Some fun, easy, piano songs.

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I have recently learned how to play Let it Be, Drops of Jupiter, and How to Save a Life. And sing while I am playing. It is fun to learn these songs, but when I try to find other songs to sing and play, they are way too complicated. I've only had about 6 months of piano lessons, and even though I am one of the fastest learners my instructor has had I still need time for the more complicated pieces. So do any of you musicians out there remember playing, or are playing some easy fun songs that I could also sing to (I have a pretty large range)? If I get good enough at a few, maybe I can start sending them out to people, or will be able to play and sing in front of some friends for a while.