It started with a warmup that looked innocent enough.
Two sides of a right triangle have lengths of 4 meters and 11 meters. Determine the length of the third side.
After a few minutes, I brought everyone back together. I wrote my answer on the SMART Board and said “Okay, I got 
A moment passed, and then they started talking.
“Wait – I got 
“Yeah, me too!”
“What’s going on? 
“Is he joking?!”
And then came the moment.
K: “Oh wait – you need to subtract!”
S: “What? Why?”
K: “Because that’s what Carlson did.”
S: “That’s not a good reason!”
And that’s when I stopped everything. I made a HUGE deal out of what had just happened.
“Did everyone hear that?” I repeated what S had just said, and then I addressed S personally in front of the entire class.
“S, you just grew up! You just went from mathematical childhood to mathematical young adulthood.”
There were probably a few murmurs, kids wondering what in the world I was going on about this time.
“You see, everybody, S decided that it’s not enough to do something JUST BECAUSE the teacher says to. S wants more! She wants a reason! THAT is what mathematics is all about.”
From there, we went into a discussion of how the prompt wasn’t specific enough to decide whose answer was correct, but it almost didn’t matter at that point. I’d already taught a better lesson than I possibly could have imagined.
Thank you, K and S, for helping us all to grow up mathematically.
