Video: Subtracting within 100 Using Compensation

Think about the difference 35 − 17. If we add the same amount to both numbers, the difference does not change. Pick a calculation that has the same difference as 35 − 17. [A] 38 − 20 [B] 34 − 18 [C] 30 − 20 [D] 38 − 17. Find 35 − 17.

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Video Transcript

Think about the difference 35 take away 17. If we add the same amount to both numbers, the difference does not change. Pick a calculation with the same difference as 35 subtract 17. Is it 38 subtract 20, 34 subtract 18, 30 take away 20, or 38 take away 17? Find 35 take away 17.

We have to calculate the difference between 35 and 17. The first bar model helps us to think about this calculation. We’re starting with 35. We’re subtracting 17. And the orange part shows us the difference or 35 take away 17. We can add three to both of our numbers to make the calculation easier. Three more than 35 is 38. And three more than 17 is 20. It’s a lot easier to subtract 20 or two lots of 10 from 38 than it is to subtract 17 from 35. This is why we added three to each number. The difference between each numbers is still the same. The size of the orange part of the bar model hasn’t changed. The calculation with the same difference as 35 take away 17 is 38 take away 20.

So to find 35 take away 17, we’re going to calculate 38 take away 20. If we subtract 10 from 38, that takes us to 28 and then subtract another 10, because we’re subtracting 20 altogether. We will get to 18. 38 take away 20 is 18. So we know that the difference between 35 and 17 is also 18. We thought about the difference between 35 and 17 using a bar model. Then, we added the same amount to both numbers, which was three. The difference didn’t change. And we were left with a calculation which had the same difference as 35 take away 17. This calculation was 38 take away 20. This was a much easier calculation to work with. We found 35 take away 17 by subtracting 20 from 38.

The difference between 35 and 17 is 18.

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