Playing with Annie Perkins’s counting problems

I saw a neat tweet from Annie Perkins last week:

HUGE debates in class today over this question: 4 people sit at a round table, and they only care about who sits next to them. How many ways can they sit at the table? https://t.co/Wox7Nm8BPl

— Annie Perkins (@anniek_p) May 16, 2019

Today I thought it would be fun to play around with this idea with my younger son. First I introduced the 4-person problem and let him think through it. His thought process is a great example of what a kid learning math can look like:

At the end of the last video he’d determined that there were 3 different arrangements of the 4 people sitting around the table. In this video I asked him to find those arrangements:

Next we moved to the 5 person problem:

Finally, having decided that there were 12 different arrangements with the 5 person problem, I asked him to try to write down all 12. This is a good exercise in using counting techniques to make an organized list:

Definitely a fun problem for students, and also a really nice introduction to counting and symmetry. Thanks to Annie for sharing!