T-SHIRT-ON-THE-BUS LESSON

In the "Playing with Abstractions" section of the Beyond Numbers exhibit, visitors adjust clothing on figures with connected arms while exploring what can change and what stays the same in linked and knotted objects.

NCTM Standards and AAAS Benchmarks addressed:

Mathematics as Problem Solving:
Students develop and apply a variety of strategies to solve problems, with emphasis on multi-step and non-routine problems.

Mathematics as Reasoning:
Students understand and apply reasoning processes, with special attention to spatial reasoning and reasoning with proportions and graphs.
Students appreciate the pervasive use and power of reasoning as a part of mathematics.

INTRODUCTION

This activity has to do with a branch of mathematics called topology. In topology, the objects are defined by features that persist even when objects are stretched, shrunk or dented. Size and shape are allowed to vary, but holes or tears cannot be made.

To solve the puzzle one must be somewhat creative and realize that the shirt can be turned wrong side out through the sleeve holes as well as through the neck and waist holes.

MATERIALS

One shirt per pair of students doing the activity Shoelaces or string

PROCEDURE

Give each pair of students a large shirt. Have one student put on the shirt (over clothes), and then tie the laces or string to join the wrists.

Challenge the pair to have the student take off the shirt, turn it inside-out and put it back on again without removing or disconnecting the string. If a shirt has a design printed on its front, ask a student to predict whether the design will be on his back or chest when he has finished.

There is a solution. If you must give a hint, direct the students' attention to the number of holes in the shift. The number of holes is a topological invariant.

last revised 2/06/01

cathysfiddle@yahoo.com