Week 41: Birdwatching

Birdwatching and math go hand-in-hand. There are statistics on populations, migrations, observations, and so much more. One of the ways to get in touch with nature is to become aware of the birds that frequent your home and walkabouts.

Birdwatching gets us to access so many areas of our mathematical minds. We see a size, color, shape, or feather and we start to put the puzzle together to identify what species. Some may use their ears and hear the minor differences in calls and trills to know what is around them and what to look for. This problem-solving activity is so mathematical in nature.

This week, I encourage learners to bring their senses to their windows, backyards, and trails to put the pieces together to identify the flighty, feathery friends that we have all around us. I recommend having a bird book (The Sibley Guide to Birds, 2nd Edition – please get it from a local store), and also using Cornell’s Lab of Ornithology. The Cornell lab will let you track your birds, see what’s in your area, and let you contribute to the birding community.

Here are some of the math activities that you can add to your bird watching:

  • Do a frequency chart for times of day vs. number of birds observed. (This would be many days or months of data that you could keep at a window or table at home.)
  • Try to find the rhythm of some of the bird calls that you hear and keep a journal.
  • Read up on your favorite birds, their stats, and behaviors and see if you can observe what you read (ex: Crows have a long childhood that may contribute to their intelligence. We have been observing baby crows play with sticks in our bird bath and try to use them as tools).
  • Be a scientist and record observations. Learners may find that they observe something new and interesting to share.
  • Draw/sketch the geometries of the various shapes and sizes of birds. You could do this in the different categories of birds (raptors, thrushes, shorebirds, etc.).
  • Map the migration patterns of birds that you see. (ex: We love seeing our Townsend Warblers come in and we love to think about where they are off to when they leave.)
  • My daughter had the wonderful idea of plotting, sketching, and observing the flight patterns of birds (rollercoaster, gliding, soaring, diving, etc.). This is a great art project idea.

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Week 40: Tensegrities

In math we find balance and equilibrium. We balance equations. We keep balance by using properties of identity (multiply by 1 or add zero), Properties of Equality (mirroring operations), and by using the many other ways to manipulate and play with structures in math.

This week’s math is about equilibrium through building tensegrities (see photo above). Buckminster Fuller coined the term “Tensegrity” by combining “tensional” and “integrity.” He described the structure as, “Islands of compression in an ocean of tension.”

For this week’s activity, grab building toys, hot glue and sticks, or straws and string to create tensegrities. Learners can work on the simple design in the photo above, or on polyhedrons, bridges, sculptures, and more. Some challenging shapes would be polyhedral structures or towers. The goal is to create a structure that uses the tension of strings and the weight of the objects in positions that reach equilibrium.

For high school or middle school students, force diagrams may be a fun activity as well. Think about the moments and forces that balance in each structure created. There is a great “Beyond the Brick” video here. For strings at angles, there are some great trigonometry applications to play with.

Week 39: Toothpicks

A box of toothpicks can lead to an afternoon of entertainment. This week learners can play with the toothpick sequence. The sequence produces really interesting geometries and lines as it grows. I recommend watching Numberphile’s Youtube video on this sequence here. There is also OEIS’ website that allows for play with variations and many iterations. Grab a box of toothpicks and let’s begin:

Start by placing a single toothpick:

And then place toothpicks centered at each end:

And then place toothpicks centered at each end again:

Repeat this process at the ends that are available:

I also made a GIF in Procreate (stop animation is a wonderful way to play with all sorts of math):

Allow for play with the toothpicks to see what other mathematical patterns and tessellations are created.

Another option is to use graph paper to draw this sequence. Have fun!

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Week 38: Knotty Math Tiles

I love playing with knots. Last year I designed a Knotty Math toy with wooden tiles. It is part of a series of toys I have been working on that help create single pointed mindfulness with math. These are for kids and adults alike. I think sand, clay, tiles, and tessellations can all be instruments for this meditatively, mindful, mathematical state.

This week learners can print paper versions of these tiles and see what amazing designs they can come up with. As a challenge, learners can try to create some of the mathematical knots in knot theory with various numbers of crossings (see comic further down).

Note: The design purposely uses only two tiles. I like limiting the tile types (no single straight tiles) to prompt more problem solving thought and as a reminder that less is more.

Here is the printable:

Print and cut along gridlines

Here is a Knotty Kitty – See if you can make an unknot (0_1), trefoil (3_1), or others on this diagram (you may need to print more tiles).

Some more examples (I have tons more, but don’t want to spoil the fun of your discovery). You can create tons of links, knots or tiled art – enjoy!

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Side note: At some point I plan to post a set of cards to go with this toy so learners can try to match the tiles to the cards, but I am still contemplating what I want that to look like.

For those of you teaching virtually, here is a google drawing you can do with your classes (please save off a copy of this to be able to edit): https://docs.google.com/drawings/d/1DfwNkRi1WbP88K6SgUyne0oSAcv3a6ILNobUe5gP8qI/edit?usp=sharing

Week 37: Cantor Set Kirigami

For this week’s activity, learners can play with Cantor Set Kirigami. The Cantor Set is created by drawing a line. Next, remove the middle third of that line (this will create 2 lines). For each of the two lines just created, remove the middle third (this will create 4 lines). Continue with this process until the lines are too thin to work with.

Menger Lux Blox

Some of the fun characteristics to notice is the pattern of the line lengths (1, 1/3, 1/9, 1/27,…), the number of lines generated with each iteration (1, 2, 4, 8, 16, …), the fact that this set is infinite, yet not countable and that it gets smaller and smaller with each iteration.

I created a fun Kirigami Cantor Set and have the template below with a video how-to. Enjoy!

Learners can also draw Cantor Set cities, roads, abstract art, and find many ways to represent this simple fractal. The Menger Sponge is one form of a Cantor set in 3d.

If you need a jpg. of the sheet: