Subtraction Methods: How Far Apart?

Oct 5, 2015 | Chattanooga

Yesterday, I was assessing a student and I asked him, "What is 23 - 18?"

He stared at me quite perplexed, and his mom interjected that it would be hard even for her to figure out the answer mentally - "Since 8 is bigger than 3, this question would require borrowing and very few people can borrow in their heads."

I agree that very few people can borrow in their heads, but if we think about the question 23 - 18 not as how much is left when we take 18 away from 23, but as how far apart those two numbers are from each other, the question becomes much simpler.

How far is it from 18 up to 20? Two.

How far is it from 20 up to 23? Three.

So how far is it from 18 up to 23? Five.

We teach this skill explicitly as the "How Far Apart?" method of subtraction and we encourage students to use it when the numbers are quite close together. Here is some practice for your student below:

26 - 18 = ?

32 - 27 = ?

41 - 35 = ?

And some challenges!

103 - 98 = ?

32 - 17 = ?

We've got lots more tricks up our sleeves here at Mathnasium and I would be happy to show them to you and your student during a free trial lesson. Stop on in and say hello sometime!

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