Park City Mathematics Institute
Geometrical Concepts from Constructions, Models, and Investigations

Paper Cup Mathematics
Jerry Neidenbach, Sue Harvey and Marilyn McArthur

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Classroom activity about the dimensions of an annulus.

Secondary geometry

2 class periods

Paper cups of a variety of sizes, large sheets of paper such as butcher paper to cover desks, yardsticks
Student worksheets:
    Worksheet 1
    Worksheet 2

Increase students' understanding of the properties of annuli through an exploration focusing on the area and dimensions of annuli traced out by rolling various sized cups on a flat surface.

The exploration focuses on the following questions:

  • Does a cup really trace out an annulus? How can you tell?
  • How does the size of the cup affect the size of the annulus?
  • How might you use the dimensions of the cup to determine its associated annulus without tracing it out and measuring it directly?

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This material is based upon work supported by the National Science Foundation under Grant No. 0314808 and Grant No. ESI-0554309. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.