A Lesson in Chaos for Middle School Students

Presenters: Marilyn Krupnick,Barbara Orlan, Jenny Kim and Joel Simon

This lesson is based on an article found in Science News, July 19,1997 entitled Exposing Chaos in a Falling Disk's Flutter

OBJECTIVES

1. The students will create a chaotic system
2. The students will display a basic understanding of the theory of chaos and be able to recognize it.
3. The students will be able to describe a chaotic system and hypothesize why a system may be chaotic.
4. The students will develop a release procedure for playing cards which will be consistent.

MATERIALS

• Large floor grid (2m. x 2m.)
• Markers
• Bucket
• Large marble
• Playing cards
• Graph paper
• Release mechanism (to be designed by collaborative groups of students)

1. Form groups of four students.
2. Place grid on floor with bucket at 0,0.
3. After explaining the method of releasing a marble into a bucket, have each student predict the location of his/her four drops.
4. Have each student in each group attempt to drop a marble into a bucket four times.
5. Record result of each drop.
6. Have students compare their results to their predictions.

PROCEDURE B

1. Explain to each group that they will be given a playing card to drop horizontally into the same bucket four times, by each student.
2. Have each student predict the location of his/her four drops.
3. Record result of each drop.
4. Have students compare their results to their predictions.
5. Have students make a list of possible variables that may have influenced the results.

1. Have each group develop a device that will limit the variables as the card is dropped. (release mechanism)
2. Repeat each step in PROCEDURE B.

1. Chaos theory is introduced as a concept.
2. Students discuss their results and the relationship to chaos theory.
3. Students will be asked to brainstorm a list of chaotic systems in real life.

EVALUATION

1. Each group of students will graph the results of each procedure. (math)
2. Each group of students will write a paper which will include a description of the experiment, their predictions, results and a conclusion about chaotic systems. (language arts)

APPLICATIONS A related effect in physics can be demonstrated by flipping a board eraser in the air about each of its symmetry axes. The axis about which the eraser has an intermediate moment of inertia will quickly exhibit unstable chaotic motion whereas the other axes will maintain stable periodic motion. For example, the design of rockets with conical shapes reduces the source of aerodynamic instability arising from the above considerations.