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!

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

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 25: Loopy Doodle Math

Doodling and math? Yes, we can play with doodles and see what patterns emerge. Finding patterns and problem-solving is a big part of math. For this week’s hands-on-math, learners are going to draw a loopy doodle where they start and end at the same point without lifting the pencil (or pen). Try to make sure that crossings are recognizable (not on top of each other). Once a doodle, or masterpiece, is created, then I encourage learners to color it in. Make lots of loopy doodles and see if any patterns or behaviours emerge. This is a great activity for discovery. Create birds, people, or city scenes with loops. Instead of coloring it in, learners can make knots by going over under, over under (erasers are good for this.)

The patterns that emerge with these doodles are fun. What do you think of the negative spaces that are created? My daughter sat down for hours last week and drew one doodle after another after another and said, “Mom, no matter how I draw these, only one color will touch the outside.” I smiled and we talked about how important discovery is. I love that we have the precious time for doodles. She was excited (and not surprised) to hear that there is a whole area of math that looks at how to shade various maps, shapes, and even doodles. My daughter’s drawings are below (with her permission – the butterflies aren’t part of the knots, but definitely needed). She gets credit for picking this week’s math activity.

Extra questions:

Do you ever need more than two colors to shade these in?

If you tangle more than one loopy doodle together, does it still work out for shading? What about knots?

Can you classify some of your knots? (count your crossings)