Freeze screen when using AirPlay

Is there a way to freeze the Apple TV AirPlay screen when I'm presenting?

I'm a teacher and I want to freeze the screen while presenting/demonstrating so that I can do something else on my computer that the students can't see.

I don't want to extend my display. This becomes cumbersome constantly switching throughout the day. My old projector had a "freeze" button on the remote that did exactly what I needed it to do.