I worked as a TA with Eric Zimmerman in Game Design class back then when I was in NYU Game Center. As a tradition Zimmerman ased every TA to design an exercise for the students to introduce a principle/method. This requires a designer to create a minimal and extensible ruleset for students to start with to apply their own modifications on it.
The topic I wanted to cover is using mechanics to shape narrative arc. I wanted students to play the game first, and to think about macro mechanics to create a full experience over turns. They had to think about metrics of the tension in the arc over several turns, e.g. the number of dice a player owns. Students were allowed to add rewards/punishments for winning/losing a turn, or they could change the fundamental mechanics of it.