Connect your MacBook Air to BYOD-Staff.
Make yourself aware of the specific input port your Apple TV's HDMI cable is physically plugged into on your TV and set your TV input to it.
On the Menu Bar on your Mac, click the AirPlay icon.
Select your room's Apple TV from the list.
A code will generate on your TV screen.
Type this into the window that appears on your Mac.
You are now mirroring your MacBook's display on your classroom TV.