Clip 4/15: Modeling with Polynomials Lesson - Part 1B

Overview

After Amy Burke’s students create their conjectures about how to cut out square shapes to maximize the volume on a sheet of grid paper, the 11th- and 12th-grade students share their conjectures with each other. Students question each other about their conjectures, and they explain thinking. They make reference to the grid paper, indicating where they would make cuts.

After students share their initial ideas, Amy clarifies some terms (e.g. “a 4 -centimeter cut,” a “type of model”), connecting to previous work students had done with linear models, quadratic models, and cubic models. She asks some students to share their original conjectures with the group and to rationalize their answers. She asks one student to further explain his terms (e.g., “a wide spread”), and she records the initial conjectures (4 cm, 9 cm, and 1cm) on the board.

Teacher Commentary

What I think was powerful, which was something that was in the lesson, and not necessarily something that I have done a ton of in my own practice, was the making of a conjecture and revisiting it. I think that I would now build in time and space in my own practice, and would like to support teachers in their practice to build in that time and space, for the students’ sense-making. Really, even before doing any investigation, I used to be like, “Let's do an investigation and then let's see what the students, how they made sense of it.” But I really liked having to just make a conjecture before we even cut the paper or folded it into boxes.