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.