Q: my apple tv won't mirror my ipad,the symbols are checked on both

You need to enable mirroring. This is done by bringing up control center, accessing airplay and toggling ON mirroring.

iOS: Use AirPlay Mirroring - Apple Support

If the icon is not appearing at all that's a network issue

Try connecting Apple TV via Ethernet

Full strength on the device won't be an accurate indication, you need a network report by going to istumbler,netstumbler or similar. Look there for signal strength, noise and nearby networks.

it does not work over the Internet so the ipads needs to be operating on wifi

and the router needs to allow the required ports to be used

TCP and UDP ports used by Apple software products - Apple Support

I am having this same issue with my iPad. However my iPhone 5s has NO problem mirroring. My iphone and iPad are both on the same account and share between them and are on the same wifi so none of this makes sense!