 3.14 * 11,1191 = 35,139.74

The last line was a bit intimating by hand. I didn’t enjoy it. It is certainly more than any grown-up would do, including the teacher that grades her work, but my student got it right.

And then came the division part:

428,983 / 35,139.74 = ?

At this point my poor student froze. She was done. Shut down. And that’s just tragic because she knew exactly what she had to do. She also knew how to do long division, but the big numbers and that pesky decimal were just too much work. She stopped caring. The right answer just wasn’t worth it to her anymore. Math sucks.

Luckily, I was able to win her back given that the nature of the question required a whole number answer and that allowed us to reduce the problem to two significant digits.

430,000 / 35,000 = ?


Which of course reduces to the much more manageable:

430 / 35 = 12 point something something

So Kevin needs 13 tanks. Yay! The answer at last. A (relatively) quick double check through multiplication (which I feel necessary given that we rounded off some of numbers) confirmed the answer.

But it is worth pointing out that 6th graders aren’t taught significant digits. No, they’re a good four or five years away from something as useful as that, and in the meantime they’ll be doing the long division that their parents can’t help them with and isn’t even used in the real world anyway. It just reinforces in them the two most frequent stereotypes us math enthusiasts have to fight:

  1. Math is hard.
  2. I’m never going to use this stuff when I grow up.

Well, screw that! I think it’s high time we just took long division out of the curriculum altogether.

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