# Growing Up Mathematically

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 $\sqrt{105}$ meters for the hypotenuse.”

A moment passed, and then they started talking.

“Wait – I got $\sqrt{137}$!”

“Yeah, me too!”

“What’s going on? $16+121$ is $137$.”

“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.