**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:

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If you want to look at my approach to this as well. It was fun, still trying to develop it toward multiplication.

http://mrpiccmath.weebly.com/1/category/integers/1.html

I’d love critique to make it better.

I LOVE the area model for multiplication of negative numbers. Seems like it would help A LOT when you get to factoring if you use algebra tiles for an area model there as well. Will definitely be putting that one in my pocket for later.