First off, at this time we cannot do this wirelessly. For now you will need to plug the HDMI connector (that is plugged into you Apple TV) into the HDMI port on the left side of your Chromebook. Note: if you do not have a connection to an Apple TV we can get you an adapter.
Once you have done that, turn on the projector. Note: you may need to hit the "source" button on the projector so it can "find" the Chromebook instead of the Apple TV.
Next, click on the toolbar on the bottom right of your Chromebook screen. You should see a message "Extending screen to "name of projector". In this case it is "LONTIUM":
Click on this message and you will get a new window, where in Options, you want to switch from "Extended Desktop" to "Mirrored", which will show whatever is on your desktop:
That's it! As always, please put in a ticket if you need further help :)