Bleh, I subbed today. That was good. I had two "informal algebra" classes (I'm not sure what the intent of the name is, but it's the lower level algebra kids), and man the second one drove me nuts. The students were like "this is informal algebra, what are you doing? We're the dumb kids." They just had a horrible attitude. The material wasn't exactly hard - we were multiplying binomials, using area diagrams. The idea that these kids had already given up, and that they didn't even want to attempt it was disgusting. I'm a firm believer in that with impressionable young minds, they'll jump as high as you ask them to. If you set high expectations, they'll reach them. (This is mentioned in School of Dreams as well.) If you set the bar too low, they'll coast, and never become better.

Anyway, area diagrams are pretty slick for teaching polynomial multiplication. Let's say you have (3x-2)(2x+4). Most of us probably learned FOIL, where you multiply the first, outside, inside and last. An area diagram for this would look like:

You then add up all your boxes, so you would have 6x

^{2} + (-4x) + 12x + (-8), or 6x

^{2}+8x-8. The reason this is slick is that first off, it scales (FOIL only works for binomials). The other thing is that you can use it backwards when factoring. You can fill in the upper-left and lower-right hand corners, and then go through picking numbers that make the rest of the diagram work for your polynomial.

(Anonymous)hairylunchidealisms