The Mobius Strip:, Study notes of Mathematics

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The Mobius Strip:

A Hands-On Exploration

Subject: Mathematics Topic: Geometry Grade Level: 8- Time: 30 min Post Show Math Activity

Introduction:

In Show Math students were introduced to topology and more specifically the concept of a Mobius strip in MC Escher’s painting. In class today students will be shown the different properties of a Mobius strip by constructing their own. This activity seeks to engage students in mathematics by allowing them to explore the Mobius strip themselves.

Learning Objectives:

By the end of this activity students should:

• Understand that the Mobius strip is a one sided/edge object
• Explore the properties of the Mobius strip
• Examine the definitions of side, edge, and area

Skills:

Students should develop:

• Observation skills
• Prediction skills
• Spatial Reasoning
• Communication skills

Material & Resources:

• Tape
• Worksheets for the class
• Strips of paper (see template attached, 2 per student)
• Scissors
• Pens/Markers

WNCP Curriculum Links:

Apprenticeship and Workplace Mathematics 10 Analyze puzzles and games that involve spatial reasoning, using problem-solving strategies. [C, CN, PS, R] Foundations of Mathematics 11 Analyze and prove conjectures, using inductive and deductive reasoning, to solve problems. [C, CN, PS, R] Analyze puzzles and games that involve spatial reasoning, using problem-solving strategies.[CN, PS, R, V]

Resources:

• http://nuclear-imaging.info/site_content/2009/02/03/moebius-mo bius-strip-in-art-and-culture/ Shows examples of the Mobius Strip in the real world.
• http://en.wikipedia.org/wiki/M%C3%B6bius_strip More in depth explanation of the Mobius Strip
• http://www.youtube.com/watch?v=JNtKcK27x1s&feature=related. A video that shows how to make a Mobius Strip

Activity Instructions:

1. Distribute to each student two strips of paper, tape, scissors, marker and worksheets.
2. Have class make a simple ring with paper by connecting one end of the strip to the other with tape (see figure), you can show a demonstration first.
3. Tell the class to fill in question one on their worksheet about the number of edges and sides their simple ring. If necessary review the definition of edge and side.
4. Have the class draw a line around their simple ring and complete question 2 (predicting what will happen when they cut on that line) on their worksheet. If you would like to engage in some group work the class can Think-Pair-Share for their prediction.
5. Now show the class how to make the Mobius strip. Take the second strip and give it a half twist and then join the ends. See video and picture below.

Think - Pair - Share

• Students will think about the questions themselves
• Pair with a partner that is close by
• Share their answers and write them down on their paper
• Engage in a full class discussion that shares their answers

6. Have the class examine their Mobius Strip and Think-Pair-Share to answer the Question 3 on their worksheet.
7. Have them draw a line on the “outside” of their Mobius Strip. Give them a chance to revise their answer to Question 3.
8. Ask the class to fill out Question 4 (predict what will happen when they cut along the line). Then tell them to cut along the line.
9. Then have class finish the worksheet with Question 5.

Discussion:

Have a discussion about the uses of the Mobius strip in the real world (toys, conveyor belt, art, pop culture). Can they think of any things that a Mobius strip might be good for? Hand out the homework worksheet. If you would like you could also engage in a discussion about the area of a Mobius Strip.