Thirty Six

I’ve never taught young children to learn their times tables, but if I did, this is instinctively how I would probably approach it. For the sake of complete clarity, nothing I have written here is meant to suggest that this is not currently done, nor is it meant to suggest that it is the only or best way of doing it. I’ve written this simply because I’ve been thinking about times tables and wanted to write down how, in an ideal world, I would do it. Mostly, it fits in with how maths is sequenced in the National Curriculum.

It will be helpful if children can count up to 100 and have a rudimentary understanding of place value before they start this.

Start with the concept that a number times one is always equal to itself.

Then introduce the idea of a decimal place and decimal point. We can write 1 as 1.0, or 1.00000. They are the same.

Then we can do multiplication by 10. To multiply by ten we move the decimal point to the right. 1.00 becomes 10.0, and 3.00 becomes 30.0 and so on. This could be done by learning the facts 10 x 1, 10 x 2 etc. and then looking at the pattern. However, I think this leads to the “add a zero on the end to multiply by 10” misconception. The decimal point/place idea is conceptually harder (currently it is later in the NC than this methodology would allow), but underpins the understanding of so much more so is worth the time and effort of doing it early.

Then introduce the commutative property of multiplication. 1 x 10 = 10 x 1 and so on. Don’t necessarily need to use the word ‘commutative’ but I think it helps if you do.

Then we can go on and learn the other 55 multiplication facts required to memorise the times tables up to 12 x 12.

You can reduce this number by teaching the tricks, such as 9 x A = 10 x A –A. Similarly, you can do the 11’s this way as well. Some would argue it adds an overhead to the recall, but to be honest, if it does its not much of an overhead. If you use these two tricks instead of memorisation then you are down to 36 facts to memorise.

The route taken above is more about mathematical understanding (there are three concepts to understand) than pure numeracy. If all you want is children who can sing the times tables then perhaps having them learn to sing it is a better way. I’d prefer they had the mathematical understanding as well. Indeed, perhaps there is an argument for learning both ways.

I would love to hear how the professionals do it. Genuinely.