GAH, I BOTHERED TO TAKE 10 MINUTES WRITING OUT ADVICE AND REASONING AND MY INTERNET BREAKS DOWN!!! *feels need to punch somebody*
1. Do any of your friends know her? Maybe they told her or she asked around. The fact that she took the time to do it means she likes you. Alot.
2. In your classes, doesn't the teacher always announce the topic? She could just have been referring to that and trying to start a conversation with you.
3. Do you have a habit of bringing similar food every day or have a pattern that you follow in what you bring? Perhaps she's noticed.
4. Do your teachers allow the more trustworthy students to grade each others' papers? Maybe she graded yours or overheard your teacher telling another teacher about it.
5. Was there anything significant sticking out, say two movie tickets in your pocket? Have you accidentally mentioned it before? Did you tell any of your friends who might spill the surprise?
*chuckles* Your girl seems like quite the detective...
If you guys are only hanging out in the morning/afternoon with no lunch included, take her to an ice cream parlor or something like that. Just sit down and chat. If you want, a movie can also fit (this will do even if you guys are going to eat together). The good thing about a movie is that you don't need to talk much, but you can still connect. Movie theaters should have tickets available (unless it's some movie that just came out and got a hundred 5 star reviews or something) right before the show. Let her choose if you can. If you guys are going to a restaurant, take her to something that isn't too fancy (too early in the relationship), but don't take her to a fast food restaurant. Not the place for some good time together. She doesn't sound like a person who really wants fancy, so simple should do it. No flowers. If you can bake something and take it to her, that would be a nice gesture, but no flowers until later on. Dress casually but neat. Act natural, girls usually like it better when they can hang out with the guy they know every day, not some stiff dude who's trying to act all gentleman. Don't go too overboard on the cheesy parts either. And when ordering food...order what you usually eat. Again, act natural.
Hope it helps. And good luck.