**Compensation in addition and subtraction? **

Here’s a more challenging example, written out in a way that might explain the thinking to someone else:

To calculate 4003 – 3196

Add 4 to the second number: 4003 – 3200

Add 800 to the second number: 4003 – 4000 = 3

Now compensate: 3 + 4 + 800 = 807

Obviously to use this strategy you have to be very good at recognising what you need to make a number up to the next multiple of 10, the next multiple of 100, and so on. This skill should therefore be a very specific teaching focus with primary-school pupils.

There are other ways of using the strategy of compensation, all of which amount to changing one or more of the numbers in order to produce an easier calculation. We can use this approach to exploit our confidence in handling multiples of five, to relate additions and subtractions to doubles, or simply to replace one of the numbers by a more ‘friendly’ number. These are explained below.