1 | Emphasise multiplication is commutative as soon and as much as possible
Knowing that for every multiplication fact you know you also get one free reduces the load. Know 4 x 6 is 24, then 6 x 4 is 24. The array is the best image for helping children get a sense of how and why multiplication is commutative. An image of a four by six array is transformed into a six by four array simply by rotating it through 90 degrees.
2 | Focus on 2 times, 10 times, 5 times and 4 times
Being confident in the ‘low hanging fruits’ of 2s, 10s, 5s and 4s facts provides a strong foundation for the remaining facts. Working on doubling is central to two times facts, and doubling twice gives you four times facts. Ten is easy, and halving helps ground the five times facts.
3 | Put the smaller number first
Pupils in Japan are explicitly taught to reverse multiplications calculations if the smaller number is second. Seven times four? Do not do that; do four times seven. This has a double pay-off. Firstly, you are often going to end up with 2, 4, 5 or 3 as the first number – and they are easy (see tip 2). Second, if you need to do some skip counting to get the answer, then that is going to be quicker with the smaller number first. Seven times two means counting “two, four, six, eight, ten, 12, 14”. But two times seven, hey, it is just seven, 14.
4 | Teach the Chinese tables
The astute reader may have noticed that I have not used the words ‘times tables’ so far. That is because I am not convinced that chanting tables is the best way of getting to know your multiplication facts. I would much rather a child knew that, say, four times nine is 18 (double nine), 36 (double again), than have to chant through the four times table. But if you think tables help, the Chinese versions are rather more sensible than ours. In China, the two times table is: 1 x 2 = 2, 2 x 2 = 4. And that’s it! Three times and four times tables: 1 x 3 = 3, 2 x 3 = 6, 3 x 3 = 9; 1 x 4 = 4, 2 x 4 = 8, 3 x 4 = 12, 4 x 4 = 16.
Each table only goes up as far as the square of the table number. So, you might ask, if the two times tables ends at 2 x 2, when do the children learn what 9 x 2 is? Well, they do not directly, but they work a lot on multiplication being commutative (tip 1) and putting the smaller number first (tip 3), so given 9 x 2, they know that is equivalent to 2 x 9 and, hey, that is 18.
Mike Askew is distinguished professor of mathematics education at University of the Witwatersrand, Johannesburg, and series editor of Oxford University Press’s new primary maths programme MathsBeat.