Improv math

It turns out that one of the hardest things for my students (both sophomores and seniors) is to figure out how to create equations that fit a story. That is, pulling mathematically tractable rules out of a "story problem", or developing solutions in context.

Mostly, I think that this is just something that needs to be practiced, and discussed, but it can be really hard to keep students focused on these bizarre, stupid little stories for long enough to catch on to how to really do it.

Enter The Hook.
Yesterday, I established the week's Big Idea as "Writing sentences without words". We then mostly spent the day working on developing definitions of 'linear', 'equations' and 'inequalities', before doing a bit of tabulating and graphing (last night's homework as a "graph these equations" sort of thing, with an emphasis on figuring out "shortcuts" to the tabulate-and-plot-points method). But, at the end of the day, I tied back to the Big Idea, and introduced a hook using improvisational comedy.

Today, we focused a lot more on that improv comedy hook: I reiterated that Chicago is a huge place for improv comedy, and pointed to Saturday Night Live, the Second City Theater, Improv Olympics and Comedy Sportz (and talked just a bit about the recruitment ladder in those groups). I also referenced Drew Carey's "Whose Line Is It Anyway" show, as an example of improv comedy. Also, Mad Libs (note to self: consider creating a Mad Libs opener?)

Then, I jumped in:
"I need a vehicle that you need a ticket to ride."
"And, the capacity of that vehicle"
"The cost of a ticket"
"A destination that vehicle goes to"
"A thing you'd do at that destination"
"The cost of doing that thing"

These all get written on the board.

Then call up two students, and privately brief them on the scenario: One is driving the vehicle in question, the other is a tourist visiting Chicago, who wants to go to the destination, and do the thing there. The tourist has to ask how much it costs to get there, and do the thing. The driver will tell the tourist those answers, and ask for a tip, but also point out that they can't get on: the vehicle is already full.

I tell the whole class: these two are about to do an improv show for us. The scenario ends when someone in it (or I) calls "scene." At that point, you have to re-tell the story, without using any words.

The scene plays out, until one actor calls "scene." Then I say, "Okay, what happened." As students start re-telling it, I cut them off, saying "Too many words. Try again." When someone gets down to an equation or inequality, I have them write it on the board.

It's gone great so far. I need more scenarios, which I'll append here as I come up with them.

Also, this is SO going to be part of my NBPTS certification next year!



Scenarios/Prompts:
Vehicle you need a ticket for / Capacity of vehicle / Cost of ticket / Destination / Activity at destination / Cost of activity; Driver and passenger (include driver's tip!).

Number 1-1000 / School subject / Something you need to do homework / Number 2 - 4; final number is number of players, who have only one of the thing you need, and are trying to do homework on page #(1-1000).

Brand of MP3 player / Capacity of MP3 player / Battery life of MP3 player / Number of hours of music stored / Number of songs / Cost of MP3 player; salesman and consumer.

Distance you can measure on a yardstick or meterstick / color / number from 3-9 / fraction; Two players cut a fraction of a colored wood, of given distance, to make a regular 3-9 sided polygon.

Distance between 3 and 4 feet / most exciting verb you can think of / even number 20 - 40 / number 10-30 / time in the evening / number to nearest hundred; Players are amusement park ride attendant and rider, you must be so tall to ride, there are so many riders at a time, park closes at given time, two hours from now, and the ride will carry even 20-40 x 10-30 each hour, with hundreds in line.


It occurs to me that part of the key here is to be flexible, but push for better and better "sentences". In one class, I had to repeatedly remind the students that "a sentence has to have a verb", referring to "equals" or "is greater than" or "is less than", while also emphasizing that "this story hasn't been written down yet-- keep going!"

The second example (homework) led to a nice discussion, in that the page number and subject are irrelevant to the mathematics...