When we lived in Vegas, I never had the pleasure of coming across an actual, live scorpion. Black widows, however, were everywhere. I saw enough of them to learn quickly to never reach into a dark corner of the garage, or behind the toilet tank, without making sure the space was clear of spiders.

Discovery can be thrilling. Or extremely unpleasant.

We’re in the midst of the Quadratics unit with my Algebra 1B classes – five sections ranging from pure multiple-time repeaters to on-track freshmen. We just finished finding axis of symmetry and vertex algebraically, and are heading towards graphing quadratic functions. Historically I’ve carved out a day for an activity that I honestly can’t remember if it’s stolen from the MTBoS, or just MTBoS-inspired. If it belongs to you and you somehow stumble on this post, let me know. Credit and thanks belongs to you.

Either way, it’s paid off in spades in years gone past.

I’ve got two sets of handouts, asking students to graph the same function, but I give them different x-inputs. One student gets 1, 2, 3, 4, 5. That student’s eventual partner gets -2, -1, 0, 1, 2. Trick is, the axis of symmetry of this function lives at x=2, so neither student gets a complete look at the function, only a sliver. Once they’ve built their table of values and graphed their fishhook, I pair them up and ask them to spend two or three minutes looking at the two tables and two graphs, and discussing what they see.

Docs here:

Axis of Symmetry discovery worksheet part 2

Axis of Symmetry discovery worksheet

I remind them that with our Themed Bellingers (Estimation 180, Which One Doesn’t Belong, 101 Questions, Would You Rather?) that they’ve been noticing and wondering and discussing and predicting and defending answers all semester long.

I’ve grown to love Math Talk. And we’re definitely on a path in my building towards flipping the ratio of teacher talk : student talk in the kids’ favor. We certainly had our moments the last couple of days.

Wait.

Last “couple of days”? I thought this was a one day thing. And it was. Until:

“I don’t get this”.

Not “I don’t understand what you want us to talk about”. Rather: “I don’t know what you want me to do with this list of numbers and strange jumble of letters”.

Oh Crap. I asked my students to evaluate a function for a given value of x and they looked at me like I had two heads.

Formative Assessment, up close and personal. Time to call an audible. Back to Step One. I ended up taking the better part of a day walking group to group, re-teaching in small groups how to plug in a value for x and simplify. No big deal, I mean, I *am* a teacher, and it *clearly* needed to be done anyway before we start trying to graph parabolas.

But still. An unexpected discovery for me. Guess I didn’t teach that as well as I thought.

Gonna let you in on a little secret. I lecture sometimes. Probably 3 out of 5 lessons, on average. Especially as part of our gradual release model. And it has its place. It’s just that what should be a 15/15 split as far as my minutes vs. student work minutes turns into more like 30/5. They’re just really bad at Sit & Get. Short Attention Span Theatre, here we come. I get frustrated, spend way too much time trying to get people back on task, nobody learns anything, and I get reminded of the words of the great Kate Nowak:

Offload the work to students, as often as possible. The one doing the work does the learning.

Wrote about it last December. Still holds.

Sometimes that reveals some uncomfortable truths. But it’s forced me out of my comfort zone.

Plan what you want them to know. Anticipate the trouble spots. Let them struggle. Get them talking.

And then, every now and then, a magic moment:

Pinch me.

I took a minute with a couple of classes to pull back the curtain and talk Standards of Mathematical Practice. The last two days we’ve spent hip-deep in SMP 1, 3, 4, 6 and 8. Not a bad payoff.

Of course, the Me that’s on an Endless Teacher Quest wants more. I love the pencil and paper aspect of this activity. Especially considering we’re gonna turn around and graph parabolas on paper. But: am I missing something? Could this be better? Is it a job for Activity Builder?

My first thought is no. To much learning eventually happened today. I don’t want to mess with a good thing.

Doesn’t mean I’m not gonna go in there and mess around tho. Because: Children Must Play.