“Why?” is a perfectly reasonable question. Fortunately, I ask it often, so when one of my students inevitably wonders, I generally have a good answer ready. Any subject can inspire such a query, but solving for the unknown ("x") is almost guaranteed to have the effect eventually.
Today my beginning algebra student asks, "What do we use this for?"
He says it rapidly, words running together with a zzzzz sound, like a bubbling consonant soup spilling out onto a hot stove. His eyes dart from notebook to textbook to table and almost to me as he freezes his pencil hand, but his feet are still fidgeting, running under the table, off on adventures he can't quite follow until he figures this out.
The expression under his pencil is 15y + 9x - 6x - 1y.
I tell him a story about apple picking, yellow and red apples, losing some, figuring out how many of each we still have.
He nods, not wanting to disagree, but still not quite there. He probably figures he’s not likely to pick yellow or red apples, so maybe I didn’t understand his question. "They said in another class yesterday, when we were talking, that after Algebra 2 the math isn't for any reason."
I'd been helping in that class, it turns out; I’d heard that. "Ah, well! About halfway through Algebra 2, you'll get to a kind of math that works with ideas and imaginary things. You can't pick up apples or boxes to explain it."
"But people who need to make imaginary things real, those people use that kind of math. Like an architect who can imagine a cool-looking building. He has to figure out if he can actually build it. Will it fall down? How can he support it? Will the wind twist it too much? How many people can move around in it?
"So that other math helps people like that, people who imagine things. It helps them make them real."
Now he's with me. "I can imagine a LOT of things."
"Well, then you might just like Algebra 2!"
The hand unfreezes and pencil hits paper. The eyes stop searching and focus first on the textbook, then on the notebook as he starts copying down the next problem. "Yeah, so if I can just figure out the formulas and just do it, I can kinda fly with it."
Or something like that. It was really fast, and kinda buzzy. But he was smiling!
I love this stuff.