I got asked today “is there a real world connection to factoring?”. I hadn’t heard that one in a while and I think it’s because I’ve been doing a good job of “starting at the end” like this awesome teacher. Factoring though, that one had me thinking I’d better just stick with what I know. So I showed them the area model for multiplying two binomials, then we worked that backwards and called it factoring. We even did some whiteboards earlier today. I told them a new student was coming and they would need to teach them the skills they just learned using only one whiteboard. Here’s what they came up with:

Not too bad. I also asked them plenty of questions to make sure each group member could explain what was on their board. And there were a few mistakes (some still in there), but that was ok because we fixed them as a group! So, clearly they’ve got this skill now. But the question still came up “is there a connection?”. **Dammit.**

I think that my techniques here were good because *they can factor a trinomial now*. And we also have made connections between quadratic equations and real world projectiles:

The constructed response portion of our last exam even had a real world connection:

**.**

**But where I failed was connecting these events.**

So I think what I should’ve done was start the unit with a video of a projectile. Then get the students asking questions like “how high will it go” or “where will it land”. Then when I show them factoring (using the same method I just did) they won’t ask “where’s the connection?”, they’ll just proceed to answer their own questions using this handy new skill they learned (plus maybe a few others).

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I’m starting this soon. I think I’m going to have them throw tennis balls in the air and time how long it takes them to come down. Then, we’ll do quadratics and build graphs from their data. It may be crazy, I’ll let you know how it goes.

Nice! I’d love to hear how it goes. This unit has totally thrown off my math modeling game this year.

Yes, I haven’t thought about how we are going to “build the equation”. I’m very glad I read your blog before starting this. Food for though for me.

Yeah, building the equation is the problem. It seems so easy to get students to do it for linear equations. But I keep “telling them the answer” when it comes to quadratics. So glad others are working on this problem too!