Out of 615 million airline passengers last year, half a million were bumped from flights. 9 out of 10 of those were voluntary. What percentage of all booked passengers were involuntarily bumped from a flight?

Yes, I had fun at the expense of United Airlines’ most recent viral embarrassment, but I had two serious questions that I needed answered:

- Should I change my air travel habits?
- How many of my Algebra 2 students could correctly answer this question?

I had my class answer both questions for me. I started class by handing them the prompt and this now famous video clip:

I then shared what I learned about the law in regards to this incident. United Airlines and law enforcement officials were legally in the right to remove the passenger from the plane. When overbooked, an airline has the right to randomly bump passengers, but they must first offer an adequate incentive for volunteers, which United did. These regulations are in the contract rules that we all agree to, but never read, when buying an airline ticket. The law also states that any passenger must comply with directions given by airline personnel or law enforcement officers. Since the unfortunate gentleman on the plane resisted the directions of the authorities, the airline and the police had the legal right to forcibly remove him.

It was the third part of the law, however, that was the most disconcerting for me. If an airline involuntarily bumps you, they must guarantee your arrival at your intended destination within 24 hours. But that is not good enough for me. I often travel to places where I am expected to be working with teachers early the next morning. A 24-hour delay would be far too late. So my new burning question is: Should I leave greater leeway in time when I am traveling? That is what I needed to answer. The students helped me think through it.

Nine out of 10 voluntarily bumped means only 10% of the 500,000 bumped passengers, or 50,000 passengers were removed involuntarily. That 50,000 out of 615 million is a whopping 0.008% of all booked passengers last year. So what does that mean in terms of my flight habits? How many times would I have to fly in order to expect being bumped at least once? 0.008% of what number equals one (1 = 0.00008x)? It turns out that I would need to fly 12,500 times. In over 40 years of an active adult travel life, I would have to board a plane nearly every day of my life to expect this to happen. Of course, probably and possibility are utterly different, so I could be bumped on my next flight, but I am not ready to start adding an extra day to every travel trip for such a small chance.

So how did my students do with this calculation? My prediction of one student was an underestimation. Five actually calculated correctly, with 3 others getting close, showing appropriate work. Why was such a simple math topic (calculating percentage) such a challenge for a group of 15 & 16 year olds? In talking with the students, I came to realize that this was the classic case of “making sense of problems.” There were multiple layers in unpacking the prompt, as well as the added layer of interpreting such a small fraction of a single percentage point and the need to make a decision based on that numerical interpretation.

It is noteworthy to reveal that I gave this problem to four adults. All four answered correctly (0.008%), and all four struggled to make sense of what was being asked.

So how do we get students more proficient at making sense of problems that require basic math? Easy. We pose those problems more often. Which I intend to do.