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 Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540
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With program support provided by Math for America

This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. 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.