Maths facts other than times tables

Nicky Morgan’s comments today have started a debate over whether pupils really do need to have to learn their times tables by the end of primary. I think they should and I’m not going to rehearse the arguments here.

What I do want to do is to ask what other maths facts it’s useful for pupils to know by heart? The new national curriculum specifically says that pupils should memorise the number bonds up to 20 and the times tables up to 12, but are there other facts it is worthwhile memorising?

I’m going to start by saying fraction / decimal equivalences. I’m not talking about ones like 0.5, 0.25, etc, which are obviously helpful but which most pupils will just know (I hope!).  I also think that memorising the decimal equivalences of less common fractions is useful: in particular, fractions with denominators of 6, 7, 8, 12 and 15.  Very often newspaper articles and statistics you come across in everyday life are reported as fractions in these terms – for example, one in seven adults has a subscription to Netflix, or one in every 12 pounds is spent at Tesco (I made those up by the way). Being able to instantly flick back and forward from that to the percentage is really useful. The reverse is also useful. A lot of data are reported as precise percentages, and being able to easily mentally flick from this to a fraction often helps with understanding. If someone tells you that Andy Carroll wins 84% of aerial duels, it can help to think instead that that means he loses about one in every six of them. (Also a made-up stat).

It’s also a classic example of why it isn’t enough to know how to work it out. You might know how to convert a fraction to a decimal, but by the time you’d worked it out, you’d have forgotten what the context of the statistic was.  The person who did know that 1/12 is 8.3% can move on to considering whether Tesco’s dominant market share is a cause for concern, estimating the share of other big chains and wondering what that might look like as an absolute sum of money. As ever, knowing stuff off by heart enables critical thinking rather than stifling it.

Some other suggestions: the 75 times tables. The person who suggested this one did so as a technique for winning the numbers game on Countdown. I wouldn’t recommend that we reorganise education around winning TV quiz shows (god forbid) but since I took this advice and learnt my 75 times tables, I have found them useful in more ways than expected. I suspect this is the case with a lot of these things – it’s only once you learn them that you fully appreciate how useful they are. A bit of the Dunning-Kruger effect, perhaps.

Any maths teachers out there, please leave your suggestions in the comments. Square numbers? Other times tables?