We’re getting ready for my daughter’s Minion themed birthday
party. She’s turning 8. Where does the time go? Since we had a snow day today, we were all
home during the day and making preparations.
My wife made the poster below.

Kayla couldn’t figure out which minion was which. She kept saying their names in different
orders.

“Kevin, Stuart, Bob”

“Bob, Kevin, Stuart”

Not expecting much conversation I asked how many ways the
three could be arranged. Without shying
away from the challenge, she sat and thought for a minute. Deciding she needed to write down her
thinking, she got some paper and made the lists below before confidently
announcing her answer of 6.

I praised her for both showing her thinking and the
organization of her method. She had been
stating aloud, “well there are 2 ways that they could stand with Kevin in
front, then there are two ways that they could stand with Bob in front, and
then there are 2 ways that they can stand with Kevin in front”.

Curious how far I could I push, I asked her about including
another minion, Dave. She struggled more
with this one, initially listing 17 possibilities. When I told her that she missed some
possibilities, instead of going back to her list, she surprised me by trying to
go into some arithmetic. She started
with a “4 times 3 times 4….48”. I asked
her how she got that and she started explaining that there are 4 minions and
then you multiply by 3 because there are three left, but she couldn’t explain
where the other 4 was from.

She revised her thinking to just the 4 times 3, but then
realized that she had already created more than 12 possibilities. I asked her what she knew about arranging 3
minions. She said she knew there were 6
ways to do it. I asked what happens when
we add another minion. She connected the
dots and was able to realize that there would be 4 times 6 possibilities for
arranging 4 minions, where the 4 was “the number of minions that could be first
and 6 was the number of ways that the other 3 could be lined up”.

To build on the momentum, I asked about adding a fifth
minion, Jerry. Here she struggled again,
so my wife asked her what patterns she noticed.
We started listing the ways to line up 2 minions, then 3, then 4. Kayla recognized the recursive nature of the
pattern that a 5

^{th}minion would mean 5 times as many possibilities as 4 minions, so she set to work on multiplying 5 by 24, which was immediately followed by 6 times 120, at which point her desire to do multiplication stopped.
My wife then gave Kayla a brief explanation about what a
factorial is, how to calculate it and how to represent it.

Besides being ridiculously excited that I could bring Kayla
into this conversation, I reflected that this is exactly the type of You do, We
do, I do model of teaching that I espoused in my Ignite talk.

You Do – Kayla had a prompt about lining up minions and
wrestled with the task with no input from me.

We Do – In the extension problems of 4 and 5 minions, my
wife and I asked Kayla questions to understand her thinking and refine her
thought process. By asking about the
origins of the values in her arithmetic, she was able to independently identify
flaws in her reasoning. Some direct
guidance was also provided. I told her
17 was not correct, but didn’t offer any additional strategies.

I Do – Once a pattern was identified, Kayla was in a place
where she could attach some new vocabulary (factorial) to an experience.