Last year I was given an Apple TV to use in my classroom. I fell in love with it when kids could sit at their desks and share their projects on their iPads with the class wirelessly! We shared all of our projects and taught each other how to use apps with the Apple TV and mirroring on the iPad. It was wonderful, but not until this year did I really start to harness the power of Apple TV in the classroom. I wanted to use it to allow me to not be tethered to the projector cart. Our projectors are not mounted in the ceiling and we each have a cart with a projector and a document camera on it. I am thankful for it, but miss the ability to move around and use proximity control when using the projector or doc camera. This year I was determined to be able to move.
To help me with this I found the apps Stage https://itunes.apple.com/us/app/stage-interactive-whiteboard/id584574701?mt=8 and iAnnotate https://itunes.apple.com/us/app/iannotate-pdf/id363998953?mt=8.
When I use either of the apps I use a stylus to help me write neatly. My stylus of choice is the Jot Pro Fine Point Stylus. It may be a bit on the expensive side, but once you use it you will realize that it is worth the price.
One of the best kept secrets of Apple TV is all of the free content that comes on it. There are channels, like the Smithsonian Channel, PBS, and the Weather Channel that have plenty of quality free content in the form of videos and video clips that can be used in the classroom to support learning. If you don't check these out and use them in the classroom you are missing a lot of great stuff!