Math = Love: Hexaflexagon Day 2015

Thursday, November 12, 2015

Hexaflexagon Day 2015

October 21st was Martin Gardner's birthday.  Every year, I have my students make hexaflexagons to celebrate.  This year, all of our juniors were taking the ASVAB that day, so classes were already disrupted.  I always feel slightly guilty about skipping out on a day of what could be state-mandated curriculum practice, but I feel like showing kids this creative side of math is important, too.

I presented on hexaflexagons at TMC14, and I made a giant hexaflexagon for that presentation.  So, that had to come out!

I used clear packing tape to connect the card stock triangles, so I unfortunately couldn't color the entire thing.  :(

Here's me and my giant hexaflexagon.  The equilateral triangles have a side length of 8.5 inches.

Since this is already glued together, I decided to make another demonstration hexaflexagon.  I printed two equilateral triangles (7.5 inch sides) to a sheet of card stock and taped them together.  This is just slightly smaller than my assembled one.  (Download file for these triangles to make your own here.)

Cut out:


Finished Product: 

This helped a lot with showing students how to fold the hexaflexagon.

I began class with a video of Martin Gardner demonstrating a hexaflexagon.  It's a 2 minute excerpt I found on youtube from David Suzuki's 1996 "The Nature of Things" program.


Next, I showed them Vi Hart's introduction to hexaflexagons video.

After watching this video and commenting about her different colored sleeves and how super fast she talks, we finally set to cutting out and creasing our hexaflexagon template.  I use this template with my students.

I emphasize to my students that the better your creases are, the better your hexaflexagon will be.  If a student gets done double creasing all of the folds before everyone else in the class, I have them go back and crease them again.

Once everyone is creased and cut and ready to go, I demonstrate folding the hexaflexagon with my giant example.  Here are some folding instructions.  I explain how to fold it to students without any of the letters, but I'd suggest using the letters the first time you fold one and then finding a way to explain that makes sense to your students.    

After they are folded and glued, I show another Vi Hart video that has lots of super cool designs.

Vi Hart actually has another video, but my students have always seemed to prefer the first and the third video.  The second one gets a bit technical for them, especially since at this point they haven't even flexed a hexaflexagon!  

Here are some of their creations.  

A hexaflexagon pocket square.  

Seeing their faces, full of excitement, after they got their hexaflexagons to successfully flex was something I needed to see as a teacher.  I saw amazement and wonder on the faces of students who often only choose to exist in my classroom.  It is a reminder that it is possible to reach every student, to engage every student.  That's not happening in my class at the moment.  So, I guess the question is - how can I make algebra as intriguing as a hexaflexagon.  #stillponderingthis

Some students finished early and were eager to try their hand at a hexahexaflexagon, too.  

I was also amazed by the number of students from previous years who still had their old hexaflexagon!


  1. Wow! Thank-you for this post! I have never heard of these and I am definitely going to do this with my grade 2s!

    1. Oooh! I can see this being super fun with that age!

  2. This is awesome. We have a testing day coming this week and I needed a fun math activity for afterwards.

  3. Amazing!!

    I will do with my students for sure they will love it.

    Thanks for sharing your ideas!!!