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:

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Wow, what an awesome activity. I’m a sucker for anything that starts with playing around with a pattern, and ends with expressing it symbolically.

I noticed you can also see the arithmetic/geometric mean inequality (well, some of it?), I suppose because it’s basically the same result.

What do the “1000 years!” markings mean??

Hi Sam!

Cool. The AM/GM connection is really nice.

The “1000 years!” and “5000 years” were me trying to get them to guess how long humanity has known about this number pattern. (They were both surprised that they hadn’t been told this at some point and that anyone had *ever* sat down and played with numbers in a way that led them to it.) I tossed out the 1000 figure as an over/under, and a kid almost at once said “5000”—just as a stab. And I thought this was pretty close, ancient Babylon-wise. And this confirms it, I think.

I hope all is well in Idaho. Thanks for dropping by!

Ah, I found this reply. Sometimes I forget where I left a comment.

All is indeed well! I’m trying to help my students get into the blogging community, which is fun. I need help getting into it too.