Exploring the knots with 4 and 5 crossings with kids

In our last project we explored the trefoil knot:

That project is here:

An introductory knot activity for kids

Today we moved on to the knots with 4 and 5 crossings. We started off by comparing the trefoil knot with the 4 crossing knot – what is the same? what is different?

Also – the 3 white knots (1 with 4 crossings and 2 with 5) that appear in this projects come from Mathematica’s knot data collection and the red knot (the trefoil knot) was designed by Laura Taalman.

Next I had the boys try to make a knot with 4 crossings out of a rope. It is not as simple as it seems! One nice thing about making these knots out of rope is that they also begin to discover some of the ways you can have crossings that can be undone.

Now we compared the knot we made from the rope to the 3d printed knot with 4 crossings. In the last project we had quite a lot of difficulty comparing the different versions of the trefoil knot. Here, though, comparing the knot in our rope to the 3d printed knot was not too difficult.

Finally, we wrapped up this project by inspecting and comparing the two knots with 5 crossings. It is very interesting to hear what kids see in these two knots, and also fun to hear their ideas for how you might determine that these two knots are actually different.

Definitely a fun project. I really like exploring these knots with the kids. It makes me wonder if there is a way to go to the next level and help them understand some of the ideas that help you understand when two knots are different?