The Cream in My Polytope

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Date

2014

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Ohio Council of Teachers of Mathematics

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Abstract

This guided discovery project provides high school math students an opportunity to solve a real-world problem by applying tools they have learned in geometry and, optionally, calculus. The task is to determine the volume, surface area, and other properties of a certain form of folded paper container, such as those used by Wendy’s for sour cream. Students first construct the containers, and then are challenged to find a geometric way to determine the volume of these objects, which do not fit conventional volume formulas. They next find surface area and, optionally, angles of the container. In the process, 2- and 3-dimensional visualization skills are exercised. Calculus students are asked to find the volume by the method of slabs, and subsequently to determine the dimensions that optimize the surface-to-volume ratio. Several additional extensions are suggested, and core curriculum standards are listed. Diagrams and calculations are provided. While much support material is provided, it is hoped that the teacher will encourage students to explore, discover and invent as much as possible on their own.

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Ohio Journal of School Mathematics, no. 69 (2014), 18-23.