In this MySpace game you maintain your own school. You and your friends take the roles of teachers, competing against other schools for the highest GPA. GPA for a school might be calculated as (your study points)/(best player's study points)*5. The teachers collect "study points" for a school by giving the students lectures in a simple quiz minigame (prototype screenshot below).
Reaching certain study point thresholds would cause events to occur, which might lead to positive or negative consequences, or cause the player to receive an item. Players would often receive the same items, and would be then prompted for example "you don't need two blackboards! how about giving this to a friend?". This would be the second viral channel after teacher recruiting.
Third one could be a minigame where you have to gather friends to upgrade a school. At first the school would be just outside on the grass. Secondly it could have walls, and finally a nice floor too. How this upgrading part would work, I'm not sure. Perhaps it could even just be an event when a certain study point limit is reached, although then it wouldn't help the virality (but would still reward players to continue playing). (Lil) Green Patch is basically just about giving items, and has thrived on just that. I tend to think in too complex terms. Maybe minigames aren't even necessary, or might even complicate things too much? Perhaps it suffices to incentivize the players by donating all or part of revenues towards building actual schools in 3rd world countries, which the best players could name.