especially this one h13..middle school bait at its finest.
She's a bit nervous around you, and from where I sit it looks like she wants to make a good impression of you to her friends. I think what you're seeing as stand-offish behaviour is just her way of showing that she's a bit shy. Nothing wrong with that. Let her come out of her shell on her own. You can help by being supportive and aware of her shyness, but confronting her and getting all bent out of shape won't do anything positive..
look at how high i can count!.