Monday was my first day back from Spring break. It’s always rough getting back into the swing of things after being away from school for a week–and due to Intersession the week before, I hadn’t seen my students for two full weeks.

Luckily, we had wrapped up our previous unit and we were starting fresh rather than trying to pick up from where we’d left off. Our unit on quadratics starts off with a boot-camp of sorts with a bunch of practice on algebraic skills such as simplifying, expanding and factoring. I told my students that some of them would love it, and some of them would HATE it, but that we were practicing and making sure we all had these skills down before we applied them to super-cool problems involving projectile motion, since everyone likes throwing things[1]. [One student immediately perked up and asked: “Do we get to throw stuff?”]

I start off by asking them the question:

What does “equal” mean?

We discuss various ideas about “the same,” “exactly the same,” “the same value,” etc. I ask them “How do they know that 2 + 3 = 5?” and then continue on to asking “Why does 2x + 3x = 5x?” We talk about how every value they substitute in for x will give them the same result on both sides of the equation. We describe what we would see in the graphs of both sides of the equation if we were to plot both on the same set of axes, or what we would see in the tables of both expressions.

Anyways, then I tell them that this “Investigation” is not a normal one. In fact, it is so different that I have renamed it “Algebra Skills Check” since they will not be investigating anything. They will be practicing their simplifying skills. And then I drop the big bomb on them…

Oh, yeah. And I’m not going to check your work for you.

I am giving them, literally pages upon pages of practice problems and not checking their work. Say what?!?

“Yep. You need to check your own work.” [Pause.] “How are you going to do that?”

At this point I hear the faint beeping of a car alarm off in the distance. This is the urban version of cricket chirping.

“What technology could you use to help you check?” I ask.

Light bulbs go off.

“We could graph them on our calculators!”

I smile and nod, and remind the little ones that have left their TI-84’s at home today about Desmos graphing calculator [2]. They get to work.

And then, for the next 50 minutes, I have nothing left to do.

[1] Not my favorite strategy for teaching, well, anything…but we’re planning on rewriting this class over the summer and I’m not going to change it all up this trimester. All you über-awesome people can just bite me. Okay?

[2] My students love Desmos. I had to coax some of them away from checking out the Desmos art. Repeatedly.