Showing posts with label trihexaflexagon. Show all posts
Showing posts with label trihexaflexagon. Show all posts

Wednesday, March 8, 2017

Toothpaste Batik at NAEA!

The NAEA convention in NY city is over, and I have so much I want to share, that I'll have to break it into a handful of posts.  Today's post is about the two workshops I taught at the convention.  One workshop, a quickie 25 minutes, was called "Sink your Teeth into Toothpaste Batik".  The goal was to simply review the process to give people the info they need to do it on their own, and to share some examples.  I think the lure of toothpaste as an art medium had people intrigued, because to say that it was crowded would be an understatement!  People were everywhere!!!!  Look at them all!!
 I've previously blogged about the toothpaste batik process and results, HERE, HERE, and HERE, and some other places too (use the labels at the bottom of the blog to find them all) so I'm not going to go over the step-by-step again in this post.  Instead, here are links to the handout and PowerPoint that were shared with workshop attendees.  They are also shared on the Document Weblinks tab on the upper right of the blog, if viewed in your browser. 
Meanwhile, what is everyone laughing about in the photo below?  It's simple, really!  I had a bottle of "not glue", the name I use for the mix of toothpaste and lotion that is used for a resist.  I wanted to pass it around toward the back of the room, so they could see it, so I tossed the bottle into the crowd.  Unfortunately, I am not an athlete, and didn't control my throw.  I believe I hit someone in the head.  Thank goodness everyone was laughing!!!
Look at this, there's even people sitting behind me on the floor, and under the beam of the  projector!
I hope it was a worthwhile workshop for everyone there!
Thanks to Kim and Karen (bloggers at Kim & Karen: 2 Soul Sisters) for your total awesomeness!  These two fabulous ladies volunteered to help me.  So handed my camera over to one of them (Kim? Karen?  I wish I could remember which sister is which!) who took these pics in the very poor light of the workshop room.  Thank you, ladies!  So glad to finally meet you, after reading your blog for so many years.

I also taught a ticketed hands-on workshop called "The Amazing Flexagon - Magic with Art and Math".  I've blogged about this project before several times; HERE's one such link
I wish I'd remembered to take more pictures, so you could see what the participants were making, but the time flew by and suddenly we were all cleaning up to go.I hope everyone enjoyed their time making these fun mathematical constructions!
Did you make it to the NAEA convention this year?  Did you have a favorite workshop you attended?  If you attended either of my workshops, and you do these projects with your students, I'd love it if you'd send me photos of their work.  And if you finished your own flexagon samples, I'd appreciate it if you'd share those with me too!!

Tuesday, September 6, 2016

Yippee! Two workshops at NAEA!

Hey, readers - I want to share some super-awesome fabulous news with you!  I submitted workshop proposals for the NAEA (National Art Ed Assoc) Convention that will be held in NYC this coming March, and a couple of days ago I received notification that they were BOTH approved!!!  There was just a 35% acceptance rate, so I'm exceptionally proud to have been approved for two out of two!
If you are going to the convention, here's what I'm presenting:
The Amazing Flexagon: Magic with Art and Math is a 2-hour ticketed hands-on workshop. 

Sink Your Teeth into Toothpaste Batik! is a 30 minute workshop, which included a hands-on demonstration.
 
These are both topics I've written about repeatedly here on the blog.  
 And both are topics/processes that I absolutely LOVE to share about.
 I'd love to see you there in NYC this March!

Saturday, August 1, 2015

One morning, two workshops, loads of fun!

I serve as a region rep for NYSATA, my state organization.  A couple of days ago, we held our second annual regional "Summer Art Blast" professional development event.  We planned it on VERY short notice, and I am so happy it was a success!  The night before, I decorated an old ugly pair or orthopedic sandals with a white Sharpie paint marker to jazz them up.  Just in time to wear while teaching workshops!
At last year's event, our members asked if we could hold some region workshops on the Common Core.  So our goal was to comply with that request.  Our Common Core presenter is an art ed professor at the College of Saint Rose,and she did two workshops, one for elementary and one for secondary.  I didn't get to attend them (but I was told they were both fabulous) because, at the same time, I taught hands-on workshops to each group.  We agreed that math scares a lot of art teachers, but it doesn't scare me, so I agreed to present the hands-on workshops.

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. 
 Here, participants are examining trihexaflexagons and learning how to make them flex and change.  (A trihexaflexagon is a hexagon with 3 faces, but you can only see two of them at once.  You have to flex them to reveal the hidden face.  Flexing them also causes the designs to rotate and change.  Very cool.)
During the workshop I also demonstrated what you can do with a 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!
Since I'm retired, I was not as familiar with the standards as many of you, but I pored over them while planning for these workshops and discovered something that helped me a lot.  The 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 precisionmaking 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.
We began (pictured above) with a "human weaving", to show how, if the weft has been woven appropriately, the warp will be all joined together.  It only takes a few minutes to do, is an activity that your students will enjoy, and will really help them to understand weaving. The people standing in line are the warp.  The person at the end of the line will hold onto a piece of rope, and another person will be the weft, pulling the rope in front of and behind the warp.  When the second row has been properly woven, if you ask one person to go to their seat, the rest of the warp will have to follow! 
In just an 80 minute workshop, we started a complex looking (but easy to do) 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! 
We held the "Summer Art Blast" at the Tang Museum at Skidmore College in beautiful Saratoga Springs, where I grew up.  The exhibit of work by Nicholas Krushenick, which I've written about before, was still there, so I got to take another look.  Then, before leaving, we viewed an odd exhibit of small painted books by Arturo Herrera, and finally, stopped at the "Sol Wall" - a piece of wall art conceived by Sol Lewitt, consisting of scribbles in graphite.
Above and below left, the "Sol Wall".  Below right, a piece from Arturo Herrera exhibit.
 Below, a piece by Nicholas Krushenick.

Sunday, December 11, 2011

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?