Update: James Cleveland adds: “When I worked with the Algebra Project, we modeled subtraction as distance. E.g. How do you get to -2 from -8? Go 6 to the right. So -2 – (-8) = +6.
- “Hot cubes and cold cubes” – You toss in 10 cold cubes (-10) and 3 hot cubes (+3) you have 7 cold cubes (-7).
- Something similar is done with “Zero Pairs”.
- This is a pretty big post from Mathy McMatherson on integer operations.
- James Tanton has a nice video on why multiplying two negatives gives you a positive.
- Tanton also uses the idea of area as a model for integer multiplication to explain why multiplying two negatives gives a positive. Here’s a picture from it: