Filing Cabinets and Precision

So this morning, as students are coming in to school, they noticed this in the back of my room (it’s normally tucked away in the corner):

One of my students in a different homeroom walks by, peeks in, and yells, “Hey Mr. Kane! It’s actually 935 not 936, you didn’t put one on the handle!” Best start to my day in weeks.

Ok, to step back, I did Andrew Stadel’s Filing Cabinet Three-Act on Friday. Short version is — I start putting post-its up on the filing cabinet in the back of the room. Students say, “Mr. Kane, what the heck are you doing?” The obvious question follows — how many post-its would it take to cover the whole filing cabinet? Conveniently enough, Andrew and I have the same filing cabinet. This is part of my current weekly Friday routine of giving my students a set of rich, non-routine problems (surface area isn’t one of our standards this year).

After we figured out how many post-its it would be, I asked the obvious follow-up question — how long would it take me to actually do it? There was a wide range of estimates, then I asked students how they might get a more precise idea. One class had me put post-its up for one minute, another timed how long it would take me to put two rows up. Estimates ranged from 45 minutes to an hour. We discussed some reasons why the actual answer might be higher or lower than what we calculated, and got some thoughtful reasoning. Then, they kids went home and I started post-it-ing. Took me one hour and 16 minutes to cover the whole thing, four sides and the top.

In class this morning, I shared the result with them, and we talked some more about the sources of error and in particular why it took so much longer. Then I asked another question I thought was pretty interesting — how long would it take to get all of those post-its into the recycling bin? This time I allowed that I might get some help — how long would it take one person? Two people? Three? Five? And got at a pretty interesting and uncommon function. We didn’t go too deep here, but it may have inspired me with an Algebra-level extension for Nathan Kraft’s beautiful Starry Night project. Will have to think more about that one.

I let eight students take all the post-its off at lunch. It took them two minute and fifty-one seconds — longer than most classes had predicted, I think mostly because they just knocked all of the post-its off then picked them up off of the floor.

Nothing like some mathematical fun.

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