Clip 11/15: Modeling with Polynomials Lesson - Part 2D

Overview

Amy Burke continues to circulate around the classroom, engaging with student pairs and probing their thinking as they model their data in Desmos applications. Students clarify and build on each other’s thinking, asking each other questions about the best way to approach the task, using their models to calculate the maximum volume of their box.

Students record their ideas on their worksheets. Amy cautions them that they will soon be sharing their pair work with the whole class. One student returns to his grid paper, testing his pair’s conjecture. He wonders whether they can use a negative number in their graph. They share their idea with Amy, and she listens to their thinking. One student says, “We want a way for our data to fit the model.”

Teacher Commentary

The multiple representations in this lesson allow different access points for students. The building is powerful: some students were really drawing some conclusions from the table. I think because of the time, we didn't see as much interpretation from the graph as I would have liked, but there were some really powerful things happening.

I heard something from a particular group that didn't then get completely shared out to the class on the video, but one of the groups was really wrestling with the fact that one of their x intercepts was a negative value. What does that mean? It was at the back table, who instead shared, “Can we use this model as opposed to our actual data that we gathered as a class?” That was the question that they came up with, which is also a super interesting question. But, I also liked that, because of that graphical representation, that was one question that came up; and the question about “What does the negative mean in this context, and can we use it?” It's leading right into domain. So, again, I think that in terms of agency, authority, identity, that the students are actually leading the learning, rather than the teacher.