# 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.