Thin Slicing Questions to Learn Exponent Laws

Today we spent grade 9 math up at the boards in random groups to work on representing exponents, and worked all the way to learning 2 exponent laws.

We began with questions like “represent 2 squared”, and got all the notations on the boards (expanded form, a 2×2 square, 4, 2^2). After some repetition we looked at some cubes, and students represented and expressed them e.g. 7 cubed=7x7x7, 7^3, and a 7x7x7 drawing of a cube. They evaluated what that would be without a calculator as well since we are working on our fluency strategies whenever we can. We looked at what fractions would be when raised to an exponent as well, again with the fluency strategies.

Next we looked at what x squared and x cubed would be, connecting to yesterday’s toothpick task. We then revisited what (2x)^3 would be. We’re working on remembering to always multiply the coefficients and the variables together and always writing down exponents when needed. We looked at multiplying variables by each other, and what to do if there are different variables and also coefficients in the mix. We then did some power of a power examples.

At the start of the class students were fidgeting and uncertain about exponents, and some were hesitant to contribute. Pacing a lesson like this is tricky because I want to make sure the majority of the class is understanding, but also give enough challenge so that those who do understand aren’t totally bored. We had a quiz/exit card at the end of the lesson to see what concepts stuck and what ones we need to go over again tomorrow. Pretty proud of the progress today!