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How can joy and sadness explain addition and subtraction with negatives numbers?

Understanding addition and subtraction with negative numbers

Good old negative numbers cause problems throughout Key Stage 2, 3, 4, 5, University, ... Students can perform any number of calculations with positive numbers but throw in the odd negative and their calculations often fall apart.

The problem is that they are trying to remember rules and then mixing them up rather than using 'understanding'.

Students are often given some rules to remember.

+ + makes +

- - makes +

+ - makes -

- + makes -

but they also have these very similar rules to remember.

+ x + = +

- x - = +

+ x - = -

- x + = -

When they are given questions involving negatives students often misinterpret or mix up the rules.

The best thing to do is give a context to the negatives as it gives students something concrete to manipulate or imagine.

In this blog we will look at the rules above in italics.

There are lots of ways to do this but I like to use a happiness score. Zero means that you are fine, neither happy nor unhappy.

Now think of something which will make you happy such as earning merit points, these have a value of +1. Then think of something that will make you sad such as being given a detention, these have a value of -1.

2 + + 3 = 5

You had 2 merits and you are given another 3 merits so you were happy to begin with and then you got happier so you have 5 happy points, that's positive 5.

3 + - 2 = 1

3 merits followed by being given 2 detentions means that you were happy to begin with but became less happy and now have a happiness score of 1.

2 - + 3 = -1

2 merit followed by having 3 merits taken away means that you were happy to begin with but you lost 3 happiness points so your happiness score is -1 (overall you are unhappy).

This is where the model is really useful as students struggle with why this is true that - - makes +.

3 - - 2 = 5

You had 3 merits followed by taking away 2 detentions (what happens if you have detentions taken away? Overall you become happier). This is a way of demonstrating that taking away a negative make a positive or that - - makes +.

-3 - - 2 = -1

You have 3 detentions so you are unhappy to begin with but then two of the detentions are taken away which removes two unhappy points and makes you happier. By the end you are still unhappy as you have a detention but you are happier than you were to begin with.

Let me know what you think of this approach, does it make the concept any easier to grasp?

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