My daughter isn't a big fan of math. Yet. (I only say that hopefully, not with any real expectation.) I've struggled for years to help her with her math homework, not just because we're a mother-daughter combo, but also because I was taught to speak math fluently, both at school and at home, and she's only taught to speak it at home. In Seattle Public Schools, the universal language of math is treated sort of like Latin-- a language that exists, and is very helpful when learning pretty much every subject in school, but one that few people take the time to learn. My daughter is down with that. I am not. She's resentful that I force her to speak math at home, and I'm resentful that the whole world (or at least SPS) doesn't.
Anyhoo, this is all a long way of saying that I wrote up a few math lessons for her, teaching her math as well as math language, and I decided I wanted to share them with you, for edutainment purposes. Here goes:
Isolating the Variable, Part One
Or, “How to see a variable naked.”
Say you have an equation that looks like this:
4x + 7 = 19.
That’s all well and good, but really, it would be nicer if it looked like this:
X = something.
Because then we would know what X really looked like. We could see X naked. But for now, we can’t see X naked, because he’s wearing 4 shirts and 7 pairs of pants. With 4 shirts on and 7 pairs of pants on, he’s a 19. But what is he when he’s naked? Well, we’ll have to take off the shirts and pants now, won’t we? Yep. So how do we do that? And which should we take off first?
Well, when X got dressed this morning, he put on the 7 pairs of pants via addition. Our equation has “+7” in it. So to undo that, we’ll need to do the opposite of addition– we’ll subtract the 7 pairs of pants. But in order to keep it an equation (An equation is an expression that shows that two things are equal), we’ll need to subtract the 7 from both sides of the equal sign:
4x + 7 = 19
4x + 7 – 7 = 19 – 7
4x = 12
X then put on 4 shirts via multiplication. In our equation, that looks like 4x, or 4 times x. So to undo that, to take the shirts off, we have to do the opposite of multiplication, or division. So we’ll divide both sides of our equation by 4:
4x = 12
4x/4 = 12/4
X = 3
Woo hooooo! X is naked! And when he’s naked, he’s a 3! Who knew? Well… um, we do. He’s a 3.