How to connect iTunes on Windows to only a specific AppleTV when several are available?
I would suggest, assuming the main function you'll be using is AirPlay, that you give each classroom's Apple TV its own AirPlay password that only the instructor in that room knows. That way, he/she can connect to it with the credentials you've given and no one else can. If a student needs to connect to it to show something, the instructor could put in the password on the student's laptop. Obviously, if the password gets leaked you can change it at will.

I know this seems a little tedious, but I think it's the only way of doing it short of re-subnetting the building (I understand why you'd want to NOT do that!).

Also, I would suggest you create DHCP reservations for each Apple TV on your DHCP server so they always get the same IP address when connecting, just in case your network gets overloaded. Just a suggestion.

Hope this helps a little. Good luck.