Beacon Lesson Plan Library

Mobius Strips

Darlene Wolfe
Orange County Schools

Description

The Mobius strip often upsets the students' expectation of the normal order of things. To practice the critical thinking and higher order thinking skills necessary to science inquiry, students construct and cut a Mobius strip in half, lengthwise twice. Logically, a piece of paper is two sided, however, the Mobius strip is defined as one-sided, “proven” by the line on only one side and the results of the first lengthwise cut.

Objectives

The student uses systematic, scientific processes to solve problems and reach conclusions.

Materials

- Copies of scientific method, instructions for pairs of students (or show Mobius Strip Information in the associated file).
- Precut strips (made from 8.5 by 11 inch paper cut into four equal lengthwise pieces) for each child. (Recommend several extras pieces in case of errors or excitement to do again.)
- Sufficient scissors for class to share.
- Sufficient tape for class to share.
- Pencil or pen for each child.
- Student notebooks to record results.

Preparations

1. Review and be comfortable with the scientific method and be familiar with rubrics and the Socratic Method. (See Weblinks) Have an established standard for writing lab reports to assure consistency.

2. First try the lab and become familiar with the Mobius strip.

3. Cut the strips of paper. Assemble the scissors, paper strips, tape and extra pens or pencils for unprepared students.

4. Provide (by overhead, handouts, presentation tools, etc.) the instructions in formats to match student learning styles. A video or picture handout that can be reviewed is excellent for students who are absent or students with special needs who require repetition for acquisition of data.

5. Do the lab, then analyze and evaluate with students.


Procedures

1. Students and teacher review the scientific method. Students define and write important vocabulary words. Define prediction, logic, reasoning and evaluation. Prediction example: How do you know how many sides a piece of paper has?

2. All students follow the safety standards in our lab agreement and write their lab reports using the scientific method. (Students should have, with parental approval, a pre-signed lab agreement on file. A sample follows at end of this section.)

3. Students receive a 2” by 11” strip of paper and a pencil or pen. Students share tape and scissors.

4. First, students make a circle on one side of the strip, turn it over, and then make a square on the other side. Students record how many sides to the strip of paper. Write down how students determine the number of sides.

5. Students hold one end of the strip of paper, make one twist in the strip of paper and tape the ends together by taping completely across the strip. The strip should now somewhat resemble a peanut shell.

6. Each student holds the strip on the desk, places his/her pencil about one inch in from the side as close to the middle of the strip’s width as possible.

7. Students now pull the strip under the pencil, lengthwise, until he/she is back to the point where he/she started.

8. Students examine their own lines and the lines made by their neighbors.

9. Students write their observations about the line and the strips of paper. Students compare their notes about the circle and square with the line.

10. Students predict (hypothesis) how many strips of paper they will have when they cut the strip in half length-wise.

11. Folding the strip width-wise, the students start a cut on the line. Once the cut is started, the strip should be opened so the scissors can cut lengthwise the entire strip of paper. (Use the pencil to draw a line and determine how many sides it now has.)

12. Students record their observations when they complete the lengthwise cut along the lines or center. Students record their thoughts and reasoning for the comparison of the strip prior to and after making the Mobius strip.

13. Students and teacher discuss their outcomes, compare and analyze their expectations with their results, and evaluate the logic or reasoning of their hypothesis compared to their conclusions. Students then explain the results, their reasoning, and their accurate or inaccurate predictions. For example, how did students determine whether strip of paper and mobius were one or two sided? What relationship do their findings have to mathematical principles or their own assurance of what "they know to be true" based on the outcome of the Mobius lab?

14. Students and teacher discuss additional activities and labs to further learn about the Mobius strip. They can be included as an additional part of this lab -- questions raised by the students for their own research or as an extension. For example, students may enjoy doing Paul Kelley’s lab at http://mathforum.org/mathed/nctm96/games/kelley/mobius.html

Sample Lab safety contract follows but please be sure that you have checked to see if you have a required school or school district lab safety contract of your own.

Student Safety Contract
Please read and discuss with your parent(s) or guardian.
I, ___________________________ [print student name] agree to the following in order to participate in labs. I will:

1. Follow all instructions given by the teacher or in the lab instructions.
2. Protect eyes, face, hands, and body while conducting class activities by either wearing protective gear or following basic safety procedures such as keeping hair and clothes away from chemicals and fire.
3. Practice responsible and safe practices.
4. Prepare and clean my work area better than I found it.
5. Know the location of first aid and fire fighting equipment.
6. Conduct myself in a responsible manner at all times in a laboratory situation.
7. Work with my lab partner and class to keep a safe, clean science lab and classroom.

My child and I have read and agree to abide by the safety regulations as set forth above and also any additional printed instructions provided by the teacher and/or district. I further agree to follow all other written and verbal instructions given in class.

Student Signature __________________________________ Date _____________

Parent Signature __________________________________ Date _____________

Assessments

(Students should have a copy of the scientific method and directions to making the Mobius strip. Associated file will help visual learners)

NOTE: The student and teacher should agree to a consistent pattern for recording the scientific method and lab activities in order for consistency with assessments of practical application of new and previous knowledge. The teacher should also select 2 to 5 critical and creative thinking questions relevant to the lab that tie into the material being studied at the time.

For each step, the students must record their lab reports using the scientific method with points for the following.

1. Student has correct steps to the scientific method for the lab report (See sample). Have sample questions for the background and discussion sections of the lab report. For example: List examples of two, three, four and more sided figures that you are aware of and how you determine the number of sides. How can there be a one sided figure?
2. The student constructs a Mobius strip and has one long line as a result of putting a pencil or pen on the center and pulling Mobius strip through lengthwise. Student predicts outcome before trying and notes actual results comparing prediction with outcome.
3. The student constructs a Mobius strip that s/he can cut in half lengthwise and have only one piece. The student demonstrates the ability to follow directions and record procedures, etc.
4. The student cuts in half, lengthwise again and has 2 interlocked pieces. The student further demonstrates the ability to follow directions and record procedures, etc.
5. The student has a record of the lab and the thought process (reasoning)that is consistent with the scientific method.

Sample Rubric for assessment:
Problem (statement):
complete/thorough (3 points)
most included (2 points)
incomplete (0 points)

Hypothesis (question):
accurately stated (3 points
majority included (2 points)
no question/inaccurate (0 points)

Background and vocabulary:
accurately stated (3 points)
majority included (2 points)
no question/inaccurate (0 points)

Procedure (must include the materials and experimental process)

Materials:
accurately listed (3 points)
majority included (2 points)
incomplete/inaccurate 0 points)

Process/experiment:
accurately listed (3 points)
majority included (2 points)
incomplete/inaccurate (0 points)

Results/data (analysis):
accurately listed (3 points)
majority included (2 points)
incomplete/inaccurate (0 points)

Conclusion (discussion):
accurately stated (3 points)
majority included (2 points)
incomplete/inaccurate (0 points)

Record of reasoning:
accurate, logical (3 points)
somewhat accurate, logical (2 points)
inaccurate, illogical or missing (0 points)

Extensions

Use longer paper and make additional twists in the paper before taping. Predict and record observations. Discuss the similarities and differences. Try to interpret the possible explanations for the differences.

Search for additional activities and labs to further learn about the Mobius strip in both science and math.

For example, students may enjoy doing Paul Kelley’s lab at http://mathforum.org/mathed/nctm96/games/kelley/mobius.html or searching for more about the Mobius Strips on the Web.

For fun, have the students teach their parents or other students and explain their results.

Web Links

This Website helps to clarify the meaning of standards-based science inquiry, and what it requires of teachers and students.
Science Inquiry


This site defines how to make and explains the uniqueness of a Mobius strip.
The Möbius Strip

Kelly outlines an activity to further investigate properties and characteristics of a Mobius strip.
Möbius Strips

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