“You Are Cleared to Land”

On a not-so-routine flight to an NCTM meeting, my colleague and seat-mate, Jim Williamson, and I had ample time to chat and ponder our surroundings. As happens many times in the West in the winter, heavy snow caused a long delay. While we waited on the runway for the airplane to be de-iced, we noticed that runway numbers were posted in pairs, as in Runway 2-20. We also noticed that some numbers had an L or an R attached to them, as in Runway 2L This observation was the only setting we needed to start a real-world investigation on how airport runways are named. Because it is hard to generalize from the small sample of numbers that we could see from the airplane, we realized that we needed more data. We talked to pilot, who furnished us with several old maps of airport runways. He did give us a hint that the runway numbers had something to do with the compass headings of the runway from magnetic north. We were now in business: we had an interesting problem, we had data, and we had Time to talk about it and think about it. This atmosphere is the type for which we strive in a middle school mathematics class. The following activity is based on our investigation and can be used for middle school mathematics.