I first saw flextangles on babbledabbledo.comand thought it would be a great STEAM Art project combining the mathematical flexahexagon paper sculpture and art patterns and color theory. My high school art 1 class applied our recent art lesson on types of color schemes along with Zentangle patterns to create this intriguing and addicting paper polygon. Flexahexagons are crazy fun to create. My students couldn’t stop flexing them after they made them! Even though this was done with high school, this lesson can be easily modified to elementary by simplifying the design requirements. There are MANY different flexagon designs depending on the number of sides and faces. This book provides some more templates for creating more varieties: Fantastic Flexagons: Hexaflexagons and Other Flexible Folds to Twist and Turn*
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Learn the history of the flexagon.
Classify and name polygons and polyhedrons based on the number of sides.
Demonstrate understanding of how to cut and fold paper to create a flexagon that rotates when the outer points are pushed to the center.
Create a hexaflexagon using equilateral, congruent Triangles.
Make math and art connections and solve problems.
Physically investigate and analyze the attributes of geometric 3-dimensional figures.
Preparation: Flextangle Template printed on Cardstock 8.5×11” paper or Ledger 11×17” Cardstock *We did a simple practice flexagon on letter size paper first, then created the final with Zentangle designs on Ledger cardstock paper.
What is a Flextangle? A flextangle is a combination of a hexaflexagon and a zentangle design.
Flexagons: In geometry, flexagons are flat models-paper polygons, usually constructed by folding strips of paper. They can be flexed or folded in certain ways to reveal the multiple faces. The flexagon rotates when the outer points are pushed to the center. Flexagons are usually square, rectangular (tetraflexagons), or hexagonal (hexaflexagons). We are creating a hexaflexagon.
Flexagon Names: The name of a flexagon tells the flexagon’s shape and number of faces. A prefix is added to the name “flexagon” to indicate the number of faces that the model can display, including the two faces (back and front) that are visible before flexing. For example, a flexagon with a total of six faces is called a hexaflexagon.
Flexagons were discovered in 1939 by Arthur Stone, then a graduate student at Princeton University who later became a lecturer in mathematics at the University of Manchester. An Englishman, Stone was trimming American notebook sheets to fit in his English binder when it occurred to him to fold the strips of paper to make figures, one of which was the trihexaflexagon (so called because it has six sides and three faces). He elaborated on this model to create the hexahexaflexagon (six sides, six faces).
Stone showed his models to his friends: Bryant Tuckerman, Richard Feynman, and John W. Tukey. They formed the Flexagon Committee.
In geometry, a tetrahedron, also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners.
Each section has two sets “tick” marks (at the top and at the bottom of each triangle) to help you line up your design within each section. When it is folded and flexed the design will come together to form a completed shape.
Notice the individual sections A, B, C, & D. In each section you will draw a new design. You will be repeating the same design in each triangle of each section.
Draw a NEW design and repeat the design in each triangle of section B.
Draw a NEW design and repeat the design in each triangle of section C.
Draw a NEW design and repeat the design in each triangle of section D.
Choose one color that you will repeat in all four sections. Choose four color schemes to use-one in each different section. Here is an example:
Repeated color: Purple
Section A Color Scheme: Complementary= Yellow + Purple
Section B Color Scheme: Split-Complementary=Purple + Yellow-green + Yellow-orange
Section C Color Scheme: Analogous=Purple + Red-purple + Blue-purple + Blue
Section D Color Scheme: Monochromatic= Tints and Shades (Values) Purple
Activity: Flextangle Paper Polygon Sculpture
Draw a NEW Zentangle design in EACH Section (A, B, C, & D). **Make sure your design lines up or connects at the TOP “tick marks” of each section.
Choose 4 Color Schemes to use. Have 1 color that is the same in all 4 sections.
Use Sharpie, colored pencils, or markers to color each section with a different color scheme. (This is a single project showing A, B, C & D Sections)
Cut along outer perimeter’s BOLD line.
Use a ruler to help fold the dashed lines face to face (design to design). Unfold.
Use a ruler to help fold the diagonal lines back to back. Unfold.
Gently fold paper back to back to match dot to dot and form a tube.
Add tacky glue on tabs marked “GLUE” and press together. Hold until the paper sticks without help.
Put glue on the BACK of the END tabs
Pinch & Hold
Put glue on GLUE sections
Spread with finger to cover entire section
Fold DOT to DOT, Press & Hold
Add tacky glue on END tabs and tuck into open end of tube. Press and hold to seal. Let dry completely before flexing.
This month, The Art Ed Blogger’s Network is writing about STEAM/Art Integration. Join us on the first Tuesday each month for new projects, ideas, and inspiration.