This feels kind of embarrassing, but my max score is only 7.
Anything with more sides than a hexagon left me guessing and I usually guessed wrong. I think there are plenty of children who would be better at this than I am. :D
The UI looks very nice. The graphics in general are simple and clean. One thing I'd note is that the player's shape quickly obscures the bottom portion of the incoming shape, making it much tougher to match them up. (Or I might be making excuses for myself.)
It would also be nice, I think, if the final size of the incoming shape and the player's shape were exactly the same, I think that would make for a more satisfying visual if they were perfectly aligned, and give a greater sense of 'fitting through' the challenge.
The music sounds good, but the repetitiveness of it did start to grate on me after a while.