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This content is taken from the National STEM Learning Centre's online course, Maths Subject Knowledge: Understanding Numbers. Join the course to learn more.

Skip to 0 minutes and 7 seconds PAULA: So let’s have a look now at how we do some addition with negative numbers.

Skip to 0 minutes and 13 seconds MICHAEL: So let’s have a look at the example of 5 plus negative 3. We can think of these as two different vectors of different lengths and different directions that we’re combining together so this add basically means we’ve got a plus five and a negative 3. So this plus 5 is going to be an arrow of length 5, moving us in the positive direction. And this one’s going to be a smaller arrow of length 3, and that’s going to be going in the opposite direction. So what does this look like on a number line?

Skip to 0 minutes and 47 seconds PAULA: So if we started from our 0, we’re going to be five places in a positive direction.

Skip to 0 minutes and 52 seconds MICHAEL: And land on the 5.

Skip to 0 minutes and 53 seconds PAULA: We’re at 5. And then because we’ll also having a negative 3, we’re going to move in the opposite direction three places that would take us down to a positive 2.

Skip to 1 minute and 4 seconds MICHAEL: OK, so what happens if we add two negatives together? So say, for example, we had a negative 3 and we are going to add a negative 2.

Skip to 1 minute and 14 seconds PAULA: So the number line again. If we started at negative 3, say from zero we go this direction to our negative 3.

Skip to 1 minute and 22 seconds MICHAEL: So we end up on negative 3 with the first part, and we’ve got a second part then negative 2.

Skip to 1 minute and 27 seconds PAULA: So our second part is a negative 2. We going to go further in this direction 2 more places, which finish at negative 5.

Skip to 1 minute and 34 seconds MICHAEL: OK, so that’s going to give us negative 5, whereas the first question positive 5 plus negative 3 we ended up on 2.

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