Here are three rhythm games where the strategy is to try to work your way to the top. Basically, someone is the leader and during a repeated rhythmic pattern they say their name followed by someone else's. Then that person says their name and someone else's at the appropriate time within the rhythmic pattern. If someone messes up they go to the end and everyone who was below them moves up one spot.
The first is Matthew, Mark, Luke, John. The top four people have the names "Matthew, Mark, Luke, John" and the rest have consecutive numbers. I remember playing this one as a teenager. Here's a youtube clip kindly posted recently of a multi-age group of people enjoying this game:
The next game is Big Booty. This clip is of some teenagers playing the game:
And, finally, this is Zoomie Zoomie. I think it came from or at least was popularized by the TV show, Zoom. Now, it's a drinking game (like Big Booty once was mainly). Here's a clip. I wouldn't show this in school, of course, but the game could definitely be adapted for school. One variation is to replace names with actions.