Playdates

Playdate focus

Use compensation to make adding and subtracting a lot easier.

Storybook properties

This has counting of groups and lots of comparison words.

Activities properties

These involve adding and subtracting, as well as a little bit of probability.

Useful and easier than you think

Compensation is a useful mental arithmetic tool for simplifying addition and subtraction calculations of all sizes. Understanding it also increases number sense for addition and subtraction. It is simpler than it sounds.

For example, suppose you were adding 99 + 15. You would recognize that 99 needs just one more to make 100, a number that is much easier to work with than 99. So you would move 1 from the 15 to the 99 – you would have the same total number of things, but they are distributed in a way that’s easier to work with. This problem becomes 100 + 14, which is very easy to do. This is the kind of thing we’ll be doing.

Compensation for addition

The idea is to give or take some small amount to make one of the numbers easier to work with. We will typically be making one of the numbers into a multiple of 10. Suppose you are adding 8 + 7. The 8 just needs 2 more to become 10, so take that 2 away from the 7. This makes 8 + 7 into 10 + 5, which is easy. We could also have done this problem by giving 3 to the 7 to make it 10. In that case, we’d turn 8 + 7 into 5 + 10.

More compensation for addition

There are other possibilities for using compensation in addition problems. Consider 6 + 8 for example. The 6 could give 2 to the 8 to make this problem 4 + 10. However, the 8 could give 1 to the 6 to make this 7 + 7, an adding twins problem. Challenge each other to think of different ways for doing a given adding problem.

Compensation for subtraction

For subtraction, we will add the same amount or subtract the same amount from both numbers. This will keep the distance between them the same but will make them easier to work with. Typically that will mean turning the number we’re subtracting into a multiple of 10. Suppose we are subtracting 13 – 8. If we add 2 to both numbers, then the distance between stays the same, but now we are subtracting 15 – 10, which is easy. Similarly, if we were asked to do 17 – 13, we could subtract 3 from both numbers and turn it into 14 – 10. Alternatively, we could subtract 10 from both numbers and turn it into 7 – 3.