Lessons in Units

CCSS UnitsHow many tickets should airlines sell? Students use probability and expected value to investigate the overbooking phenomenon and why airlines make the decisions they do.

Should stores open on Thanksgiving Day? Students use game theory, payoff matrices, and the famous Prisoner's Dilemma to explore why stores keep opening earlier and earlier. And earlier.

How much should vowels cost on *Wheel of Fortune*? Students use ratios and percents to explore what would happen if *Wheel of Fortune* charged prices for vowels based on how often they come up.

How long does it take to burn off food from McDonald's? Students use unit rates and proportional reasoning to determine how long they'd have to exercise to burn off different McDonald's menu items.

How much should you bid in an auction? Students use probability, expected value, and polynomial functions to develop a profit-maximizing bidding strategy.

Why do certain pairs of notes sound better than others? Students use ratios and fraction division to explore what makes two notes sound good or bad when played together.

How far away from the TV should you sit? Students use right triangle trigonometry and a rational function to explore the percent of your visual field that is occupied by the area of a television.

How much does it cost to drive at different speeds? Students use unit rates and proportions to explore how a car's fuel economy changes as it drives faster and faster.

How much do you really pay when you use a credit card? Students develop an exponential growth model to determine how much an item really ends up costing when purchased on credit.

What does it mean for a playlist to be "random?" Students use probability to explore the idea of randomness, as well as the patterns that can emerge from random processes like shuffles.

In how many ways can you personalize a license plate? Students use the Fundamental Counting Principle to determine the total number of possible messages.

When you buy a concert ticket, where does your money go? Students use percents and proportional reasoning to describe how revenue from tickets is distributed among the various players in the concert game.

Do taller sprinters have an unfair advantage? Students use proportions to find out what would happen if Olympic races were organized by height.

How do cell phone towers identify your location? Students describe geometrically the location information provided by a cell phone tower, explain why loci from at least three towers are required to pinpoint a customer's location, and consider the tradeoff between coverage and "locatability" when a phone company chooses a new tower location.

In basketball, should you ever foul at the buzzer? Students use probabilities to determine when the defense should foul...and when they should *not*.