SchoolArts Magazine

March 2018

SchoolArts is a national art education magazine committed to promoting excellence, advocacy, and professional support for educators in the visual arts since 1901.

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58 2" All Handy Art ® products are proudly made in the USA Visit us online! Quality products, reliable service since 1974. 3. Place the end under the beginning, and fold the last triangle over the first triangle. 4. Tape the last triangle in place, using double-sided tape or small rolls o f clear tape. Tape under the triangle; do not tape over any edges . To Flex 1. Pinch together two adjacent trian- gles that have an opening between them, pushing the crease up. Then push the opposite side down and into the center. 26 MARCH 2018 SchoolArts SCHOOLARTSMAGAZINE.COM 27 cise cutting, measuring, and folding, trihexaflexagons are easy to create, and the design possibilities are endless. And a bonus: You will be introducing oodles of math vocabulary, making this a great STEAM project. Marking and Measuring To prepare, measure and carefully cut lightweight tag board or other heavy paper into 3 ½ x 22" (9 x 56 cm) strips. Use a paper cutter, as accuracy is critical. You'll also need clear tape, rulers, and pencils. First, make sure your students understand that the end of the ruler is not at the zero. There is extra space on the end of the ruler; all measuring must begin with the zero for accuracy. I call this "zeroing the ruler." Distribute strips to students and have them make tiny marks on the paper's edge, marking off the top of the strip, from left to right, in 4" (10 cm) intervals, leaving 2" (5 cm) at the end. Mark the bottom of the strip, again moving left to right, beginning with a 2" segment and then continuing to the end with 4" intervals. N ext, using the ruler, begin at a corner and connect the marks diago- nally, ending at the opposite corner. You will end up with a right triangle at each end of the paper, and ten equi- lateral triangles in between. To create straight lines, make sure your students know how to hold their rulers steady. I recommend holding the hand arched over the ruler, creating two points of contact. When this step is complete, cut off the right triangle at each end of the strip with scissors. Students are almost ready to assemble their trihexaflexagons, but first they must score the lines to cre- ate clean, sharp folds. Holding the ruler steady against the lines, gently score using a pointed wooden stick or the point of a pair of open scissors. Once the lines are all scored, fold and crease them back and forth. Folding the Trihexaflexagon 1. Count three triangles from the left and fold them to the back. 2. Count the next three triangles, then fold the other end of the paper to the front. With precise cutting, measuring, and folding, trihexaflexagons are eas to create, and the design possibilities are endless. 4" 4" 4" 4" 2" 4" 4" 4" 4" 4" 4" 2 CONTINUED ON PAGE 58. Only two faces of a trihexaflexagon can be exposed at any time—the third is buried inside. Use this diagram as a reference when marking the paper strips for your trihexaflexagons. H ave you ever heard of a tri- hexaflexagon? Combining art with mathematics, my sixth-grade students cre- ated these intriguing mathematical constructions. What in the world is a trihexaflexagon, you might ask? Let's break it down: The "tri" prefix represents the three faces (what you might call sides) of the construction. The "hexa" indicates it has six edges (again, what some might refer to as sides). In other words, it's a hexagon. "Flexagon" simply indicates it is a polygon that flexes. Therefore, a trihexaflexagon is a three-faced, six- edged, flexible polygon. Only two faces can be exposed at any time as the third is buried inside. By flexing the con- struction, the third face emerges. Each flex not only exposes a different face, but also rotates the segments of the visible images kaleidoscopically, creat- ing a total of six different designs. Inspiration from Memory My inspiration to incorporate trihexaflexagons into my art cur- riculum began more than twenty years ago, when my son, then in the fourth grade, became fascinated with mathematical games. His research revived a memory from my own childhood, when Scientific American magazine was always in my home. Articles about flexagons, with build- ing instructions, had been published in the magazine's Mathematical Games column written by Martin Gardner. My brother and I eagerly fol- lowed the directions. As I shared this memory with my son, I again became intrigued with the flexagons and rec- ognized a strong art connection. As a result, they became a curriculum staple for me, continuing long after my son's interest had waned. Set aside your math fears. With pre- The Art and Science of Phyllis Levine Brown E L E M E N T A R Y TRI HEXA FLEXA GONS By flexing the trihexaflexagon paper construction, a third face emerges. CONTINUED FROM PAGE 27. 2. Flex outward from the center to reveal a new face, like a flower blooming. Adding Designs Now it's time to add designs. Have students draw with pencil, flexing repeatedly to see how the design changes with each flex. For planning designs, examine kaleidoscopes, dis - cuss repetition and symmetry, and r emain cognizant of the hexagonal shape. Look at the work of M.C. Escher or examine Middle Eastern and Islamic art for inspiration. Add color with media that won't pen - etrate the paper surface. Water-based m arkers or colored pencils are best. If you are inspired by this project, explore online to learn to construct other flexagon configurations. You'll likely become addicted, like me. Phyllis Levine Brown is a retired art teacher from North Warren Central School in Chestertown, New York, and founder of the after-school art enrichment program, DragonWing Arts. plbrown3 Get Published! Write for SchoolArts! Go to WritersGuidelines for information. Author benefits include: • free one- ear print and digital s ubscription. • up to six free copies of the issue in which our article was published. • honorarium of up to $100 per article. • tw ears of access to Davis Digital. 58 MARCH 2018 SchoolArts

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