Middle School STEAM: Mobius Strips and Mathematical Patterns

Mobius strips and related mathematical shapes (i.e., loops with more than just half a twist) are inherently fascinating.  Even better, there is a simple pattern that emerges when loops with different numbers of twists are cut down the middle.  Although the pattern is simple, it takes some effort to discover it, because of the messy, curly, loopy nature of the results.  I created this lesson plan with my Middle School STEAM class in mind, but I’ve used versions of this activity with younger and older students as well.  It’s fun, interesting, inexpensive, and genuinely thought provoking.  I think it’s a particularly good lesson to start the school year with.

Mobius Strips and Mathematical Inquiry

Getting Started
• Do Now: What do you think the words “edge” and “face” mean in a mathematical context?
• Class discussion: Discuss the Do Now. Look the words up if there is not a consensus about their meanings.
• Randomly divide the class into pairs.

Mobius Strip Investigations
• Show students how to make a Mobius strip. Explain that they will use their Mobius strip worksheet to guide them in collecting data about Mobius strips. Emphasize that being neat is important.
• Demonstrate making loops with 0 twists and ½ twists to ensure that all students understand the naming conventions used in this class.
• Ask students what they think it would mean to cut a strip in half the long way. Mime the cut (but do not actually make it) so that students are clear on what cutting the strip in half the long way means.
• Expect students to have trouble counting the number of turns in the shapes they create (especially the shapes they get after cutting). Expect to pause the activity at a certain point to allow the class to discuss counting methods and to come up with a solution that everyone can agree on.

The results when loops with 0 twists, half a twist, and a full twist are cut. How will the pattern continue?
The results when loops with 0 twists, half a twist, and a full twist are cut. How will the pattern continue?

Reflections
• After students have completed their investigations, conduct a class discussion of their observations.
• Watch “Wind and Mr. Ug” by Vi Hart https://youtu.be/4mdEsouIXGM and discuss the story. Discuss. Will Wind be separated from her dog forever?

Homework
• Make a piece of art that uses a Mobius strip. You may use any medium. Your piece should be creative and well-crafted.

Materials
Adding machine paper, tape, scissors, stickers, markers, video equipment, handout “Moibus Strip Explorations”

Bibliography
“Classroom Activities in Topology.” Classroom Activities in Topology. N.p., n.d. Web. 20 July 2015. <http://www.davidparker.com/janine/mathpage/topology.html&gt;.
Wind and Mr. Ug. Perf. Vi Hart. YouTube. N.p., 17 Jan. 2011. Web. 20 July 2015. https://youtu.be/4mdEsouIXGM

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