# Shortcuts - Abstract Subtraction

Eva was 7 years and 9
months at the time this video was made.

**The Problems**

At this point Eva has had enough experience with all kinds of subtraction word problems that it is possible to phrase the questions in this stripped down form.

- How much is 51 take away 27?
- How much is 63 take away 27?

**What To Look For In This Video**

- Here is how Eva computes 51 - 27:
- She starts by taking 20 from 50 to get 30.
- She then takes 7 from that 30 by counting backwards - 29, 28, 27, 26, 25, 24, 23.
- She then adds back 1 to get 24.
- She next computes 63 - 27 in the same way.
- Eva's overall logic is excellent. (It really is
**her**logic - it is not something that she was taught.) It is only that the execution, particularly in the first problem, is not terribly smooth. She needs to count backward from 30, stumbling a little, and then she gets confused about whether to add 1 or subtract 1 at the end. - Eva clearly needs my help. But the help is in supporting
**her argument**. I could have told her another way to solve these problems, or complained about the fact that she has to count backwards to take 7 from 30. But, it seems to me that by supporting her reasoning I am helping her build confidence in her own ability to think. It is the ability to think that is important.**If all I wanted her to be able to do was to solve arithmetic problems, I would teach her to use a calculator.**