It looks like everyone has given you great advices.
Your teacher probably has a system of teaching beginners. Take one step at a time. The pieces you'll be playing now might sound silly or childish, but you'll learn certain technique from eachone. Don't forget to relax from shoulder to wrist. A lot of people don't realize this and end up with injuries. I highly recommend "Freeing the Caged Bird". You can get it either as DVD or VHS tape. It's a piano pedagogy based on Alexander Technique.
Good luck and most of all, have fun. I am a piano teacher as well. So if you have any question, just let me know.