Hey prost - I'm not just a CrewChief here in the virtual world but I also play one in real life so I LOVE the racing theme. My last school had a NASCAR game at the carnival. A not quite life sized profile of a NASCAR was made out of plywood. Two wooden 'wheels' were attached with real bolts/lug nuts. Two players would run up to the car - one to the front wheel and one to the back wheel- grab the impact wrenches, remove the old tire and replace it with a new one. The first one to replace their wheel won a prize token. It was one of the most popular games at the carnival.
Just a few other ideas:
*Tricycle or pedal car Drag or Oval Track races
*Prize Redemption Booths called "The Winner's Circle" (or the concession area if there are no prize booths)
*I don't know if you can rent them or not but there are drag racing Christmas Trees that allow folks to test their reaction time. That would be a fun game. It goes quick though so I'd allow each player two or three shots per turn.
Poll your parents. You might be surprised to find out that you have some real live racers in your school who would have some fun ideas!
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