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Skip to 0 minutes and 8 secondsPAULA 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 secondsMICHAEL 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 secondsPAULA 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 secondsMICHAEL 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 secondsPAULA 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 secondsMICHAEL 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 secondsPAULA KELLY: OK, so we have 8.

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

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

Skip to 2 minutes and 41 secondsSPEAKER 2: 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 secondPAULA 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 secondsMICHAEL ANDERSON: OK, so something like that?

Skip to 3 minutes and 15 secondsPAULA 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 secondsMICHAEL 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 secondsPAULA KELLY: OK, so negative 3, add negative 5 is going to give us negative 8.

Addition with negative numbers: using counters

Whilst a number line can be very useful to help students understand what is happening when adding numbers some students find the concept of adding a negative numbers confusing especially if the difference between a negative number and the operation of minus is not clear.

In this video, Michael and Paula take a different approach, and consider how double sided counters, where each side of the counter is a different colour, can be used to aid understanding when performing addition calculations which involve negative numbers.

Task

Try these calculations using double sided counters. If you do not have any double sided counters you can make your own out of card by printing off this counter template and gluing the counters back to back.

a) (+5) + (-3) =
b) (-3) + 4 =
c) (-2) + (-5) =

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This video is from the free online course:

Maths Subject Knowledge: Understanding Numbers

National STEM Learning Centre