Baby's first gold tooth

Yesterday, I came up with my first "hook". Okay, maybe not exactly my first, but definitely my best, meaning my most useful, most engaging, and first that isn't really a languistic trick.

(I also came up with a new linguistic trick, see below).

Systems of Equations:
So, I have this ball in my hand, and I'm eager to show it to you, because I don't know much about it yet-- it's all wrapped up inside my fingers-- but I think I can unwrap my fingers, and, yeah, there: a ball.
This is kind of like unwrapping an equation: 2x + 5 = 11 -> 2x = 6 -> x = 3 and now you can see the ball, I mean the unknown, x.

But, what if I have two balls in my hand? Now, when I try to unwrap it, I'm liable to drop one, which just messes up the whole thing. (Dropping one ball). So, if I want to show them to you, they've got to keep moving (starts juggling two balls in one hand). This is like this equation: l*w = 12. The two balls could be 3 (timed to one ball rising) and 4 (the other ball), or else 1 and 12, or 2 and 6, or 8 and 1.5, or -3 and -4, or anything. If one ball moves, the other one will too. So, in order to stop this whole thing-- I need another hand.
(Taking one ball into each hand), And then I can show them both to you.

This is how equations work, too: if I have two balls in one hand, they have to either keep hidden, or else they're both going to be moving (or at least, movable). But once I add a second equation (w = 6), then I can stop the whole thing, and tell you what is what.

Try it with a volume problem, now: You have a square-bottomed rectangular prism. It's twice as tall as it is wide, and the total Volume = 54 in^3. How tall is it?
So far, I have just one equation (V=54 in^3), but I can add another one really easily, because I know something about volume: V= lwh.
Now that's TWO equations (hold up both fists) with FOUR variables (show that there are two balls in each hand). Not so good. I need more hands-- I mean, equations.
The bottom is a square, so l=w. That's THREE-- just one more now. The height is twice the width: h=2w.
Now some algebraic substitution, and V=lwh becomes 54=(w)(w)(2w). Solve that, and w=3, so h=6.


So far, this skit has worked really well with two classes. It helped to review algebra... I've always liked that "algebra" is from the Arabic (al = the, gebra = change). I love telling my Latino students that they have an advantage in learning math, because so much of it makes more sense in Spanish. This is a great example. In English, that direct translation isn't so good. In Spanish, I'd translate "al gebra" as "el cambio", which is great, because "cambio" captures more of the idea of replacement or trading, which is a huge concept in algebra (substitution of equivalents).

So, the big linguistic breakthrough today? The Currency Exchange two blocks from the school has a neon sign in the window: "Casa de Cambio". So, in English, don't translate "al gebra" as "the change". Translate it as "the EXCHANGE". Emphasize that this is synonymous with "the SWAP" or "the TRADE".

Maybe it's just me, but I saw a lot of lightbulbs over heads today. "And there's another swap..."