Oh @gailcalled! She’s thirteen. You expect her to be able to get her mind off the high status boy sitting next to her to concentrate solely on the class?
She just wants to talk to him. This is not about a relationship. This is about learning how to socialize and how to talk to people that intimidate you. These are important lessons to learn, and I would argue that she can learn both Shakespearean Drama and social skills at the same time. Indeed, it’s not just an issue of “can,” but that she has to. That’s what high school is mostly about. The education stuff is mere window dressing. (That last is a joke)
So how do you get over your inhibitions to talk to him? First, realize that he’s actually a boy. He might be stuck up on himself, or he might not. In any case, he should be polite, and if he isn’t, you don’t want to talk to him, anyway.
He may be popular, but in order to be popular, you have to be nice to people. So he should be a nice guy, unless everyone just likes him from afar.
I suggest you talk to him about something you are learning in class (see, socializing and school do go together). You might make a comment about something he said. “I thought your comment about Hamlet was really interesting. For me, it meant something different, blah blah blah.” Or “The teacher seemed especially nice (or mean) today, don’t you think?”
All you want is a conversation. You want it to be interesting (I hope). All this relationship stuff (other than friendship) is nonsense and fear on the part of other people here. Focus on getting to know him. If anything else happens later, that’s for then. Right now, remember that he is an ordinary person underneath his glamor, and he probably just wants real people to talk to (not girls who fawn all over him).
In any case, your only goal, for the moment, is to get up the gumption to talk to him. If you manage to do that, then you can think about another goal. Ok? You’re young. If it doesn’t work out, you’ll be mortified, but try to think that this is just one guy on one day and you have a gazillion days ahead of you. Or you could be like my 13 yr-old daughter and just not be all that worried about how quickly you start to get into the dating scene.
Just remember you don’t have to do anything. You can wait. Just do what you are comfortable with, ok?