Adding and subtracting negative numbers is easy enough to put into a context, but it can be tricky to find a good way of representing the multiplication of negative numbers so that it makes sense. A trainee teacher asked me about it last week and it made me think afresh about teaching this.
I remember seeing this quote from some time ago, so cannot recall where from (although it reads as rather Shakespearean!):
“When you love love there is love, if you hate love there is hate, but if you hate hate there is love.”
Why not use this scale of emotion to help us describe calculating with integers.
Looking at patterns on a multiplication grid is a better model, starting with the well-known positive numbers and then extending each range to include negative numbers and continuing the pattern.
If you can think of a way of linking this to love and hate, then do let me know.
You can download this negative numbers multiplication grid here.