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).