This was an excellent video! The key take-away for me was that we need to help students use patterns and reasoning to determine things that are hard to model.
I loved how Sarah used the strategy of reasoning with patterns to develop the concept of multiplying two negative numbers. I’ve used a similar sequence to teach exponents. We know that:
2^3 = 8
2^2 = 4
2^1 = 2
Then, noticing the dividing by 2 pattern going down the lines, we can reason that 2^0 should be 1, and 2^-1 should be 1/2…