Historically, this lesson is easily tied into the concept of Japanese origami, developed about 800 years ago, and done by the Japanese royalty. Only they could afford to "waste" luxurious handmade paper this way. A detailed history of both paper and origami can be found at the Origami Resource Center's website: www.origami-resource-center.com, click on their history link.
Alternately you could focus on the history of flight. Paper airplanes may date as far back as 2000 years with the invention of paper and Chinese kites, but we know for sure the Wright brothers used paper models and airplanes to test out their theories of aerodynamics before their first manned flight in 1903. (http://goo.gl/mtrSWK)
The essence of flight is controlling the four forces on an object: Drag, lift, thrust, and gravity.
Once we understand these basic concepts we can start to make planes. I strongly urge you to make sure students always put their first and last names on every paper they use. I walk around and check before I teach them a model. Though I tell them it's so no one steals their awesome design, my real reason is that at the end of the day there are often planes in the school yard and students protesting it's not theirs. I remind them that the vice principal can look at it, and give them a detention for littering, and it seems to keep the liter to a minimum.
If you are short on time, have one or two plane models ready to demonstrate. There are many diagram sheets on Google you can search out, as well as video tutorials. A student favorite is a stunt airplane with directions here: https://goo.gl/PA3XZ6 More diagrams can be found here as well: http://paperairplaneshq.com This site seems to have additional helpful information too: http://paperplanedepot.com/pilots/tips/
Always end lessons with a short closure discussing what direction was best for flight (into, away from, or sideways to the wind). It's even better if they can take a minute to write a short paragraph about their findings, even if they write directly on the plane.
If you have more time, students can visit the library or computer lab and investigate paper airplane designs. Have a ream of copy paper available for them to fold with as they research. Some tape and a scissor may be helpful to have as well. Have them look up world record setters, gliders, and unusual designs. Give them a deadline as well, and require a little bit of writing: What do they expect of their design, how would they assess its lift, why did they choose the designs they picked?
They should save their work, and test it outside or in a gym, recording their results. Longest flight, most time aloft, most stunts (like twists and turns.) Writing and recording their process is an important skill.
You could end with a contest and a winner for different categories like distance, time aloft, most unusual plane that actually flies, etc. A simple gold foil plane might make an awesome trophy, or a paper airplane book. Those are often in Barns & Noble's discount bin.
Take photos and share your STEAM based lesson with administration. You should always be promoting what you do especially if you have a lesson like this one that ties in so nicely to history, writing, science, engineering, and physics!