In high school, we did play one improv game I always really enjoyed. We would do it while we were reading a novel (The Hunger Games, for instance. I'll use that since it's popular). There would be a certain number of characters from the book chosen (this is determined by the teacher. So, let's pretend I'm the teacher and I chose three characters: Catniss, Cato, and Peeta).
The audience (the rest of the class) sets the scene (For example, they'll say "Let's pretend Catniss, Peeta, and Cato went fishing...") Then, students will volunteer to play one of the characters. After the three lucky students volunteered (or were chosen), they came to the front. The audience then made up three rules.
The rules were usually silly like "the person playing Catniss can only talk in questions" or "none of the actors can say words ending in 's.'" After the three rules were established, the scene began. The scenario had to be played out, with each character behaving as they would in the book, and all three of the rules had to be obeyed.
When an actor broke a rule, the class caught them by yelling "Off with his (or her) head!" and booed them until another actor jumped in and took over his or her place as the character in that scene.
To add some twists, the teacher made up new rules. Sometimes, she would pause and tell everyone to perform an action. It would quickly turn into a game of Simon Says or memory.
It was a good ten minutes of fun :) and educational, believe it or not. Just thought I'd share!