Art + Math = Magic!! It's a trihexaflexagon!

This is a trihexaflexagon. It's got three sides that each change, or "rotate"once. This is one of the sides and its rotation. Confused?

One of the workshops that I taught at my recent state conference was a hands-on workshop where the participants each learned to make a trihexaflexagon, a tetratetraflexagon, and a kaleidocycle - all a bunch of fun combining art and math.

Last year I posted about these amazing constructions right here. If you want more specific details about the process of creating a flexagon, or how how I got started making them, please check out that post.

My students this year faced several "challenges" on this project. One was to incorporate their name, initials, or some other word on one segment. This was traced in mirror images around the hexagon using carbon paper, resulting in a kaleidoscopic design.

Another "challenge" was to design one side using a ruler to connect corners and then adding additional lines and curves as desired, "flexing" as they drew to make sure their design connected in all rotations.

A third "challenge" was a color challenge. Students needed to color one side of the flexagon using either complementary colors, triadic colors, or, as chosen by both the students below, an analagous color family.


Here's a couple more student examples.


Making these can be a starting point for many lessons. You can teach tessellation, M.C. Escher, and Islamic design, or you can use them to teach color, or symmetry, or many other concepts. And then there's the ruler and construction skills required in building them.

As you know, I'm retiring. But somehow I know this isn't the last time I'll be constructing a flexagon. I'm hooked!! Perhaps you will be, too?

A little of this, a little of that

Sixth graders are finishing up their Blue Willow china patterns after learning about monochromatic color. (*Note that some of these are just works-in-progress, and I don't know why that last one rotated 90 degrees.) They are looking GORGEOUS. They actually began this project last spring, after reading The Willow Pattern Story, but I was out for 2 weeks due to minor surgery. Things moved rather slowly with the sub, and we would have had to rush to get them done before the end of the school year when I returned. I had planned for them to be on paper plates, but when I looked at their design plans, they were so good that I agreed to put the designs away and hunt down plates in yard sales all summer. (Their designs were either based on an element or elements of the story, or told their own story. They were to include a border design, and some of the plates had a raised pattern that I allowed the kids to use if they desired.) As a result of my yard sale shopping, everyone gets to paint on a "real" plate! The kids are using a variety of blue Sharpies for drawing, and painting with Nasco Bulk-krylic paint in pthalo blue, ultramarine blue, cobalt blue, and white. We are then sealing with a gloss acrylic varnish. I'm so proud of these kids!

Here's some other things we've done to start the year:


Today first graders used watercolors to paint some variations of the sunflowers in my art room (from the school garden).

Second graders started the school year with a warm and cool variation of "A Bad Case of Stripes"
Fifth graders' first project of the year was a quickie symmetrical name design. I've seen similar projects posted on other blogs.

The Amazing Trihexaflexagon!!

A combination of math and art, this annual 6th grade project intrigues everybody. We began making them when my 22 year old son was in 5th grade, and for an enrichment class he researched math puzzles and games. His interest in them waned many years ago, but I've been intrigued ever since, and so have the kids. First we break down the word: tri = 3, so it has 3 sides, or 'faces'. Then hex = 6, and it has 6 edges. Then of course flex = bend, so we have a 3-faced, 6-sided, flexible polygon! Then, an added bonus, each face has an additional 'rotation'. What you see above is the first side, and its rotation.

Above is side 2 and its rotation, and below you see it being flexed, or rotated. The final step would be to reach into the center and 'bloom' it like a flower.

And below is side 3 and its rotation, still being colored (by one of the Sarahs).

It all starts with a sheet of bristol or tagboard, 3-1/2" x 22", measured into triangles. Accurate measurement is critical, so it is a good exercise for these kids. Then they learn to score the paper for it to fold cleanly. It's easy to do with good instruction, but hard for me to explain here on the blog. Here's a video of one: http://video.google.com/videoplay?docid=5757289930789567532#

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The story of the origin of the flexagon is really interesting and fun. If you type "flexagon" into google, or even "trihexaflexagon", you'll find endless information on how to make them, and much more. (The trihexaflexagon is only one of many flexagons, but easy enough for kids to put together. We also make a tetratetraflexagon,which is even easier to make, but a little less dynamic a result.)

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I've taught workshops on making flexagons at my NY state art teachers' conference, and may teach one again next year, so if you are in NY and are interested, I'll see you in Westchester in November! It's much easier to learn hands-on than from printed instructions, believe me!!

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If you've read this far, you're in luck, because..Ta Da!! Here's a scan of my instructions that I used for my workshop! Feel free to copy and use them: