Clip 3/15: Modeling with Polynomials Lesson - Part 1A
Overview
As she opens the lesson focusing on modeling with polynomials, Amy Burke introduces her 11th- and 12th-grade students to the multimodal task, which will challenge them to build models, to gather data and organize it, and to make use of Desmos as a technological tool to support their modeling and interpretation of data.
She reminds students that, because they will converse with each other to deepen understanding, they will facilitate the process by serving in different group roles.
Amy poses a problem: students will be given a paper that is lined with a rectangular grid in centimeter squares, and will need to determine how to use the grid paper to build an open-top box with the largest volume. She invites students to draw on the paper, clarifying that they can only cut squares out of the sides (e.g., 3 x 3 cm). Amy asks students to visualize what they will do beforehand, individually creating a conjecture about how to approach the problem.
Teacher Commentary
Teacher Commentary
Some students, what they want is for someone to stand at the front whiteboard and go through the steps. I don't do that. I have had students say that I like to get them to do the thinking, and then highlight it and have them share it. I'm so thrilled with my current position; I just love getting to do my role. It's also so easy to walk into someone else's class and do something that you had time to prepare, and that you didn't have to teach five other sections that day, it's a lucky position. I have this amazing position where I do a lot of classroom observations, and I get to pull from the best. To be like, “Oh that was brilliant, what she did there. I'm going to try that next time I do something, or at least share it.”
For 10 years I shared a classroom on my prep time basically; I never had my own classroom during my prep, which, some people really just don’t like. ... I loved it though, because it's like a daily informal observation of someone else's interactions: how did they deal with a possible disruption, how did they explain a concept, how did they invite students in, or redirect. Then, similarly, I would get informal feedback from my peers; we would have to because you were in the room, grading their papers while someone else was teaching.