# Sharing Federico Ardila’s JMM talk with kids

This is the second in a little project I’m doing with the JMM talks. Some of the invited talks were published earlier this week:

I’m definitely enjoying the talks, but also wondering if there are ideas – even small ones – that you can take from the talks and share with kids. My hope is that kids will enjoy seeing ideas and concepts that are interesting to mathematicians.

The first project came from Alissa Cran’s talk:

Sharing an idea from Alissa Cran’s JMM talk with kids

Today I tried out an idea from Federico Ardila’s talk with my younger son (who is in 6th grade). The idea related to an interesting shape called the “permutahedron.”

We began with a quick explanation of the idea and looked at some simple cases:

Next we moved to building the permutahedron that comes from the set {1,2,3}. At the end of the last video, my son speculated this shape would have some interesting symmetry. We used our Zometool set to build it.

One thing I’m very happy about with this part of the project is that building this permutahedron is a nice introductory exercise with 3d coordinates for kids.

Finally, we talked about the permutahedron that comes from the set {1,2,3,4}. My son had some interesting thoughts about what this shape might look like. Then I handed him a 3d printed version of the shape and he had some fun things to say 🙂

The 3d print I used is from Thingiverse:

Permutahedron by pff000 on Thingiverse

Definitely a fun project for kids, I think. Making the hexagon was fun and also a nice little geometric surprise. Exploring the 3d printed shape was also really exciting – it is always great to hear what kids have to say about shapes that they’ve never encountered before.

# Sharing an idea from Alissa Crans’s JMM talk with kids

Yesterday videos of several of the invited JMM talks were published:

I was skimming through the talks to see if there might be anything fun to share with kids and came to this slide in Alissa Crans’s talk “Quintessential quandle queries”

I had a hunch that kids might find it strange that an expression like $A B A^{-1}$ would be something of interest to mathematicians, so I decided to see what the boys thought:

When we played with numbers, the expression $A B A^{-1}$ was just $B$. So now I tried a few non-number ideas with A and B representing certain moves on a grid. The first set of moves seemed to behave just like the numbers did, but the second set of moves produced a little surprise:

Now we looked at a completely new situation -> in the video below A and B will represent moves of a Rubik’s cube.

Here I got a really fun surprise when the boys saw that doing repeated applications of the “move” $A B A^{-1}$ was actually really easy to describe mathematically 🙂

Definitely a fun little project. There’s no real need to show the boys the complete talk – they don’t need to learn the complete content of the talk. It was fun to show them an idea that is interesting to mathematicians, though, and especially fun to give them a peek at some simple operations that don’t commute.