Split screen iPad and MacBook app while using airplay

Hello! I am a math teacher, and I would like to make a video for my students. I want to use Airplay to display my notes on the screen that I am taking on my iPad, but I want to split screen it with a calculator application that I have downloaded to my MacBook. It seems as though when I airplay my iPad to my MacBook, it takes up the entire screen and shows me no option to minimize it or make it smaller (or split screen it with another running app on my computer). Is there a way I can have my iPad airplay to one side of the computer, and I can open up an app on the other side? Thank you!!