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In Calculus, one of the problems students must solve is to find the volume of solids generated by rotating a curve around a given line or finding the volume of a solid with a known cross section. The mathematics of the topic is quite simple, but often students emerge with a correct answer which is completely unconnected to the actual solid whose volume they have found. One of the practices I find most effective is to arm students with jars of Play-Doh. I ask them to picture the rotation of one element of the rotation, a rectangle, then to build the actual physical shape it would generate when rotated around a line. I give no further instruction than that. It takes very little time before they begin to look around, notice that other students have disks (or washers, or shells) of different sizes than theirs and to have someone gleefully walk around the room and assemble the entire solid out of parts made by the different students. If they are not motivated to then build for themselves the actual solid, I encourage them to do so-- but that’s rarely necessary. We follow up with some great SmartBoard demonstrations available on this topic, but I think they learn more from the Play-Doh than from the Internet on this one. Volume is often one off their favorite topics; they are fearless in the face of complex problems on the topic.
Catalog of Lessons by Category > Hands-On Lessons > Math Linda Anderson 2017-10-04T00:54:26+00:00