Hex-a-Huddle Board Game

This week Quanta Magazine published an article on penguins and their hexagonal behavior. I shared this article with my 14yr old daughter, Opal, and we started discussing how this would make a great board game.

We designed pieces, drafted our prototypes in Affinity Design, and then utilized a Glowforge to cut. After gluing for a few hours, we finally got to play, and we played our hearts out. My other two children played as well and helped refine the rules and game play.

A brief summary of the game:


26 x penguins with hexagon and dial, 2 x hexagonal boards, 2 x wind tiles, 1x Game Play Indicator, and 1x Game Play donut.


  • Each player has 13 penguins, a wind tile and a board.
  • To set up the game the players set each penguin’s dial to 3 hearts and the wind tile facing from left to right.
  • Each player makes a huddle of penguins. Every penguin must touch at least one other penguin. They can be in any arrangement.

Turn Play:

  • Each Round:
    • Wind Chill: Penguins with an exposed side to the wind lose one heart. Exposure means not touching another penguin on that side.
    • Assess: Remove dead penguins and turn the wind tile 60 degrees clockwise.
    • Waddle: Roll D4 and multiply die by five to determine number of moves. Penguins can move that number of spaces. They must be able to slide to an adjacent space and must always touch at least one penguin.
    • Recover: For penguins with no sides exposed, set hearts to 3.
  • Play two full rotations of the wind tile for a full game, or one rotation for a short game.


At the end of a game, players count the hearts on the board. The player with the most hearts wins.

Below is a draft (very rough) video of play:

For sale? We have one copy for sale currently – it could be sold by the time you read this. There are hours that are put into making a game and we can’t charge a competitive price currently given materials and labor. We are working on this.

Behind the Scenes:

Here is some of the behind the scenes questions that were asked:

Opal: “How are we going to indicate loss of life?” Me: “Not sure, I’ll think about it while I run…” My headphones coincidentally weren’t charged, so in the silence, the design came to mind for hexagon penguin dials.

How many moves would work and how many penguins? – We tried various multiples, constraints, and rules for hours.

Can we use dead penguins as a shield? – Since they aren’t likely to stay upright – no. Maybe we should call the scientists.

Me: “Are you sure you want a game and not just an army of penguin toys?” Opal: “I am pleased with the army…”

Me: “Should we use a unit circle with unit vectors? Everyone would love pi!” Everyone: Blank stare…

Opal: “Maybe we should only use hexagonal numbers for the penguins…” 2n^2-n

Should we use all 45 penguins or 13? 13 works well for game play. 22 also works well for a 2 player game. We actually came up with various versions that use different multiples for die roll, different numbers of penguins, and no board. We also looked at cooperative play.

Like what you see?

Week 51: Block Prints

I love thinking of mirror images when I am block printing. I will never forget the time I printed SPARK backwards on accident for a summer art camp and my kids laughed at the reverse phonics. This week I encourage learners to take a math concept, tessellation, or shape and create a print.

Ways to create plates for printing:

  • For younger learners, foam boards easily take impressions.
  • For those that are semi-comfortable carving, potatoes, apples, or rubber blocks can provide semi-soft mediums to carve.
  • For those that are skilled with sharp objects, wood or lino-blocks may be preferred.

When I teach I say these words at least a few dozen times:

  • Do not ever force a blade.
  • Do not cut towards yourself or others.
  • Keep your tools sharp and cleaned.
  • Be in control.

If you are going to carve on a block, foam, or rubber sheet:

  • Sketch a design on paper with a pencil. (Keep in mind the size of your carving surface.)
  • Transfer the design by rubbing the pencil onto the carving surface.
  • Carve your design. (You can either carve in, tracing your lines, or around them.)
  • Roll ink on the block with a brayer.
  • Place a sheet of paper (or fabric) on the block and burnish (or rub) it with a flat surface to make sure that it makes contact with the block.
  • Peel the paper/fabric off. (This can take a few tries to get it right.)

For this post I carved a circle composition with the Fibonacci sequence in mind. I think I run faster with math shirts, so I printed one as well:

One of my children jumped in and we did a Sierpinski potato triangle. To use potatoes: Draw a sketch on the potato, cut out the design, and then treat it like a stamp.

If you like what you see, please consider donating to this website.

Week 50: Flip Books

This week I encourage learners to play with their animation skills. Take a math concept, problem, or design and play with ideas to animate it. Start simple to warm up and then build on the ideas. Flip books are fun. I recommend using thinner paper that can be seen through so it is easier to draw on top of the previous frame. Try the paper out before spending the time to draw. Flip books are an analogue GIF.

Here are the basic steps to drawing a flip book:

  • Decide on your math topic to animate. (Fractals, projectiles, growth, decay, etc.)
  • Draw the starting frame:
  • Draw the next frame by tracing and/or using the previous sheet as a reference:

  • Repeat the process of making new frames by referencing the previous:
  • Once your frames are complete – flip it!

There are other ways to animate as well. There are apps such as iMotion to make stop animation films. I also enjoy using Procreate and Looom to create animated GIFs. Learners may prefer to use technology for their animations. I plan to cover this in some STEAM posts at some point. Please share your animations!

If you like what you see, please consider donating to this website.

Week 49: Pendulum Labs

Pendulums are wonderful physics toys that are great for exploring periodic functions. For week 49, I encourage learners to get out some string, weights, and stop watches.

Here are some ideas for playing with math and pendulums:

  • Start with a string and a weight to observe basic pendulum motion. Nuts, bolts, tennis balls, and other objects can work as weights.
    • Record how long it takes for the pendulum to return to its start (this is called the period).
    • Change the length of the string to see if it changes the period.
    • Change the mass of the weight to see if it changes the period.
    • For older learners, you may want to try to find the relationship between time, period and length.
    • With all ages, it can be fun to look at trigonometric functions with this activity.
  • Another activity is to create a wave pendulum. This can be done with a broomstick and weights, or other construction toys. I like to bring in a maker box and materials and have learners devise a way to make a wave pendulum. Once you have one working, then see if learners can explain why it’s called a wave pendulum. For those that like to code, look at creating a wave pendulum . My code is here and running below. At the bottom of this post I have a portable laser cut pendulum I designed.

See the Pen jOqOJNL by Sophia (@fractalkitty) on CodePen.

  • Another activity is a painting pendulum. Hang a cup full of paint over a canvas and push it into a circular motion and watch the curves that are created as the pendulum is dampened. These can be a lot of fun with large tripods in bigger spaces.
  • Finally, I love to create chaotic pendulums because they are such a contrast to the previous activities. To create a chaotic pendulum, you can use building toys to create a tripod with a pendulum and then put a magnet in the weight. Put other magnets just beyond the reach of the pendulum and kick it off. The motion observed will be nothing like the periodic and predictable motion of the previous exercises. This is a great opportunity to talk about dynamic systems, chaos, and unpredictable behaviors.
  • Another topic that can be discussed is how pendulums dampen and why they do. What would happen in a vacuum?

If you like what you see, please consider donating to this website.

Week 33: Ultimate Tic-Tac-Toe

Games don’t have to be complicated to require some good thinking skills. We all learn tic-tac-toe when we are younger. We soon learn how to always come to a stalemate with an equal opponent. Once you get the strategy, it can get a little boring… But what if we add a layer (or two) of moves. What does this do to the strategy of the game? Is it so easy to predict your opponents next move?

This week I recommend learners create a tic-tac-toe board that has tic-tac-toe boards in each square. Here is a video of how to play:

My learners contemplated:

  • How many times can you nest the game before it’s too complex?
  • With each layer added, how much longer and more difficult would it be? (how many moves are there?)
  • How is this like a fractal?
  • Could you keep a game going with one move a day for how many days with 2-nested?, 3-nested, 4?
  • What does the game tree look like?
  • How many ways can you play tic-tac-toe vs ultimate tic-tac-toe?(think combinations). What is the combinatorics calculation look like for this?

If you are wondering how I was able to do this in the time of Covid… I use a digital white board and label squares so it is easy to say the next move. You can also use a shared google drawing or a google spreadsheet to play (here is one for you.)

Another blog (Games for Young Minds) that does a great post on this game is here. Math with Bad Drawings also has a great post here. As you can see, this is a fun game with us mathy folks everywhere.

Flipping Origami Class Video

After teaching this a few times this week, I created a video for those that missed it or want to go back. We made two different origami toys that have some flipping fun. Feel free to contact me if you have any questions.

Week 32: Isometric Drawing

Let’s get out our pencils, isometric paper, and thinking caps this week! Isometric drawings are often used in engineering and design as a way to display 3D ideas. They can also be used to create optical illusions and escheresque works of art.

To start, print some isometric paper, or set your digital drawing program to isometric drawing guides. Start by drawing simple objects, like a cube, and play with shading.

Once comfortable with basics, start making skeletons for shapes, linking sides that don’t make physical sense, and thinking about objects that would allow you to go up and down at the same time. Below are some examples and videos to play with:

Opal’s sketch (13yrs old)

Week 31: Angle Inquiry

Sometimes the simplest things have wonder hidden within. This week, learners can play with the angles of polygons. How many degrees are in a triangle? In a quadrilateral? In a hexagon? Is there a pattern?

Here is a warm-up activity:

Draw a triangle (any triangle), and cut it out.

Next, rip the corners off:

Now, here is the fun part… put the pointy angles together. What do you get? Try it with lots of triangles and see if you always get a straight line. Rather than lecturing or telling learners that triangles have 180 degrees (or pi radians), let them discover. They can even create art ( I like to make my angles into perspective path doodles.)

Now do the same with a four sided shape. What do you notice? Is it the same for all the ones you can create?

Now do the same with 5, 6 or more sided shapes. There is a rule to be found. Try to discover it if you don’t know. I will put the rule at the bottom of this post.

I did this twice last week with virtual classrooms through the Covid-19 isolation. Students from kindergarten to middle-school ate it up. We used it as a warm up activity (10-15 minutes) prior to doing some loop-doodle math and/or other activities.








The rule for simple polygons is that for n sides there are 180(n-2) degrees. Or you add 180 degrees every time you add a side.