Hands-on Activity: Moebius Strips

Contributed by: Integrated Teaching and Learning Program, College of Engineering, University of Colorado Boulder

A prism-colored, 3-D drawing of a twisted loop.
Figure 1. A Moebius strip.
copyright
Copyright © http://www.cut-the-knot.org/do_you_know/moebius.shtml

Summary

Students make Moebius strips and use them to demonstrate the interconnectedness of an environment. They explore the natural cycles — water, oxygen/carbon dioxide, carbon, nitrogen — that exist within the environment.
This engineering curriculum meets Next Generation Science Standards (NGSS).

Engineering Connection

It is incredibly important for environmental engineers to be familiar with the water cycle, oxygen/carbon dioxide cycle, carbon cycle and nitrogen cycle as they make decisions that ensure that environments are safe for its inhabitants. Environmental engineers use their knowledge of the abiotic (physical) parts of our environment to design systems that provide us with clean water to drink, safe air to breathe and natural resources that are protected for future generations.

Learning Objectives

After this activity, students should be able to:

  • Describe the water, oxygen/carbon dioxide, carbon and nitrogen cycles.
  • Describe how cycles are connected within an environment.
  • Understand why engineers need to know about environmental cycles.

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Educational Standards

Each TeachEngineering lesson or activity is correlated to one or more K-12 science, technology, engineering or math (STEM) educational standards.

All 100,000+ K-12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN), a project of D2L (www.achievementstandards.org).

In the ASN, standards are hierarchically structured: first by source; e.g., by state; within source by type; e.g., science or mathematics; within type by subtype, then by grade, etc.

  • Develop a model to describe the movement of matter among plants, animals, decomposers, and the environment. (Grade 5) Details... View more aligned curriculum... Do you agree with this alignment?
  • Create and evaluate models of the flow of nonliving components or resources through an ecosystem (Grade 4) Details... View more aligned curriculum... Do you agree with this alignment?
Suggest an alignment not listed above

Materials List

Each student should have:

  • Four 2' strips of approximately 2" wide adding machine tape (available at office supply stores)
  • Four 2" pieces of transparent tape
  • Four 1" pieces of masking tape

Introduction/Motivation

In 1858, a German mathematician named August Ferdinand Moebius came upon a loop of paper with a truly astonishing property: it had only one side. This strip later became known as the Moebius strip. Such an unusual loop can be used to demonstrate how the abiotic components of an environment are recycled (used again and again), including the water cycle, the oxygen/carbon dioxide cycle, the carbon cycle and the nitrogen cycle.

Have you ever heard of one of these cycles? For example, do you know that oxygen is breathed in by animals and then breathed out as carbon dioxide? Then in turn, plants take in that same carbon dioxide and then release oxygen for those same (and many other) animals to breathe in again? This is an example of a cycle in nature — the oxygen cycle. Another example of a cycle in nature is the water cycle. Have you ever thought about water being a cycle? Think about how the water from a lake evaporates into the sky and later comes back down to the lake in the form of rain or precipitation. Is that a cycle? Yes, it is; that's part of the water cycle. Nitrogen and carbon have similar cycles. All cycles are important abiotic (non-living) parts of nature. Most every biotic (living) part of nature needs all these abiotic cycles to exist. There are so many connections in nature!

Why do you think environmental engineers need to know about these cycles? Any guesses? Well, environmental engineers work with all of these cycles to help us maintain a safe environment in which to live. Engineers need to understand how water, oxygen, nitrogen and carbon cycle through the environment to help clean up pollution and protect the areas in which we live and the air that we breathe. Environmental engineers also use what they learn about these abiotic parts of the environment to design and create technologies to make our water cleaner to drink, the air safer to breathe and protect our natural resources so they will be around for a long time into the future.

Today we are going to learn about the abiotic cycles in nature. We are also going to make our own Moebius strips to demonstrate the connections in nature.

(Note: This activity is adapted from: Science is...A source book of fascinating facts, projects, and activities, by Susan V. Bosak.)

Procedure

Before the Lesson

  • Cut enough 2' strips of adding machine tape so that each student has four strips.
  • Consider pre-labeling the strips with the cycle phases (see steps #4 & #6 in the With the Students section), or prepare a transparency with the cycle phases on it for students to copy onto their strips.
  • If possible, find pictures of the four environmental cycles (water, oxygen/carbon dioxide, carbon and nitrogen cycles) for students to see and have on hand for the activity.

With the Students

  1. Review each of the four cycles of nature (water, oxygen/carbon dioxide, carbon, nitrogen). Ask students to share what they already know and then share the pictures you found.
  2. Distribute 4 strips of adding machine tape and 4 pieces of transparent tape to each student.
  3. Ask students to label each end of one side of each strip with an "A" and the other ends of the opposite side of each strip with a "B" (see Figure 2, left). In other words, each strip has an A printed on the ends of one side, and a B printed on the ends of the reverse side.

Three photos: (left) hand-written letter "A" on the end of a long strip of adding machine tape with a piece of sticky tape adhered to half of its edge, (center)  hand-written word "Plants..." on a long strip of paper, (right) hand-written words "take in carbon dioxide" that finish off a description of one cycle of nature.
Figure 2. Steps 2, 3 and 4 of creating a Moebius strip.
copyright
Copyright © Images photographed by Jessica Todd, University of Colorado at Boulder, 2004.

  1. Ask students to write the words for each phase (see The Four Cycles of Nature handout, attached) of the cycles on side A of the four paper strips, as shown in Figure 2, center and right. Students should write in one long sentence, horizontally on the strip.
  2. Once done, have the students flip each strip over (i.e., the side B phrases should start at the same end that the side A phrases start, but will end up being written upside down to side A).
  3. Ask students to write the words for each phase (see The Four Cycles of Nature handout, attached) of the cycles on Side B of the four paper strips, as shown in Figure 2 (center and right), center and right. Students should write in one long sentence, horizontally on the strip.
  4. Have the students pick one of their A strips to work with first. They should twist the strip a half turn and tape the "A" end to the "B" end. (This is the tricky part and it takes some students awhile to get it.)

Photo shows a strip of paper with side A taped to strip side B after it was twisted one-half turn.
Figure 3. Step 7 of creating a Moebius strip.
copyright
Copyright © Images photographed by Jessica Todd, University of Colorado at Boulder, 2004.

  1. Ask students to find the cycle's starting phrase (at the "A" label) and mark it with an "X." Starting at the "X," draw arrows from word to word.
  2. The Moebius strip should have no beginning and no end, but just keeps constantly repeating the cycle (see Figure 4).

Photo shows a strip of paper, twisted and taped, so that it has become a completed circle with no beginning and no end.
Figure 4. A completed Moebius strip.
copyright
Copyright © Images photographed by Jessica Todd, University of Colorado at Boulder, 2004.

  1. Ask students to describe, in their own words, how these strips are related to environments.
  2. Ask the students to repeat this process for each of their three remaining strips.

Attachments

Troubleshooting Tips

To save time, label the strips in advance.

Students may need assistance understanding the "twisting" procedure. It is important that students only twist their strips one-half turn each.

Assessment

Pre-Activity Assessment

Discussion Questions: Solicit, integrate and summarize student responses.

  • Ask the students if they can think of any cycles in nature. Have they heard about the water cycle, the oxygen/carbon dioxide cycle, the carbon cycle, and the nitrogen cycle?
  • What do they know about these four abiotic components of the environment?

Activity Embedded Assessment

Discussion Question: Ask students to describe, in their own words, how the strips are related to environments.

Post-Activity Assessment

Drawing: Fold a piece of paper into fourths (or into half and use both sides of the sheet). Number each section 1 through 4. Have the students draw a picture in each section to illustrate the sentences and cycles on their four Moebius strips. Have them label their drawing or write a sentence describing it in their own words. (An alternative to this exercise is to have each student pick one of the Moebius strips to illustrate.)

Create Your Own Moebius Strip: Ask the students to come up with their own phrases about a cycle in nature and make new Moebius strips.

Activity Extensions

Demonstrate that each cycle is part of the bigger world ecosystem by cutting the Moebius strip down the center to create one very large loop.

Demonstrate that each cycle is intertwined with the others by making a full twist of the strip before taping the ends together. Then cut the loop down the middle to get two interlinked loops.

Try other twist and cut combinations.

Activity Scaling

  • For lower grades, simplify the activity by making and labeling the strips in advance. Or, have students make just one strip, such as for the water cycle, and do the other strips as a class demonstration. Or, have students work in groups of four and give each student a different cycle to make, which gives each student a chance to make one and allows all four cycles to be discussed.

References

Bosak, Susan V. Science is...: A source book of fascinating facts, projects, and activities, "Strip Tease," Markham, Ontario: Scholastic Canada Ltd., pg. 207, 2000.

Contributors

Amy Kolenbrander; Jessica Todd; Malinda Schaefer Zarske; Janet Yowell

Copyright

© 2005 by Regents of the University of Colorado.

Supporting Program

Integrated Teaching and Learning Program, College of Engineering, University of Colorado Boulder

Acknowledgements

The contents of this digital library curriculum were developed under a grant from the Fund for the Improvement of Postsecondary Education (FIPSE), U.S. Department of Education and National Science Foundation GK-12 grant no. 0338326. However, these contents do not necessarily represent the policies of the Department of Education or National Science Foundation, and you should not assume endorsement by the federal government.

Last modified: June 16, 2017

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