I have recently had quite a few discussions around the awful misconceptions many students have when dealing with negative numbers (recently discussed by @srcav here). I wince every time I hear “two negatives make a positive” and have, over the years, used various strategies to help my students develop a better understanding of what happens when we add or subtract directed numbers (they tend to be ok with the more abstract concept of multiplying and dividing).
Anyway.. I have in the past used negative and positive cards to visually demonstrate the ideas which seems to hit home with some but add to confusion for others. I have also tried various analogies such as “hot and cold” etc, again with varying levels of success.
My latest attempt was from an idea I found in this nRich article which describes the “Happiness Model”. I put together a lesson activity around this which went particularly well (according to my class!) so I thought I would share. The key ingredient was the use of language such as “adding positivity” or “taking away negativity” and getting them to think carefully which direction on the number line we would need to go.
Feel free to use and adapt the lesson file found below and I welcome any comments.