# Introducing…ZEQUALS

18 February 2013

The new draft maths curriculum for primary schools wants ten year old children to be able to do long division calculations involving four digit numbers divided by two digit numbers, for example 8384 / 27.

Now personally I am quite a fan of long division, it's an efficient method and it's a good mental workout. But I can't remember the last time I actually needed to do it, for the simple reason that life is too short, and these days we all have calculators and spreadsheets. Meanwhile for any child not confident in arithmetic, long division represents a form of torture. The example I gave above, 8384/27, might take a less able ten year old almost half a lesson to work out, and even then the chance of an arithmetical slip is quite high. There are surely better ways to spend valuable classroom time than this.

There's a related skill that is much easier and I think is much more important. Its name (which I invented) is ZEQUALS, and it's a method of estimation. The symbol for Zequals is (it's the letter "h" written using the Wingdings font).

Zequals means you have to reduce any number to a single significant figure, followed by Zeroes (so the Z is for Zeroes, and also for the ZigZagness of the symbol). For example 67 becomes 70, and the calculation 7 x 8 = 56 becomes 7 x 8 60.

Using Zequals, the calculation 8384/27 becomes 8000/30, which is the same as 800/3, which when zequalled gives the answer 300. Compare that with the "exact" answer 310.52 and you can see that Zequals is often remarkably accurate, yet the maths involved is relatively easy.

If a typical teenager could emerge from school able to do ZEQUALS, I reckon many employers would think that was ten times as valuable as being able to do a long division calculation.

[Footnote: many people have commented that this is just another name for estimation and that maths already has a symbol that means approximately equal to (it looks like a wiggly equals sign, rather than a zig-zaggy one). Yes, Zequals is a type of estimation, but unlike normal estimation Zequals has a strict rule that can't be broken. When approximating, there's nothing to say you can't round a number like 417 to 420. But in Zequals you HAVE to round to one significant figure, so 417 becomes 400, and 6.3 always becomes 6. The Zequals technique isn't new - over the years I've come across a couple of people who have used it, or something very similar. I have just given it a name].

Here's my discussion of Zequals on Numberphile