As more schools implement wireless networks, BYOD programs, and Apple TVs, they are quickly finding that on properly configured and subnetted networks they are unable to locate their wired Apple TVs with their wireless iPads, iPhones, Andriod devices, etc and therefore are unable to use Apple's "AirPlay" to stream music or videos to their Apple TVs, and are also unable to mirror their iPad's screen to the Apple TVs.
This is because the protocol by which Apple devices announce themselves and locate other Apple devices on a network does not work when these devices are on different subnets.
To find other Apple devices on a network, Apple devices use a protocol called "multicast DNS" (mDNS), and Apple has named their implementation of the mDNS protocol "Bonjour."
AppleTVs and other Apple devices on home networks don't have any problem locating each other. All the devices appear to magically "just work"(TM) together because all the devices are on the same subnet (broadcast domain) and Bonjour works perfectly fine in this type of small, non-routed network.
However, Bonjour is a multicast (broadcast) protocol, and as such does not traverse across routers to other subnets. When Apple devices are on a larger, properly segmented (subnetted) network, Apple devices on one subnet will not be able to locate Apple devices on another subnet.