Hot Coffee + Show Your Work

02 Nov

I’ve written about this lesson before, but I wanted to write again because of several observations from last spring.

I know that I need to find a way to provide students the opportunity to engage in math modeling more often and earlier in my geometry course. I’m having a hard time finding a way to do that. (Ideas for providing students the opportunity to engage in math modeling while proving theorems about congruence and similarity are welcome!) For now, we focus on modeling during the last unit of the course.

I decided last year to show students the modeling cycle from CCSS at the beginning of each lesson so that students would recognize what I am asking them to do differently and why I’m not giving them all of the information they need up front.

Our learning goals: I can model with mathematics, and I can show my work (leveled learning progression from Jill Gough).

Once we decided what questions to answer after watching Act 1 of Dan’s World’s Largest Hot Coffee Three-Act, students estimated responses.

And then teams made a list of the information they needed. I gave them information only as they requested it. Most teams realized later rather than sooner that they would need some type of conversion for cubic feet into gallons.

When they decided they needed to know how much coffee a regular cup would hold, two of the girls remembered that the teacher with whom I share the classroom always had a cup of tea. They asked to borrow her cup so that they could come up with an agreed upon amount for a regular cup of coffee.

At one point, a student asked whether getting the right answer mattered. I asked why. She and her teammate didn’t have the exact same calculation.

It struck me that what we were really working on today was identifying a problem, determining what was essential to know, and creating a model to answer the problem. It’s not that the calculations aren’t important, but for this lesson, the questions were more important. By the time I got back around to that team, they had resolved their computational issue because of a conversion error. Even so, I’m glad I was asked whether it mattered that everyone got the same answer, as it helped shape how I launched our remaining modeling lessons.

And so the journey to provide students the opportunity to engage in all steps of the Modeling Cycle continues …