As Pi Day this year fell on a Saturday, I decided to celebrate it in every one of my five sections on each of the two block days encompassing them: Thursday (3/12/15) for two honors precalculus sections and Friday (3/13/15) for two AP Calculus AB sections and one honors precalculus section. The celebrations were a success for all of my periods except first period as I forgot to tell them in advance! We will make up for my forgetfulness this week with another celebratory day.
Each period brought in one or more pies of a wide variety. Some students baked their pie while others brought in store bought.
I believe I put on five pounds those two days! Fortunately, it is masked in the following photo where I sport my styling “Pi Day” shirt bought for me by a family friend, and some of the approximations for Pi I dug up.
Pizza Pi Happiness?
I graduated high school in 1982 never imagining I might end up a teacher like Mr. Hand, or Nick Nolte’s Mr. Jurel in Teachers (1984), although I fondly recall the “…but I’m a teacher…” line Nolte quipped.
Nothing as hilarious as Mr. Hand sharing Spicoli’s pizza with the class played out, although my AP Calculus students devoured the two pies in moments flat. Earlier in the day, I chipped in money for a few slices for my lunch, but did not count on the hungry student factor, which left me on the overpaid side of the ledger, and still hungry.
While I lamented my loss, I decided to share my learning moment with my honors precalculus students later in the day. The table below summarizes the brief problem solving activity students worked through as I wrote out on the white board the historical and multinational evolution of approximations for Pi from Babylon’s simple “3” to four times the limit of the infinite sum of the inverse tangent of the inverse of a Fibonnaci sequence. I could not help but be amazed at the accuracy with which the ancient Greeks, Chinese, Indians, and others approximated Pi. Specifically, the Chinese, I believe, approximated Pi as 355 / 113, which yields Pi accurately to seven digits, or 3.141592. Utterly amazing for those without electronic graphing calculators, computers, or iPhones! I use this last exclamatory line on my students frequently.
The table summarizes data I provided students along with the results of interim computations involved in deciding the overall fairness of my Pizza Pi Day experience.
Students rapidly worked through the problem; it was not difficult in the least and likely could be solved in a 4th grade level class if the circumference were provided, or the relationship between Pi, diameter, and circumference. However, the dearth of spontaneous problem solving activities like this in their prior courses left them ill-prepared for my course as they struggled first semester with straightforward word problems.
Nonetheless, all decided that my contribution exceeded my consumption; hence, I overpaid. However, most arrived at vastly differing expressions for whether or not I overpaid, or, in the terms of my question, received a fair deal. Expressions varied from decimal values without units to percentage values to square units. No one tied the values to any meaningful measure of the pizza slice or my payment in dollars. After specifying a common measurement unit, inches of pizza arc length, each team stated the same amount of pizza I should have received for my contribution, which turned out to be another 6.8 inch arc length of pizza. I wonder how a server would respond to that request?
After five or so minutes, we moved off of this activity so student groups could present their homework exercises to the class. Afterwards, I proved the Pythagorean relationship for an ellipse relating the difference in the square of the semi-major axis and square of the focal length to the square of the semi-minor axis. The proof typified one of my unit test questions, which I elected to reveal to students in advance of the test, in hopes they could remember it on test day in a few weeks. It is the first time I provided students with an exact question on an upcoming test. It may be the last, however, time will tell.
Once the mathematics lesson and discussions finished, we spent the next forty-five minutes eating pie. Yum!