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Strip Tease

Program Area

This activity can be used in the Grade 9 Mathematics, Science and Technology program within a unit on Food and Energy or as part of a geometry unit. It can also be used in the Grade 10 Community Ecology unit or in Grade 10 Geometry. It is best used after the activity "Can Our Planet Feed Us All?"

Learning Outcomes

Teaching, learning and evaluation will focus on the student's ability to:

  • Make a moebius strip;
  • Understand the concept of the "cycles of nature;"
  • Appreciate that the producers of our food must work within the cycles of nature;
  • Determine how changes within our own habits can enable us to live in harmony with nature's cycles.

Classroom Development

  1. Provide students with the following:
     3 cm widths of paper, cut from the long side of 28 cm x 43 cm sheets, enough for 2 per student; tape; pencil crayons;
    an overhead projector (optional); scissors (for the extension).
  2. Give each student two strips of paper.
  3. Explain the history of the moebius strip included with this activity.
  4. Display, or provide the students with copies of the scenarios.
  5. Starting one cm in from the one end, the students will draw the scenes as explained for PIGS, ensuring that the scenes are evenly spaced along the strip,and a one cm gap is left at the end as well. Once the one side is complete, they flip the strip over and starting at the same end, draw the same scenes again.
  6. The same is repeated for the strip entitled ME.
  7. Next, instruct the students to take the PIGS strip, in both hands, and give it a half turn. Tape the one end to the other.
  8. The students now have a moebius strip.
  9. Now, after analyzing the "ME" strip, they determine if it can be made into a moebius loop.
  10. Students complete their wrap-up questions (which you have copied onto the board) and do the extension (which is fascinating and fun!).

Background Information

The making of a moebius loop is well covered in Math and Logic Games, a book of puzzles and problems, by Franco Agostini, Harper and Row.

Timing

Allow 40 min for this activity. Some students will finish more quickly than others, but they may then spend time exploring the moebius loop.

Resources

"Growing for You" is a fabulous video or film which explores the entire food production system within Ontario. Narrated by C.B.C.'s Peter Gzowski, it can be borrowed from the Ministry of Agriculture's A.V. Library by calling 1-519-767-3681.

Cross-disciplinary Links

This exercise ties in geometry and the concept of the cycles of nature. Students who have not had much experience with nature, tend to see themselves as separate from it. It is the intention of this activity to have students see themselves as part of nature, and to appreciate that the people who produce our food must be respectful of their relationship with the earth.

Student Activities

Scenarios

PIGS

  • Plant the grain crops (chiefly corn, barley and soya beans).
  • Crops sprout and the field turns from brown to green.
  • The crop continues to grow for the summer in the presence of sunlight and moisture.
  • The grain gradually turns a golden colour.
  • The grain is harvested by a machine called a combine.
  • The grain is stored in large containers called bins.
  • The grain is fed to the pigs.
  • The pigs use this feed to grow.
  • What is not used for growth leaves the pig as urine and feces (manure).
  • Manure is spread on the fields because it is a very rich source of nutrients and organic matter. The manure is spread with a machine called a manure spreader.
  • With the natural fertilizer of the manure the crops can again be planted and grow.

ME

  • A family member drives to the store.
  • S/he purchases potatoes grown in the U.S., and orange juice processed in Brazil.
  • S/he pays for the goods
  • S/he drives home.
  • Your family eats the potatoes and drinks the orange juice.
  • The potato bag and the orange juice container go in the garbage.
  • The potato peels go in the garbage.
  • Like the pigs the food you have eaten makes you grow.
  • Like the pigs you also produce faces and urine.
  • But unlike the pigs, your fertilizer is treated as waste. It either enters your family's septic system, or the city's sewage system (with this method the sewage is either treated and returned to the water, or dumped directly into the nearest body of water).

History of the Moebius Strip

In 1858, it was discovered by a German mathematician called August Moebius (pronounced Moy-bus) that a strip of paper could be made into a loop without beginning and end, upper and lower side, inside and out. This design has been used over and over through the years to represent systems without a beginning and end. Escher demonstrated in this model that an insect walking along a moebius loop never comes to the end of the paper.

This model is often used to represent cycles found in nature, such as the carbon cycle. In the carbon cycle, when an animal dies, the carbon compounds remaining in its body are acted upon by decomposers, and in the process, the carbon is converted to carbon dioxide gas which enters the atmosphere. The carbon dioxide is then taken in by plants to form carbohydrates. The carbon is once again found in the body of the animal that eats the plants.

There really is no beginning and end to this cycle. Your job is to now take the information provided and make two strips. In doing this you will determine which scenario (Pigs or Me) cannot be made into a moebius loop.

 

Answers

1. Which scenerio could not be made into a moebius loop? Explain at least three points where the loop broke down.

Answer: The "ME" strip could not be made into a loop. The cycle broke down when:

  • The shopper bought food produced elsewhere (preventing the nutrients which made up the food from ever returning to the soil it came from).
  • Your family discarded the potato bag and orange juice container.
  • Your family discarded the potato peels, rather than compost them. d) Your sewage was never used as a fertilizer, but became a pollutant.

2. Could a moebius loop be created if one farmer grew the corn and sold it to a pig producer?

Answer: No because the nutrients in the manure would not be returned to the soil that it had come from.

3. What could you do to make your food consumption patterns fit into the cycles of nature?

Answers: Buy food which is produced closer to my home. Grow much of my own food. Compost my sraps. Alter our family's sewage system so that the sewage is used as fertilizer for the garden or neighbouring farms.

Extension

There are more uses still for the moebius loop: scientists use the loop as a model for research on subatomic particles. An industrialist recently used the model to design a conveyer belt which is subject to wear on both sides. His belt now has twice the life span of other conveyor belts.