For the secondary workshop, I taught the participants how to construct a trihexaflexagon, a tetratetraflexagon, and a Möbius strip. We also looked at the more complex hexahexaflexagon and a kaleidocycle. (Have I confused you yet?) I've taught this many times before, so I'm really confident about it, and everyone was 100% successful! If you don't know what a hexaflexagon is, I've seen posts recently calling it a "flextangle". That's a newly invented name, I presume a play on the Zentangle craze. The original name goes back to the origin of flexagons in 1939, and was made popular by an article in Scientific American in 1956.
Möbius strip, which is simply a strip of paper that is twisted one and connected in a loop. It becomes one-sided. But when you cut it in 1/2, it changes into a double twist and becomes two-sided again. Cut it in 1/2 again, and it becomes two linked loops, which is what I'm holding in the photo below!
Standards for Mathematical Practice, which are basically the same at all grade levels, include (among other things) the following: using appropriate tools strategically, reasoning abstractly, attending to precision, making sense of problems, looking for and making use of structure, constructing viable arguments and critiquing the reasoning of others.
And here are my workshop participants, using appropriate tools (rulers/pencils) strategically. We talked about using multiple contact points to keep the ruler from sliding. I tell my students to make their hands into a rainbow bridge, and to anchor the ends of the bridge on the ruler. We also always look closely at the rulers we use. Often, there's an extra gap at the end of the ruler, beyond the first inch. I discuss with my students the need to know where the "zero" is on the ruler, for accurate measurement.
Here we are, measuring accurately (attending to precision),
cutting, scoring, and folding (again, attending to precision).
Looking for and making use of structure, and making sense of the problem, too!
And when we were done, everyone had met some CC Math Standards,
everyone survived the process, and they were still smiling, too! (below)
When the flexagon workshop (with secondary teachers) was complete, it was time for the elementary workshop, which was an introduction to assorted weaving activities for various grade levels.
paper weaving activity, began to make a woven pouch on a cereal box cardboard loom, learned to do Kumihimo and strung a loom, and learned about a couple of other weaving projects. Busy, busy! Participants again explored the math standards, and talked about ruler use and measuring. And took home everything they needed to finish all the weaving projects they'd started!
Above and below, the aftermath of two workshops all piled together in one magical mess!
Above and below left, the "Sol Wall". Below right, a piece from Arturo Herrera exhibit.
Below, a piece by Nicholas Krushenick.