20lb paper, scissors, glue or tape for each patrol.
Markers to decorate planes.

Set aside 5 minutes for all scouts to create their own paper airplane.
Have a "Fly-Off" in each patrol for 10 minutes to find the "best distance" and "best aim" airplanes.
Gather the troop and have the best distance airplane from each patrol compete for the best of the troop. Repeat for the best aim airplanes.

See http://www.xplanes4u.com/ for some high-tech templates to print beforehand if you'd like.