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!
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:
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!