# Fun with long division

May 30th, 2013 by dadA fellow parent in Dorje’s class posted recently on the horror of Grade 4 maths. In particular, the long division problems they are getting.

Dorje is a bit like me, likes to be right too much for his own good, so he was horrified to have corrections this week. For two of the three corrections he got the same answer as he originally did, which turned out to the be the right answer, so either the teacher was wrong – I remember my Standard 5 teacher being unable to do maths, so much so that he was sent for remedial lessons, as his “I was just testing you” five times a class got a bit much – or more likely he miscopied the question.

The third one, however, he did get wrong, so he asked for help. Maybe he was hoping I’d give him the right answer, but no such luck. First I got him to check if the answer was right – he should be able to multiply back, and so be absolutely certain about his answer.

His answer was wrong, so he showed me how he was doing it.

I can’t remember how to do long division, school-style. It’s horribly tedious. Divide here, carry this, remainder that. I can see why schools teach it, as it’s a technique that doesn’t require any thought, but people doing long division outside of school either:

- use a calculator or, if they’re doing it in their head
- use a shortcut

A calculator defeats the purpose of doing maths homework, and I couldn’t follow Dorje’s explanation of his method, so I decided to show him my way of doing it. It’s useful to look at different ways of doing a problem – people who can do maths well in their heads almost always have a shortcut technique.

As a simple example, let’s say the problem is R1735 divided by 17. My easy technique is to use multiples of ten to simplify the problem. So, 17 times 10? 170, far too low. 17 times 100 is 1700, which is about right. So that’s 100 remainder 35. 35 goes quickly into 17 twice, so the answer is 102 remainder 1. It can all be done quickly in the head, much quicker than tediously carrying this carrying that.

I showed him my way, and he correctly worked out the answer, and then saw the mistake he’d made using the school technique.

Dorje and I used to play number system games at breakfast, although it’s been a while now. I’ve introduced him to the wonders of binary, where 1 and 1 is 10. We’d also make up maths rules. So for example we’d make up a problem where 12 gazunk 6 is 78. 11 gazunk 5 is 60. And the other person would have to work out what “gazunk” is (in this case, both times and plus).

I’m guessing if it’s up to me, Dorje will be quite good at maths. Luckily he has other influences too, as if it was up to me in visual creativity, Dorje would be in trouble, as our deer prancing vs monster behind the hills draw-off showed.

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