Playground permutation

Count how many ways kids (and mom) can sit on rides. You can do it at home with chairs and stuffed animals.

A few days ago, we were at a playground with three bouncing rides. I asked the kids how many different ways we could sit on the rides.

“Do you mean backwards, sideways, upside down (see picture)…?”
“I mean Bel on the elephant, Nia on the frog, and mommy on the squirrel is one way.”
We started counting and moving around until we got to four and then we lost track of what was already counted and what wasn’t.

I decided to help them a little and asked:
“How many ways with Bel on the elephant?”
Bel answered 2, then Nia said 2 (I am not sure if she was copying her older sister or she actually saw two possibilities).
“How many ways with Nia on the elephant?”
Bel said 2, then followed with “and two more with mommy on the elephant so the answer is 6”. Nia lost interest and was running playing with something else. I think she just does not want to try when Bel is so much faster.

With social distancing, Nia and Bel have been playing together all day every day. They have had a lot of fun but an unwanted consequence is that Nia is less confident in her math abilities. I will start asking questions just for her.

Extensions

• An immediate next step is to have four people on four rides/chairs for example.
• I would also ask how many ways can 3 people stand in line. (The answer is also 6 – it is the exact same problem as above – and I curious to see if the kids catch on to it)
• there could also be three people sitting around a round table (each person cares who is to their left and who is to their right but does not care where exactly they sit around the table). Then four people sitting at a round table.

I will ask Bel and Nia and report on it in a few days.

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