**Compensation in addition and subtraction? **

The strategy can be used to change any subtraction into an easier one. For example, 453 – 178 looks a bit daunting. I would rather do 453 – 180. (But remember: I will have taken away 2 more than I should and this will have to be added on again later). If I’m still struggling with 453 – 180, I could instead choose to do 453 – 200, which is 253. (Now I have to remember there’s an extra 20 to add on.) So the answer is 253 + 20 + 2, which is a relatively easy addition, giving 275.

This approach is particularly effective with precisely those subtractions that cause most problems using the decomposition algorithm: those with zeros in the first number. For example, the image shows a typical error made by a 9 year old boy attempting to calculate 101 – 97 set out in vertical format.

** **(a) A 9 year olds unsuccessful attempt to calculate 101 – 97: and

(b) His successful use of compensation

He was then given the question in horizontal format and encouraged to work it out mentally. This he did successfully by first dealing with 100 – 97 by counting back and then compensating. Part (b) is his response to the invitation to ‘write down how you did it in a way that shows your thinking to someone else’.