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Skip to 0 minutes and 8 seconds PAULA KELLY: So let’s see how we can use some counters to help us to if positive and negative numbers.

Skip to 0 minutes and 13 seconds MICHAEL ANDERSON: OK, so we’ve got some counters here. One side are yellow, and the other side are red. So we’re going to say that if we’ve got yellow facing up, that’s worth 1, positive 1. And if the red side is facing up, that’s worth negative 1. So using these counters, if I have these four, they’re all yellow so that’s positive. So that diagram there would give me a value of positive 4.

Skip to 0 minutes and 41 seconds PAULA KELLY: OK, if we added some red ones then, so say for example, let’s put two of these red ones in. So we have four positive, so I might make a note of this. So we have four positive counters. We’ve added on two negative counters. I’m going to write that with a negative sign. And keep that negative with those counters, I’ll put in brackets. Just to be complete, we’ll put this number here in brackets too.

Skip to 1 minute and 10 seconds MICHAEL ANDERSON: OK, so this now is represented by the sum 4 plus negative 2. So if we look at these counters, we can probably figure out what value that gives us. If we think of one red counters and one yellow counters, because this one’s a positive one and this one’s negative one, they cancel each other out to be zero. So we can almost just get rid of these. And the same here. I can match up a yellow with a red, a positive with a negative, and they cancel each other out as well. So we’re left with just two yellow counters.

Skip to 1 minute and 43 seconds PAULA KELLY: OK, so we had positive 4 add negative 2. Our final answer is just going to be 2. So that was one example of an answer of positive 2. Could we use some other counters to give us the same answer?

Skip to 1 minute and 59 seconds MICHAEL ANDERSON: Yeah. Well I suppose, because we paired them up, I can put as many counters as I like on here. Because we’ve got these two extra yellow counters, so long as I’ve got the same amount of yellows and reds that are going to cancel each other out, all of these diagrams are going to also be equal to positive 2. So I can use as many counters as I like so long as we’ve got them paired up. So this one for example, well we’ve got two, four, six, eight yellows.

Skip to 2 minutes and 30 seconds PAULA KELLY: OK, so we have 8.

Skip to 2 minutes and 34 seconds MICHAEL ANDERSON: And we’ve got 6 m so that’s a negative 6.

Skip to 2 minutes and 37 seconds PAULA KELLY: So you add negative 6, OK.

Skip to 2 minutes and 41 seconds MICHAEL ANDERSON: So we can do the same kind of thing. So if we match up the yellows and the reds, negative 1 and positive 1 like that, they cancel each other out. Again, they cancel each other out. And I keep on going until I can’t much anymore yellows and reds, any more positives and negatives together, and I’m left with 2.

Skip to 3 minutes and 1 second PAULA KELLY: Just positive 2. That what we had before, just positive 2. OK, so what about then if we had just negative counters, all red counters.

Skip to 3 minutes and 11 seconds MICHAEL ANDERSON: OK, so something like that?

Skip to 3 minutes and 15 seconds PAULA KELLY: Yeah, so we’ve got here, we have negative 3. If I added to this some more counters, so say for example I added on. So we had your negative 3 counters. So negative 3. Then I added one, two, three, four, five, so I added negative 5. What would happen now?

Skip to 3 minutes and 40 seconds MICHAEL ANDERSON: Well this is pretty simple really. We don’t have any yellows to match it with any reds, so all we have to do is count the counters. We’ve got five plus another three, so that’s going to give us 8, and because they’re red, it’s negative 8.

Skip to 3 minutes and 54 seconds PAULA KELLY: OK, so negative 3, add negative 5 is going to give us negative 8.

Working with negative numbers: number line

Students will be familiar with working on a number line and will be able to represent positive and negative numbers as positions on a number line. Adding numbers is often represented as a succession of ‘journeys’ along a number line. The positive and negative signs indicate in which direction the next ‘journey’ should be.

In this video, Paula and Michael demonstrate addition using a number line.

Teaching resource

This SMILE resource contains a variety of activities which use number lines to aid addition involving negative numbers.

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This video is from the free online course:

Maths Subject Knowledge: Understanding Numbers

National STEM Learning Centre