Molly McNinch sits down with a group of students and uses questioning to extend their thinking. She asks them to consider other analogous problems they’ve worked with in the past. The group discusses matters of proportionality between the cup diameter, slant height, and the roll radius.

9th Grade Math - Modeling through Geometry: Circumference of a Cup’s Roll*Molly McNinch, Woodside High School, Sequoia Union High School District, Woodside, California*

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For this group, they had a lot of calculations and one diagram that I had them put in at the end. This one, when we look at what their data is, again, they're also doing a lot of calculations. You can tell that they're trying to see how the relationships [between cup diameter and slant height] develop that roll radius. When we look at their data, this just completely went from, "Okay. I'm brainstorming. I'm brainstorming," to, "Okay. I have it and now I'm proving it with all of these examples." I think this is a great representation of "I was working through it here. I was kind of getting an idea," and, again, they're still just focusing on the diameters and not anything regarding that slant height. Once we focused there, once we bring in the slant height, which was given from the other student work, that was helpful.