Flextangle: Fusing Math and Art
Hexaflexagon , Color Schemes & Pattern
Middle School & High School Art STEAM Lesson
Wall Pocket Instructions:
I first saw flextangles on babbledabbledo.com and 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.
Download and print template: https://babbledabbledo.com/wp-content/uploads/2015/03/Flextangles-Template-BABBLE-DABBLE-DO.pdf
- 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.
- History of Flexagons (Resource: HEXAFLEXAGONS AND OTHER MATHEMATICAL DIVERSIONS: The First ‘Scientific American’ Book of Puzzles and Games by Martin Gardener University Of Chicago)
- 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.
- Review Color Wheel.
Types of Color Schemes
- Complementary colors are colors that are directly opposite from each other on the color wheel.
- Analogous colors are 3-4 colors that are NEXT to each other on the color wheel.
- Monochromatic color scheme includes the tints and shades of ONE color. “Mono” means one.
- Split complementary color scheme includes one color plus the two colors on either side of the color’s complementary color.
- Triadic color scheme includes THREE colors that are EQUAL distance from each other on the color wheel. “Tri” mean three.
- Zentangle Patterns: Zentangle is an art form that requires a pencil, pen, and paper and a relaxed focus on creating basic repeating patterns (http://tanglingart.com/history-of-zentangle/). Zentangles are beautiful pieces of art that focus on pattern and design.
How to make our flextangle:
- Download and print template: https://babbledabbledo.com/wp-content/uploads/2015/03/Flextangles-Template-BABBLE-DABBLE-DO.pdf
- 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.
- Add tacky glue on END tabs and tuck into open end of tube. Press and hold to seal. Let dry completely before flexing.
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