Integers Misconceptions

Why is it that so few of my pupils have a real understanding of performing calculations with negative numbers.

I have recently been working on finding the equation of a line in slope-intercept form with my S3 class. They investigated how to calculate gradient and have a great understanding of how to calculate gradient. The problems arose when actually calculating the gradient. So many errors with calculations such as -4 – (-5).

Listening to conversations at various tables I hear statements like “two negatives make a positive” and “I hate negative numbers”. The main misconceptions seem to be that since 6 – (-3) = 9 then -3 + (-4) = 7 since two negatives make a positive.

At this point I make the decision that before we can continue with the equation of a straight line the class needs to spend more work on negative numbers.

The next lesson, I put this up as a starter discussion.


I found this resource at

In groups I instructed the pupils to discuss each statement and decide whether they thought it was always, sometimes or never true. As I walked around the class it was interesting to hear pupils trying to convince each other about which statement was always, sometimes or never true. When we came back together as a class to discuss their findings each group gave numerical examples to back up their answer.

Taking the numbers out of the questions and focussing on the word statements really allowed my pupils to think about the meaning of each statement rather than trying  to calculate an answer.

Afterwards, the class worked independently on some practice problems and overall most pupils were far more confident and accurate when answering.

These few lessons have made me focus on how I teach integers including phrases I use to try to make calculations easier. But I have come to the conclusion that in the long run they detract from pupil understanding. I’m hoping to never say two negatives make a positive again.

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