Flexagons

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Flexagons Other Fun Art and Math
ConnectionsTully Jr. High SchoolVirginia
Killmore
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What you will Learn

• How Art and Math can create meaningful
  connections for students in your classroom
• You will learn by making 4 samples for your
  classroom As well as take home instructions for
  these samples
• Share websites that teach students about art and
  math

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Why Create These connections

• Students observe and learn from connections
  between Art and Math
• Reinforce what is learned in both disciplines and
  create meaningful activities for middle school
  students
• Students will learn measurement skills
• Students will learn to recognize and be able to
  classify geometric shapes
• Students will to use vocabulary learned in Math
  and reinforced in Art
• To physically investigate and analyze the
  attributes of geometric shapes.
• Students will visually understand abstract
  concepts learned in Math

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Samples We Will Make

• Mobius Strip
• Tessellation
• Flexagon
• Kaleidocycle

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Mobius Strip

• A mobius strip is a loop of paper with a half
  twist in it.

• Supplies
• A 1X 11 strip of paper
• Scissors
• Pencil
• Ruler
• Tape

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How to Make a Mobius Strip.

• Using a ruler and pencil Make a 1strip on a
  piece of paper.
• Cut out the strip
• Give it a half twist (turn one end over).
• Tape the ends together.

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What to do With a Mobius Strip

• After you make your mobius strip, take a pencil
  and draw a line along the length. How many sides
  does the mobius strip have?
• Take a pair of scissors and cut the mobius strip
  along the line you have drawn. What happened?
• What do you think will happen if you cut it down
  the middle again? Try it.

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Flexagon

• Flexagon is a sheet of paper folded and cut in a
  special way so that as well as having a front and
  a back you can fold them to reveal hidden sides. 

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Flexagon

• Supplies
• 3 ½ X 22 Strip of oak tag or heavy paper
• Ruler
• Pencil
• Colored pencils or markers

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Flexagons Instructions

• Mark the strip in 4 and 2 intervals as shown
  below and connect the marks to form ten
  equilateral triangles and a right triangle at
  each end of the paper

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Instructions

• Cut off the right triangles at each end
• Lightly fold and score at each line

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Flexagon instructions

• Fold as follows
• Count 3 triangles from the left and fold them to
  the back
• Count 3 more triangles, and fold the other
  triangle to the front.
• Place the end under the beginning and fold the
  last triangle over the first triangle.
• Glue or tape the last triangle in place (do not
  tape over any edges)

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How To flex

• Pinch together two adjacent triangles, pushing
  the crease up. Then push the opposite side down
  and into the center
• Flex outward and from the center to revel new
  face
• If it doesn't work try the next Triangle

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Tessellations

• Supplies
• Pencil
• Marker
• Scissors
• Tape
• 2 sheets of Colored paper Draw a grid with
  3X3 inch squares on one sheet
• 3X5 Card Cut 2inches off creating a 3X3
  template
• Instructions

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Tessellation Instructions

• Cut a wavy line from the bottom left corner to
  the top right corner of the square
• Slide the left piece to the right side and tape
  it down
• Cut a wavy line from the bottom left corner to
  the bottom right corner of the square
• Slide bottom piece to the top and tape it down

3X3 Square
Step 2
Step 1
Step 3
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Instructions Continued

• Trace the template to one of the sheets of
  colored paper and cut them out.
• Align a shape with the top left grid Square and
  glue it down
• Continue to paste the cut outs in a checkerboard
  pattern on the grid
• Erase the grid lines and create details to make
  recognizable shapes.

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Build a Kaleidocycle

• Start with pattern included in kit
• Enlarge it as desired I usually enlarge to fit a
  12X18 sheet of paper
• Cut out pattern
• Trace the pattern by taping it to oak tag board
  and drawing over lines using a ruler
• Cut and score over each line
• Fold and glue as instructed on pattern

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Related Web Sites

• Tessellations http//library.thinkquest.org/16661/
  http//www.tessellations.org/index.htm
• MC Escher and Math http//www.mathacademy.com/pr/m
  initext/escher/index.asp
• Flexagons http//www.mathemagic.org/MathsAndArt/fl
  exagon.htm
• http//www.mathematische-basteleien.de/flexagons.h
  tmFlexagons20in20the20Internet
• Geometry http//ccins.camosun.bc.ca/jbritton/jbru
  bbergeom.htm

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Disclaimer

• I am not particularly brilliant
• All this information is accessible on the web
• Just do a google search on words like Moebius,
  flexagons, math activities
• Ideas and printed publications provided here were
  shared with me by other teachers and found on the
  web