What's this anime called?

It begins with a girl who's very popular at school, and at home she's like super funny/crazy and is always saying how cool people think she is. Then this guy comes in, and he's as smart as her. They kind of compete against each other and I remember a scene when he goes to her house and she thinks it's someone else so she goes outside in her PJ's. I remember there was an episode for each explaining their story or something. Also something about him making her do his homework?