Lessons in Units

CCSS UnitsWhat's the ideal size for a soda can? Students use the formulas for surface area and volume of a cylinder to design different cans, calculate their cost of production, and find the can that uses the least material to contain a standard 12 ounces of liquid.

What's an acceptable dating range? Students use linear equations and linear inequalities to examine the May-December romance, and ask whether the *Half Plus Seven* rule of thumb is a good one.

What are some ways to encrypt secret messages? Students explore function concepts using ciphers to encrypt messages both graphically and algebraically; they try to decrypt some messages too. In the end, they’ll learn what makes for a useful cipher, and what makes a cipher impossible to decode.

How do you determine the best scorer in basketball? Students compare LeBron James and Tyson Chandler in various ways, from total points, to points per game/minute, to a new measure called *net points* in order to decide.

How big is the White House? Students build scale models to determine the surface area and volume of America's most famous home.

How 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 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.