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9th Grade Math - Modeling through Geometry: Circumference of a Cup’s Roll

Clip 19/19: Modeling through Geometry: Post-Lesson Debrief Part 2


Molly McNinch and math colleague Jim Karditzas continue their debrief of the lesson, discussing next steps after the lesson that was videoed. Molly observes that she’ll engage the students in examining fictional students “Heather,” “Judi,” and “Gerry’s” work, connecting their sample work to her own students’ work, and observing and evaluating her students’ strategies and outcomes. Molly anticipates how she will lead her students into subsequent investigations of geometric similarity.

Teacher Commentary

When we look at the student work, one of the group members had a lot of ratios and tried to calculate a common scale factor, it looks like. They're comparing the wide and narrow diameter, which is great, but if we look at this, there's not any mention of the slant height, which is something that factors into the circle and the roll radius. I think that by helping them see, “What are the similar triangles and how does that help you see these?", that was very helpful. With this group in particular, I actually gave them an example with the diagram and then input values that they already had on their table. Then I put an x for the length between the base of the cup and the center of the circle, which is what they're searching for, because they need that value to find the roll radius. Once I separated it like this, it was easy for them to see that they shouldn't be focusing on the diameter so much as focusing on the slant height and the roll radius and how those two relate.