How should I approach her? 10pts for helpful answers.?

[J]

So we're both sophomores in high school. I have 2 classes with her. She sits across the room from me in one class, and in the other class she sits behind me.

I really like this girl and I can't stop thinking about her. I can't decide how I'm going to approach her. I can't talk to her before or after school because she's always talking with her friends and If I just went up and said hi, I would feel like a creep. I don't have any way to contact her friends. I'm not sure if she has a boyfriend or not. We attend a college prep. school and the teachers give a lot of work (we're always busy) I can't drive yet because I have to own my permit for a few months before I can get my license so I can't take her anywhere.

This might sound like a bad idea, but I think I might just message her on facebook and say "Hey, do you know what the homework is for ___?" And carry on a conversation from there.

Any suggestions? I'm not sure what to do. (feel free to criticize my idea above lol)

[Dragon]

it would be helpful to know her personality, but i like your idea with the homework thing, but maybe introduce yourself and get a conversation going, once you get to know her a little better, you can ask if she would go out with you or ask if she has a boyfriend.