I’ve been struggling with my Algebra 1 class on and off for a while now. They often pretty clearly seem to find each other more interesting than the math I’m trying to share with them.
As we’re beginning to start looking at polynomials (operating with them and manipulating them), I decided today to pull out a number trick that I ran across I forget where. The fun part about it is that you do the whole thing in silence—it adds some showmanship and mystique. Briefly, by looking at the squares of numbers and the product pairs of surrounding numbers, you run across some nice number patterns that lead you to the factorization of the difference of two squares.
It went over okay, although there were still kids who just weren’t into it.
Once the miming was over and we talked about difference of squares and did some geometric and algebraic justifications of the numerical patterns, I got in a nice groove and said some good things about the project of algebra and what’s interesting about polynomials. I think both they and I got a little energy from that. Still, I have no illusions about the hard sell that will probably face me in class tomorrow.
As a coda: When my Geometry class came in, they asked me about what was on the board and whether we were going to do that today. I figured, why not, so I did the shtick again. Rapt attention and participation. Felt good. And one of my students fondly shared a memory of us doing something along these lines when he was in a seventh grade class of mine.
Here’s more of the board: