TeachRock

Materials Required for this Lesson:

1. Scissors (one for each student)
2. Marker (one for each student)
3. Tape (two pieces for each student)

Motivational Activity:

1. Display Image 1, Works by Neil Gaiman. Ask students:
   • Are you familiar with any of these books? Do you know who wrote them?
2. Explain to students that all of these books were written by Neil Gaiman, an internationally renowned author who has written novels and comics that have been adapted into plays, TV series, and films.
3. Inform students that Neil Gaiman expanded his portfolio to include music when he debuted his first album Signs of Life in 2023 with Australia’s FourPlay String Quartet. The music can be described as a blend of classical and folk music stylings paired with poetry and prose.
4. Play Clip 1, “Möbius Strip”  from the beginning to 0:52. Instruct students to consider what the song might be about as they listen. Then ask students:
   • Who are some of the people mentioned in the song?
   • What do the lyrics describe the people doing?

Procedure

1. Distribute Handout – Lesson Vocabulary. Pre-teach the vocabulary that will be used throughout the lesson. Work together with students to create meaningful context for each word as needed. Then ask students to draw a picture in the last column of the Math Vocabulary table. (Example: Hold up a rectangular object [such as a plastic pencil case] and ask students how many faces the object has. Using the same object, ask students to identify where the edges of the object are. Discuss properties by looking at a familiar shape; ask students: how do I know this is a triangle? [because it has three sides]. Discuss orientable by considering a compass; no matter how you stand or sit in the classroom, North will always be in the same location.)
2. Distribute Handout – Mӧbius Strip Activity Packet (Teacher’s Guide Available Here). Inform students that they will be investigating the geometric figure, and the subject of Gaiman’s song, called a Mӧbius strip through a series of short experiments.
3. Read page 1 of the handout with students. Inform students that they will come back to this page after completing each experiment to fill in the properties table.
4. Part 1 of Handout: Display Image 2, Mӧbius Strip and Loop Models. Tell students to rip off the last page of the packet, and follow along with the directions on page 2 to create a model of a loop and a Mӧbius strip.
5. Part 2 of Handout: Divide students into groups and instruct them to complete the experiments on pages 3-7. You may wish to stop after each experiment to review the results and fill in the properties table together as a class. Encourage students to refer back to the vocabulary sheet when explaining their findings.
6. After completing the properties table, ask students to return to the vocabulary sheet and create a definition for loop and Mӧbius strip.
7. Part 3 of Handout: Using the Mӧbius strip created in Part 1, instruct students to complete the transformation activity on pages 8-9. Display Image 3, Cutting a Mӧbius Strip and model for students how to cut along the center of the Mӧbius strip. (To begin, you’ll need to cut a small slit, then insert your scissors into the slit and continue cutting all the way around.)

Summary Activity:

1. Display Image 4, Conclusions and Connections 1. Inform students that they will examine lyrics from Neil Gaiman’s “Mӧbius Strip” and share their connections to today’s activity with the class. Then ask students:
   • What part of our experimentation today do these lyrics connect to?
   • How can the scientific method help determine whether or not something is truly impossible?
2. Display Image 5, Conclusions and Connections 2. Then ask students:
   • What part of our experimentation today do these lyrics connect to?
   • Is the transformation of the shape truly “magic”? What properties of the shape may explain how it is able to transform in such a way?
3. Display Image 6, Conclusions and Connections 3. Then ask students:
   • What might be the meaning behind these lyrics from “Mӧbius Strip”?
   • What do you think the Mӧbius strip can be used to represent in real life?

Extension Activities:

1. Show students the artwork Moebius Strip II. Explain to students that the artist, M.C. Escher was inspired by mathematics and regularly used mathematical principles in his artwork. Ask students to interpret the artwork then create their own Mӧbius strip-inspired art.
2. Ask students to research what a Mӧbius strip can be used for in real life.

Handout – Lesson Vocabulary Handout – Mӧbius Strip Activity Packet Handout – Mӧbius Strip Activity Packet (Teacher’s Guide)

Next Generation Science Standards

Energy

4-PS3-3: Ask questions that can be investigated and predict reasonable outcomes based on patterns such as cause and effect relationships.

4-PS3-2: Make observations to produce data to serve as the basis for evidence for an explanation of a phenomenon or test a design solution.

4-PS3-1: Use evidence (e.g., measurements, observations, patterns) to construct an explanation.

Common Core State Standards

Geometry

CCSS.Math.Content.4.G.A.2: Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

College and Career Readiness Anchor Standards for Reading

Reading 1: Read closely to determine what the text says explicitly and to make logical inferences from it; cite specific textual evidence when writing or speaking to support conclusions drawn from the text.

Craft and Structure 4: Interpret words and phrases as they are used in a text, including determining technical, connotative, and figurative meanings, and analyze how specific word choices shape meaning or tone.

Integration of Knowledge and Ideas 7: Integrate and evaluate content presented in diverse media and formats, including visually and quantitatively, as well as in words.

College and Career Readiness Anchor Standards for Speaking and Listening

Presentation of Knowledge 4: Present information, findings, and supporting evidence such that listeners can follow the line of reasoning and the organization, development, and style are appropriate to task, purpose, and audience.

College and Career Readiness Anchor Standards for Language

Vocabulary Acquisition and Use 4: Determine or clarify the meaning of unknown and multiple-meaning words and phrases by using context clues, analyzing meaningful word parts, and consulting general and specialized reference materials, as appropriate.