Clip 6/15: Modeling with Polynomials Lesson - Part 1D

Overview

Amy Burke asks the whole group of 11th- and 12th-grade students to examine the entire table of the class’s work, talking aloud to share what they observe about the data generated from the class-constructed boxes.

As students discuss, Amy rotates around the classroom, engaging small groups and probing their thinking. One student observes that “They’re all from the same paper, but they all have different volume,” and his partner says, “It’s because of the cut size.” Another student says, “The bigger the length and the height, the greater the volume.” Another says, “I wonder if the cubic volume shown on the table could be graphed into a parabola.” Amy calls the group back together, reminding them to answer the questions from the table: “What’s the maximum volume, and what’s the cut size for that maximum volume?” One student corrects her group’s work on the board; Amy praises this student’s revision of her thinking.

Teacher Commentary

After Deidre and I reviewed this video, we shared this clip of their noticing and wondering with the students. In the wondering, it's kind of at one of the back tables, and everyone's sharing at the back table. Then one of the students says, “I wonder if this is going to be a parabola,” He was making assumptions himself, of how is this data going to be represented graphically. We thought it was a showing of everyone was sharing their own ideas, and here was a student going to this next level, without being completely prompted, which is what students can do when teachers get out of the way. They can go there without us, you know? I didn't hear a ton of feedback from students other than they were like just grinning, and like bashful and excited.