1. Flexagons & Other Fun Art and Math Connections Tully Jr. High School Virginia Killmore

2. 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

3. 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 Why Create These connections

4. Mobius Strip Tessellation Flexagon Kaleidocycle Samples We Will Make

5. Mobius Strip A mobius strip is a loop of paper with a half twist in it. Supplies A 1”X 11” strip of paper Scissors Pencil Ruler Tape

6. How to Make a Mobius Strip. 1.Using a ruler and pencil Make a 1”strip on a piece of paper. 2.Cut out the strip 3.Give it a half twist (turn one end over). 4.Tape the ends together.

7. 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.

8. 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.

9. Flexagon Supplies 3 ½” X 22” Strip of oak tag or heavy paper Ruler Pencil Colored pencils or markers

10. 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 4 4 4 4 4 2 2 4 4 4 4 4

11. Instructions Cut off the right triangles at each end Lightly fold and score at each line

12. 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)

13. 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

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

15. Tessellation Instructions 1.Cut a wavy line from the bottom left corner to the top right corner of the square 2.Slide the left piece to the right side and tape it down 3.Cut a wavy line from the bottom left corner to the bottom right corner of the square 4.Slide bottom piece to the top and tape it down 3X3 Square Step 1 Step 2 Step 3

16. 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.

17. Build a Kaleidocycle Start with pattern included in kit Enlarge it as desired I usually enlarge to fit a 12”X18” 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

18. Related Web Sites Tessellations http://library.thinkquest.org/16661/ http://www.tessellations.org/index.htmhttp://library.thinkquest.org/16661/ http://www.tessellations.org/index.htm MC Escher and Math http://www.mathacademy.com/pr/minitext/escher/index.a sp http://www.mathacademy.com/pr/minitext/escher/index.a sp Flexagons http://www.mathemagic.org/MathsAndArt/flexagon.htm http://www.mathemagic.org/MathsAndArt/flexagon.htm http://www.mathematische- basteleien.de/flexagons.htm#Flexagons%20in%20the%2 0Internethttp://www.mathematische- basteleien.de/flexagons.htm#Flexagons%20in%20the%2 0Internet Geometry http://ccins.camosun.bc.ca/~jbritton/jbrubbergeom.htm http://ccins.camosun.bc.ca/~jbritton/jbrubbergeom.htm

19. 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