So… teaching exponents as dimensions: the movie.
We look at what looks like ‘one.’ Then … we rotate it so that we can see that it’s actually 2 dimensions. It’s really 1 x 2. That’s two to the first power/dimension.
Then we turn that “two” line up and realize that actually it’s two by two square. (I’m trying to think of a food item or concrete thing to use… chocolate?)
NExt scene, we take the square and rotate that and we can see that a 2 x 2 x 2 cube has 8 cubes.
Then we get all abstract and just show two cubes for two to the fourth… but maybe not right away. Maybe that’s a “spiral element” to add. (A Sue Jones idea: if you teach one small chunk to mastery, then teach something else whlie that’s at the practice stage, then go back and add a little ‘thing,’ you get to review the original again and make it more likely to stay a concept, not a fake-it-’til-you-make-it entity.)
Okay, changed my mind. Do that with three — then see if students can do it with two?? or four? BEcause the whole 2 + 2 = 2 x 2 can confound things.