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Mobius Bands

In this activity, students play with paper strips and learn that a sheet of paper can “lose” one of its sides, if it’s twisted correctly.

A Mobius band, or Mobius strip, is a mathematical oddity that can be used in magic to produce unbelievable results.

A Mobius strip is a strip of paper which has been given a half-twist then connected end to end. It has only one side and one edge. Once you have made this loop, run your finger around the edge. It will first go around the outside of the loop, then when you reach the twist, your finger will go all the way around the inside of the loop. Then, when it reaches the twist again, it will go all the way around the outside - again! 

It literally has only one side and one edge!

Objectives

  • Explain the importance of observation when doing science or math.

Materials

  • Per Student:
    2-4 Strip of paper (greater than 30cm length)
    Staplers or tape
    Pencil

Key Questions

  • What seems unusual about this strip of paper? How many sides does it have with one twist?
  • How many sides does the strip of paper have have?
  • How many sides does the loop have with one twist?
  • How many sides would this loop have if you didn’t twist it?

What To Do

  1. Take one end of the strip of paper and twist it 180º.
  2. With the twist still in the paper, secure the ends of the strip with staples or tape. You should now have a twisted loop.
  3. Ask students what they think will happen if you try to draw a line on each side of the paper.
  4. Take a pencil and see if you can draw on both “sides” of the looped paper without lifting your pencil.
  5. ​What happens if you cut your loop in half along the middle of the strip?

​Teacher Tip: Have students start the cut at one end and then carefully cut in a straight line, staying in the centre of the band and working your way around the centre of the entire band until you reach the point where you began. Predict what will happen, and see what occurs!

Extensions

  • What happens if you cut your loop in half along the middle of the strip?

    Teacher Tip: Let students know that it is important when you cut or tear the bands that you stay in the centre all throughout the cut. Start the tear at one end, or place the scissors in, then carefully cut in a straight line, staying in the centre and working your way through the entire band until you reach the point where you began.

  • Take another strip of paper and twist it 360º clockwise (one full twist) before stapling it. What happens if you cut this loop in half?
  • Cut into a Mobius strip along 1/3 of its width. Continue cutting through the strip until you meet your starting place. It will take two “rounds”. What happens?