Mobius Strip: Math with a Twist and Math Adventure E-Books

Here is a fun activity that will get you thinking!  Cut some strips of paper and follow along with these instructions.

Cut strips of paper about 2 inches wide and 11 inches long.  Make a long strip (2 inches by 22 inches) by taping two pieces together.  Make sure the tape goes across the whole width of the strip.

You will be making Mobius strips!  What is a Mobius strip?  It is a strip of paper that you add a twist before you attach the ends together!

Make a Mobius strip by twisting one end before taping the ends together.  
With a marker, draw a line down the middle of the strip until the line meets up with itself.

Make a regular circle by taping two ends of a strip together without a twist.  Draw a line down the center on top until you get where you started.  On the other side of the paper, draw a line in the center in a different color until the line meets up with itself.  This photos shows that the regular circle has two sides-an outer side with a green line and an inner side with a purple line. 


When you drew the line on the Mobius strip, it was one continuous line!  The Mobius strip only has one side!

Let's see what happens when you cut on the line on both the circle and the Mobius strip.  Predict what you think will happen.  How many pieces will you have?  


To get started, crease a small section and cut on the line.  Now you have a little room to put the blade of the scissors.  Cut on the line on both the circle and Mobius strip.  


See below the results we had when we did this experiment.  Did your shapes match ours?

Now, make another Mobius strip with one twist.  Draw a line 1/3 from the edge.  Continue drawing the line until you get where you started.  Before cutting on the line, predict how many pieces you will have and the shapes.  Compare your results to ours!
On your next Mobius strip, twist the end twice before taping to the other end.  Draw a line down the middle.  Predict what will happen when you cut on the line. What were your results?
See if making three twists to a new Mobius strip gives you a different result!
Use this template to make the next Mobius strip project.  On the short end, draw a solid line in the middle on both sides.  Extend the long side with extra paper.  Draw dashed lines 1/3 from the edge.
Fold the small ends up and tape as a circle.  For the long part of the cross, make one twist before taping the ends to make a Mobius strip.  Predict what shape(s) you will get when you cut the two parts.  CUT THE LONG MOBIUS STRIP FIRST!  Cut 1/3 from the edge until you get where you started.  On the small circle, cut on the middle line.

Here are our results.  

Strip with one twist.  Result:  One long circle

Notice the two full twists!

Strip without a twist.  Result:  Two circles

Strip with one twist and cut from 1/3 from the edge.

Result: One small circle within a large circle

Strip with two twists and cut in the middle.

Result:  Two medium circle attached to each other

Strip with three twists and cut in the middle.

Result:  One small circle attached to a very twisted long circle

Cross template with circle on the short side and a Mobius strip on the long side.

Result:  Large square with attached small circle

For further fun, look at this list of math e-books!

Math E-Books with a Twist @SCCLD Kids


Explore these recreational math and math adventures in e-books!

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