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Möbius Magic

Möbius strips are fascinating objects that have useful applications. Students will learn about their characteristics, then create a strip that will undergo a magical transformation.

Lesson Plan

Supplies Needed

Gather all the supplies needed to bring your craft ideas to life! From paints and markers to glue and scissors, our crafts section has everything to spark creativity and make every project truly special.

  • Paper
  • Ruler
  • Tape

Steps

  • Step 1

    The Möbius strip shape has appeared in ancient Roman mosaics, but its use as a mathematical object was discovered by August Ferdinand Möbius in Germany in 1858. (Another mathematician, Johann Benedict Listing, had actually discovered it a few months before Möbius, but published his findings after Möbius.) Discuss some of the characteristics of the Möbius strip, such as it is a 2-D surface embedded in a 3-D space, and it is an example of non-orientable surfaces in topology. This means that there is no way to distinguish left from right across the surface.

  • Step 2

    Have students create a Möbius strip. They will take a long strip of paper and draw a straight line down the center on both sides. They can decorate the front and back of the strip with colorful patterns and lines. How many surfaces are there? How many edges?  Now have them put a single twist in the strip and fasten the ends with tape. How many surfaces and edges are there now?

  • Step 3

    Ask students to predict what will happen when they cut the strip along the line down the center. Discuss their hypotheses. Then have them cut the strip. Were the results as expected? Encourage a discussion of what might happen if they cut the strip in half again.

Standards

MATH: Analyze, compare, create, and compose math ideas using written, oral, and drawn lines, shapes, forms, and patterns. 

MATH: Use and connect mathematical representations.  

Adaptations

Ask students to create another strip with two twists instead of one. Encourage them to discuss what they think will happen when they cut this one. Then have them cut it and watch the magic happen!

Encourage students to investigate some practical applications of the Möbius strip. For example, they are used in conveyer belts, recording tapes, and rollercoasters.