## #8 When your students subtract, can they explain how they got their answer?

Date: *December 30th, 2015*

By: *Tom Schersten*

**Tom Schersten**: In this video, I’m going to model subtraction on the My Way Highway. Usually when we teach subtraction, we are using the removal model, where what we’re taking away is already embedded with what we’re starting with.

Today we’re going to be using the comparison model so you get to see what we’re starting with and how much we’re taking away. When we do the comparison model, we’re actually letting the yellow blocks stand for negative quantities.

This is like a positive 42 and a negative 27 that we’re combining. When I do this, the first thing I would like to do is I would like to do this problem by splitting my 42 into a 30 and a 12.

I’m going to record this, that I’m splitting this into a 30 and a 12, and then I’m coming over to my 27 and splitting that up into a negative 20 and a negative 7.

Then I’m going to combine my positive 30 and my negative 20. When I do, these zero out and these zero out, and when I combine them, I’m left with just a positive 10.

I’m now bringing this over the overpass to join up here, and I see that I have some zeroing I can do with the ones. Those zero out, and these zero out, and what I have left is both positives and negatives here.

I’m going to trade my 10 stick in for 10 ones 2, 4, 6, 8, 10. Then I can start zeroing out my ones.

There’s zeroing out, zeroing out, zeroing out, zeroing out and zeroing out, and when we zero those out, we see that we’re left with a positive 5 and I’m going to combine my 10 with my 5, and I have an absolute 15.

That’s one way to do it, but we have other options. Let me show you another way.

I’m again starting with my 42 up at the top and a negative 27. This time, I think I would like to split my 42 out into a 40 and a 2. I’m going to split my 27 up into a negative 20 and a negative 7.

Then I’m going to combine my positive 40 and my negative 20, and when I do, I zero out and I zero out, and I see that I’m left with a positive 20. When I combine my 2 with my negative 7, I will zero out and zero out, I see that I’m left with a negative difference of a negative 5.

We still have to zero out, so I’m going to trade one of my 10 sticks in for 10 ones 2, 4, 6, 8, 10. Those ones can come over to the ones column, and then we can zero out.

Zeroing out, zeroing out, zeroing out, zeroing out, zeroing out, and we see that when we combine our 20 and our negative 5 we end up with 15; the same answer.

Notice all we’re doing is using this mat to keep track of where all the blocks are.

The next video will show you how to make explicit connections, so the kids will make the connection between concrete based ten blocks and the symbolic representations.

If you are interested in having a copy of the My Way Highway template, please see the link below.