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Bumpy Flight (Updated!)

Should airlines oversell their flights?

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Bumpy Flight (Updated!)

Should airlines oversell their flights?

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Check it out! This lesson was just updated in September 2024, and we hope you love the new and improved version. If you've already prepped an earlier version, fear not, you can still find those here through Thursday December 5, 2024.

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Bumpy Flight - Student Handout.pdf
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Bumpy Flight - Teacher Guide.pdf
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2023-2024 Versions

In the fall of 2024, Citizen Math released updated versions of every lesson in our library, plus a few new ones! We know you may have already prepped an earlier version or planned a repeat of last year, so we're continuing to make these earlier versions available through Thursday December 5, 2024.

You can find the new lessons through the regular search, and we hope you love them as much as we do. You can read more about these updates in Our Community.

Should airlines overbook their flights? Airlines routinely sell more tickets than there are seats on the plane. This isn’t a problem if enough people miss the flight, but it can lead to major frustration if everyone shows up at the gate.

In this lesson, students use compound probability and expected value to determine the optimal number of tickets an airline should sell and discuss whether airlines should be allowed to overbook their flights.

REAL WORLD TAKEAWAYS

  • On average, less than 100% of passengers show up for flights. Airlines often overbook flights so that they’re not missing out on revenue on empty seats.
  • If more passengers show up for the flight than there are seats on the plane, then some passengers may be involuntarily “bumped.” If this happens, the airline is required by law to pay them (in addition to rebooking them on another flight).
  • Even with the penalties, airlines typically expect to make more money by overbooking the flights than by not.

MATH OBJECTIVES

  • Calculate expected value and use it in decision making
  • Calculate combinations and compound probabilities in a real-world context
This complex task is best as a culminating unit activity after students have developed formal knowledge and conceptual understanding.
Algebra 2
Probability (Adv.)
Algebra 2
Probability (Adv.)
Content Standards A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. S.CP.9 (+) Use permutations and combinations to compute probabilities of compound events and solve problems. S.MD.5 (+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. (a) Find the expected payoff for a game of chance. For example, find the expected winnings from a state lottery ticket or a game at a fast- food restaurant. (b) Evaluate and compare strategies on the basis of expected values. For example, compare a high-deductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident. S.MD.7 (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).
Mathematical Practices MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.

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