Rotating Students in Class – A Solution!

I’m currently gearing up for midterms, and, as I expect my students to talk one-on-one with me for 3 minutes, I figured it would only be fair to give them some practice.

In class they have to speak a lot, but usually in groups. When in pairs it’s normally with students they work with every lesson. They clearly needed some practice speaking to the other students in class – especially those they don’t know so well.

No problem, I thought. I’ll just rotate them as though they were speed dating! Halfway through class, of course, they wound up back with their original partners only having talked to half the class. Logically, I should’ve expected this:

A B C     E A B    F E A     G F E
E F G     F G C    G C B     C B A – The pairs are the same already!

I tried a few different ways to solve this problem each class, but couldn’t find a simple method. After fruitless google searches and a few classes of resorting to “find someone you haven’t spoken to yet” – hardly an elegant solution – I gave up hope of finding an answer.

Now that midterms are coming back round, I thought I’d do another google search. There has to be a simple, elegant solution! As I was about to throw my hands up in defeat, I came across a maths website with exactly what I was looking for. Kind of.

Someone was asking on a forum about rotating guests at a dinner party (<– prepare for some algebra before you go in!). Not all of the answers here were helpful, though most of them work. Just one of the solutions met the simple answer I wanted:

Put everyone in pairs in a line and rotate all but one of the students – keep one person in the same spot. You end up with this pattern:

1 2 3     1 4 2      1 5 4    1 6 5
4 5 6     5 6 3      6 3 2    3 2 4… and so on. Everyone talks to everyone else! No matter what size the class!

After spending so much time last semester feeling like an idiot for not working out something I felt should be really simple, I can now relax knowing that the answer really was as simple as I had imagined.

I’m uploading this in the hope that I can help other teachers in my situation – hopefully this will pop up in some search results and save another teacher some time down the line.

Now just to make sure my students can change seats without confusing matters…

Cover image by Anton Yankovyi (Own work) [CC BY-SA 4.0 (, via Wikimedia Commons


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