Understanding Multiplication Tables

Times tables is more than memorising facts: in maths lessons, children will develop their understanding. Using apparatus, models, images, play, investigations and more, the children will gain a deep understanding of multiplications. This includes:

1. Multiplication is repeated addition

In other words, 5 x 5 is the same as 5 + 5 + 5 + 5 + 5. 

Children need experience of using apparatus and equipment, such as counters or multilink cubes and pictorial representations of objects which show this repeated addition. 

2. Multiplication is commutative

In other words, 4 x 5 is the same as 5 x 4.

Children build on their existing understanding using arrays such as the one above, turning the arrays around to show that you now have 5 groups of 4 and they will still total 20. This can then be linked to recalling multiplication facts; i.e., if they know their 5 times table as facts but not their 4 times table, they can use 4 x 5 to work out 5 x 4.

4. Number families

In other words, there are related facts connected to each times table fact:

4 x 5 = 20, 5 x 4 = 20, 20 ÷ 5 = 4, 20 ÷ 4 = 5

Due to their commutative understanding, children will develop their understanding of whole number families. For many children this will need to be pointed out and discussed. Many children will be able to explore this in its abstract form (like in the list above), but this is usually investigated through arrays like the grid above.

From here it is only a short jump to understanding that any missing number can be worked out through knowledge of number families; for example, 4 x [ ] = 20 or [ ] ÷ 4 = 5.

There are other methods children can use to work out missing numbers, but our goal is to increase working memory in order to increase instant recall from long term memory. Being able to bounce around a number family will achieve that.

Please return to the menu page for more information about the stage your child may be at in their understanding. Teachers are always happy to discuss your child's stage and needs.