How to see the un-mirrored displays on os x mavericks?

I just updated to OS X Mavericks from Mountain Lion on my Macbook Air 2011. I am a school teacher and found the advantage of turning off mirroring and swiping up my top right corner to display what was on my external display compared to my laptop screen, and being able to drag program back and forth from this screen. Now I cannot figure out how to see what program is on my projector in the classroom without having the projector turned on. Also, I can't open another window on my laptop screen of the same program without it automatically going to the projector. But the problem is that I can't figure out how to see the projector screen on my laptop and be able to do other work. I hope this is making sense. I really need some help asap! I upgraded over the weekend and tried to teach a lesson this morning and everything is messed up! Super stressful with a room full of 8th graders.