I have been experimenting for approximately a month with Apple TVs located in each of my four labs. For the time being teachers that want to use the Apple TV will need to visit their computer lab, but the plan is to eventually outfit our classrooms with them. What an Apple TV adds to the classroom is flow from one iPad to another seamlessly. We already know that students take pride in their work and to foster that feeling we help them find ways to share their work. With an Apple TV there is no more going up to the dongle and battling the chord to get it plugged in, nor those moments when you turn the iPad just so and the connection becomes loose, "Oh, sorry class, just a minute!" Students can not only share their work with one another, but also their thinking. One more way to encourage collaboration! If you have a class of iPads, next step is an Apple TV. Because they are not all that expensive, $99, your PTO may even be able to purchase one for your classroom.
A quick video to visualize students using an Apple TV.