# Lunchtime Probabilities

You don’t need a degree in mathematics to assign Upper School lunch tables—but it helps. Upper School Mathematics Teacher Fred Lange gives us a lesson on the complexities involved with preserving a time-honored USM tradition.

As a newbie USM teacher in 1985, jazzed to take on new responsibilities, I volunteered to take over the Upper School lunch rotation duties—to assign students and faculty to specific lunch tables. Having assigned seating at lunch is one of the things I love about USM, and something alumni often tell us they loved, too. It builds community, adds structure to our days, and enhances student-teacher relationships. It is essential to school culture in all three divisions. And, it would be pretty easy to set up the rotation—or so I thought.

Back in 1985, my main goal for the lunch rotation was to have new groups at each table every two weeks—shuffling grade levels and genders. To do this I devised an elegant mathematical solution using a computer spreadsheet, with all the tables arranged horizontally on the top eights rows, representing the eight chairs at each table. Faculty would stay at the same tables, and for each rotation I would shift the second chair two tables to the right, the third chair three tables to the right, the fourth chair five tables to the right, the fifth chair seven tables to the right, the sixth chair 11 tables to the right, the seventh chair 13 tables to the right, and the eighth chair 17 tables to the right.

With a total of 19 tables in the lunch period, this system of rotation guaranteed that there was always a completely different set of people to talk to in each rotation, because the amount of rotation and the number of tables were relatively prime. It also ensured a balance of gender and grade levels at each table.

Over the years, with a few tweaks here and there, the system worked reasonably well. But in 2014, the Upper School launched a new schedule that, while distributing classes more evenly, wreaked havoc on the lunch rotations. According to the new schedule, each class period (1–8) met over the lunch period once per eight-day cycle (A–H). In other words, each letter day has a different configuration of students and faculty in the lunch period for that day. In addition, we added an Upper School lunch period, going from two to three. In short, our system of having a fixed lunch table for two weeks would no longer work.

The new schedule greatly complicated our lunch rotation and almost led the Upper School to throw up its hands in frustration and drop the tradition altogether (which our consultant recommended), but I, and others, were not willing to give up so easily.

We decided that we would have assigned seating in the early lunch and open seating in mid lunch, with faculty as heads at every table in early lunch (because there weren’t enough faculty to go around for all three lunch periods). The late lunch became a hybrid of open and assigned seating, with each day of the cycle having a different theme, including sitting by grade, gender, house, alphabetically by first or last name, etc. In late 2018, we decided to organize both early and late lunches by house to support more camaraderie within the four houses (click here for more information about USM’s house system).

With two of the three lunch periods having assigned seating, there is a fair amount of work involved with creating the rotations. I start by downloading each student’s schedule data to a raw spreadsheet, then gather each faculty member’s lunch preference (early, mid, or late), and then check each student’s schedule and fill in the missing periods when they have free periods. The table assignments in early lunch are carefully randomized to avoid excessive repetition of tablemates. Each day, I print out a master assignment sheet and post it outside the Upper School offices so students can check where they’re sitting. Organizing the lunch rotations is a lot of work, but it’s a labor of love. The opening of the new Jack Olson ’67 Commons and subsequent increase in the number of tables enabled us to invite more administrators and staff to head lunch tables along with faculty, increasing the sense of community in the school. For me, while it’s very important to preserve our traditions, I like that our new lunch system combines open and assigned seating. While the assigned seats are important for building community and contributing to a sense of security for new students, the open seating at mid lunch gives students a chance to sit with friends, and encourages them to negotiate the social challenge of finding’s one place at lunch, which is also a valuable learning experience.