A short instructional video transcript where presenter Rebecca explains the mental-maths strategy of compensation: swapping numbers for easier ones during calculations and then adjusting the result. She gives worked examples (15+9; 297−44; 273−52), explains the adjustment steps, and suggests using concrete apparatus to help pupils grasp the adjustments.
Chapters
Hi, I'm Rebecca, and in this film we're going to have a look at using compensation as a strategy to calculate mentally. Now, compensation is all about spotting opportunities to swap a number in a calculation for one that is simpler to work with. And we then need to simply adjust our answer to allow for the change that we made. So let's have a look at what that looks like. Here I have a calculation. Fifteen, add nine. Now, what we can do here is we can compensate by adding 1 onto our 9 to make it into 10. And then it's much easier to work with 15, add 10, we know gives us 25. Then we need to adjust our answer to allow for the change that we've made. So here we added one. That means that here we need to take one away, which will give us a final answer of 24. Let's have a look at another example. Here I have 297, take away 44. It makes more sense to adjust this number because it's close to 300. So I'm going to add three on to turn it into 300. Then I can take away my 44, which will give me an answer of 256. Again, I need to adjust my answer. I've added three. So now I need to take three away to the answer, which will give me 253. Let's have a look at one where it's not quite so straightforward. Here I have 273, take away 52. Now, it makes sense here to turn my 52 into 50 because it's closest to work with. So I'm going to take 2 away from the calculation and then take 50 away from 273, which is going to give me 223. Now here, because I've taken 2 away from the number I'm subtracting, I haven't actually subtracted enough. So to compensate and adjust my answer, I've actually got to take away another two this time, and that will give me an answer of 221. Now, pupils can find this concept a little bit tricky, so using some concrete apparatus such as Dean's would really help them see how much they need to adjust their answer by. So there you go. That's using compensation to calculate as a mental strategy.
