This contest gives students that are not the best mathematicians a chance. They are given 2 chances, one per sheet to draw the most perfect freehand circle. They may not turn their paper, or hold their hand as if it were a compass. Just one simple loop. Circles must be the approximate size of a coffee cup.
Students then hand in the one circle they want to have entered.
I do this on a class-wide basis and believe it or not it's an easy contest to judge. I make them draw the size of a coffee cup because we always have one lying around and it may be helpful to judge. Students are given 2 minutes to write down as many things as they can think of that are circles. CD's, Buttons, coins, etc. Winner is the student with the most.