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

Paper Cup Mathematics
Jerry Neidenbach, Sue Harvey and Marilyn McArthur

Go to: activity
Download:
    papercup.pdf
    papercup.worksheet1.pdf
    papercup.worksheet2.pdf

WHAT IS IT?
Classroom activity about the dimensions of an annulus.

GRADE LEVEL/STRAND
Secondary geometry

CLASS TIME
2 class periods

MATERIALS
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

OBJECTIVES
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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IAS/Park City Mathematics Institute is an outreach program of the School of Mathematics
at the Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540
Send questions or comments to: Suzanne Alejandre and Jim King

With program support provided by Math for America

This material is based upon work supported by the National Science Foundation under Grant No. 0314808.
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.