Over the weekend I was excited to attend my first baby class.  As a teacher, watching others teach triggers an unrealistic urge to by hypercritical. My wife is also a teacher so we left for lunch shocked at how much of the teacher’s time was spent talking at the unhelpful Powerpoint. She basically talked the whole time, constantly referring to the stuff we had to “get thorough”.  We had all sorts of pedagogical wisecracks about the experience while we ate at this greek restaurant that seemed a lot like Chipotle, and I thought about that lunch today in class.

Today’s class did not begin how I would have liked.  Unable to find a star wars themed Estimation180 kind of task, and unable to make one that would only appeal to fan boy trivia geeks(e.g. “Estimate the number of parsecs needed for the Millenium Falcon to complete the Kessel Run?”) Chipotle popped back in to my mind. The menu specifically.  Since we were talking about combinations and permutations, I thought let’s make an estimate of all of the things that are possible to order at Chipotle.  I gave them a menu that had all of the meals and proteins, and asked them to be specific about what they were taking into consideration.  I gave kids this menu that showed the meat and the menu choices.  To avoid over-scaffolding, I didn’t mention all of the sides, in hopes that the kids would think of the sides on their own.

Lots of kids immediately noticed that there would be more to it than the options listed, but they all seemed to shrink in the face of such a number.  I had a lot of exchanges where the kid would say ” Oh, that’s like a million?!?” as if they were comically startled to think of a number that big.  I would ask them to try and use the multiplication rule to take it into account.   Instead they would get overwhelemed and settled for 24 (four meals, 6 proteins), which would be the safe choice.

 I wanted to show them all of the other possibilities that it seemed most people were scared to explore. At the board I walked through the rest of the possible meal options, one at a time.  “What are the choices for beans? Brown and black?” Ok, that’s 2 more, so multiply by 2″ in as engaging a manner as I could.  At the end we multiplied it out and got something like 516,094, allowing kids to have two kinds of meet, any of the salsas, and also getting an optional extra tortilla on the side.

Yes, I am fully aware that this sounds like I’m defending a teacher led call and response.  I felt the full irony of me doing pretty much what our birthing class instructor was doing over the weekend. At that moment, with the do now almost over I genuinely wanted to see what we could up with, it’s hard to turn that off. At the same time, kids were watching me do math and sort of cheering along.  The argument could be made that this diversion was not really valuable.

What I think makes this valuable is that I am making explicit the process that one has to go through in order to both think through a problem, and really justify their thinking.  This process is important, and now I can refer back to this component of the lessons when I want to explain to students how to think through and justify their reasoning with similar problems, and I can assess this I provide an opportunity for them to do a similar type of counting on their own in the future.