The Equations of Horizontal Lines

If you have bleachers anywhere on campus, take your students on a field trip. No explanation.

Have everyone lie down head to toe on the same row of bleachers, starting at the top. (They don’t have to be touching.)

“Everyone stand up, move down to the next row, and lie down again.”  Work your way down the bleachers.

After the bottom row of bleachers, possibly after giving the students some extra time so that they’re nice and relaxed, ask them how many want to lie down on the ground. (If you’re lucky, it’ll be yucky down there.) In the best case, no one (or almost no one) will want to do so, and you can skip actually having them do that. Then tell them that it’s time to go back.

Hopefully the kids have been asking you why they’re doing this. Don’t answer them, or put them off in your own way.

Back in class, everyone seated, quiet. You have a presentation (PowerPoint, SmartBoard, handwritten under the document camera, whatever) ready to go.

“So, you want to know why we did all that? Why we lay down in horizontal rows over and over at different heights? Here’s why:”

Pull up the slide (or whatever) with nothing but a huge letter y, one that fills the screen or board. Just stand there, as if that’s all that needs to be said. Maybe a mouse click reveals an = sign next to the y. Give ’em time to soak it in.

In the best case scenario a student realizes what’s going on and shares their “a-ha” with the class. Maybe they yell it out without raising their hand because they’re so excited about the pun. 🙂

If not, you get to tell them: Every time they lay down horizontally they represented a line. At different heights, different lines. But what they all had in common was that they were horizontal. And what do the equations of horizontal lines all have in common? They are written y = (a number).

See if that doesn’t firmly connect y= with horizontal lines in their minds. (Fingers crossed, everyone!)

What about the lying on the ground? If no one wanted to do it, you could use that as a metaphor for the x-axis equation being y=0.

(Zero people wanted to lie on the ground, right? But if you did have some students, or many, who did want to lie on the ground, maybe you can connect zero feet off the ground with zero units above the x-axis. That’s a stronger analogy, really, though possibly not as memorable as, “Eew! There was zero chance of me lying on the ground!”)

And how shall they remember x=? Well, a vertical line is the other special case, the one that’s not y=, of course. 😉

I came up with this in response to a Twitter plea from Sarah yesterday. I haven’t tried it, and I’m not currently teaching Algebra, but it sounds like fun to me. If anyone gives it a shot, I’d love to hear how it goes.

ADDENDUM (a few minutes later)

So I had my son Isaac, who is in Algebra 2, read this post and after he got over the fact that the punch line is a pun, he turned right around and came up with a pun of his own for vertical lines:

“And those girls who refuse to lie down at all because it will mess up their hair? They were the x-tras who stayed vertical.”

X-tras? Vertical? X=? Ah, my son, you bring honor to the family name. 😀


4 comments on “The Equations of Horizontal Lines

  1. jnewman85 says:

    Wow, it took me two reads through spaced quite some time apart before I realized what your pun was! Yeah, and I’ve realized that I’ve become quite as punny as my own father, even though I rolled my eyes at him back in the day.

  2. Indeed, Jonathan, though I didn’t mention it in the post, I got my sense of wordplay from my father as well. As I was adopted, I know it wasn’t hereditary. Therefore it must be a learned behavior, which I’ve clearly passed on to the next generation. My daughter does not seem to have it, though. Could it be a predominately male trait? And if so, why?

    You make me wonder if I should explain the pun here, but I won’t. The explained joke is always the poorer for it. Hopefully folks who didn’t catch it will give the post another read and see if they can find it for themselves. If anybody can’t figure it out but is dying to know, feel free to email me.

    A hint, though, if you like: In my view, the pun is really the whole reason *why* this might work as a mnemonic device. You could do the same exercise to try and get “horizontal line = zero slope” into students’ heads with a summation like “you did zero work while you were lying on the bleachers”, but I like to think that would have much less power due to its lack of an appropriate pun.

  3. Amy Zimmer says:

    Awesome! Can’t wait to try it and report.

    PS I thought word pundom was a product of being raised in Brooklyn. ( btw…both my girls have it…and their dad is from Brooklyn)

    • My dad spent much of his youth in Chicago. I have no idea if there’s a connection to Brooklyn there, but I grew up smack dab in the middle of suburbia, and my kids are pretty much suburban as well.

      *I* thought it was a male thing. My daughter does not have it at all. Funny…

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