This is a scientific method/creative problem solving unit that my GT students look forward to every year! After using the scientific method to test several different variables that can affect the flight of a basic "dart" design paper airplane, students design their own paper airplanes using their findings and have a competition to decide who designed the "ultimate" paper airplane!
Before testing, we build basic dart paper airplanes, fly them around outside, and have a discussion of what variables (design and external) can affect the flight of the airplane. Then we have a discussion of how to eliminate all of the non-design variables (fly indoors to avoid wind, use a launcher for consistent launches).
I use a paper airplane launcher that I designed for this unit, it's basically a big, long slingshot. You can also buy paper airplane launchers online. I use a launcher to control all the variables unrelated to the actual design of the paper airplanes. It's not absolutely necessary.