This game from Simple Politics is great for Open Days, End-of-term, Taster lessons and everything in between.
If you've played 'Cards Against Humanity', it works in a similar way (but is much more PG!). Players take it in turn to select a 'problem' card at random, and then the other students submit one of the 'policy' cards in their hands, with the 'best' policy winning.
Packs are available here. You need one pack per group and you can just about get away with groups of 3-8 but I would say that groups of 4-6 are ideal.
I'm sure I'll find other uses for the cards too - I'll post an update if/when I do!