Mobius Magic

1. Invite students to discuss how the repetition of lines and shapes creates patterns and designs.
2. Review some basic mathematical shapes and symbols. Invite students to use Crayola Dry-Erase Markers on a classroom white board to demonstrate how some patterns are developed. Discuss each illustration. What shapes are visible in each?
3. Inform students that each will be creating a Mobius strip. Provide each student with a strip of paper approximately 24” x 2” (60cm x 5cm).
4. Ask them to use a ruler to draw a line down the center of the strip on both the front and the back. Then ask them to create colorful patterns down each column on each side of the paper using Crayola® Washable Markers. Encourage the use of lines, shapes, and mathematical symbols to create interesting patterns.
5. Invite students to compare designs and discuss the effects of various shape and color combinations.
6. Show students how to put a single twist in their paper strips and tape the ends together forming a twisted loop.
7. Ask students what they think will happen if they cut their paper strips in half by cutting along the center line. Discuss the possibilities and the reasons for their suggestions. Then have them cut along the center line and see what happens. Are the results what they expected? What do they think will happen if they cut what they have in half again? Try it.
8. Review the various branches of mathematics such as applied mathematics, algebra, geometry, and calculus. Introduce students to topology. Discuss how the Mobius strip experiment falls into this category.

LA: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade level topics and texts, building on others’ ideas and expressing their own clearly.

MATH: Analyze patterns and relationships.

MATH: Solve real-world and mathematical problems involving area, surface area, and volume.

MATH: Draw, construct and describe geometrical figures and describe the relationships between them.

VA: Students will investigate, plan and work through materials and ideas to make works of art and design.

Encourage students to experiment with other forms of the Mobius strip. What happens if a second twist is added?

Create Mobius strips with undecorated strips of paper. Once the two ends are taped together, challenge students to begin drawing a line down the middle. What do they observe about what has happened to the line once they get around to the point where they began?

Encourage students to research the branch of mathematics known as “topology,” and report their findings to the class.

Cutting a Mobius strip is an activity many special needs students will find fascinating, too. Provide help as needed when putting the twist into the strip of paper.