Lessons in Units

CCSS UnitsDoes the same sound always sound the same? Students come up with equations in several variables to explore the Doppler Effect, which explains how sound from a moving object gets distorted.

How much Tylenol can you safely take? Students use exponential functions and logarithms to explore the risks of acetaminophen toxicity, and discuss what they think drug manufacturers should do to make sure people use their products safely.

In which Major League Baseball stadium is it hardest to hit a home run? Students find the roots and maxima of quadratic functions to model the trajectory of a potential home-run ball.

How has the iPod depreciated over time? Students compare linear and exponential decay, as well as explore how various products have depreciated and what might account for those differences.

Are coupons always a good deal? Students use unit rates and percents to explore the math and psychology behind retail discounts.

Should you buy a camera lens with vibration reduction? Students interpret graphs and use right triangle trigonometry to explore the relationship between focal length, viewing angle, and blurriness.

When is it worth buying a Powerball ticket? Students count combinations and apply basic rules of probability and expected value to determine when the Powerball jackpot is large enough to justify the cost of playing the game.

How much should people pay for cable? Students interpret scatterplots and calculate the costs and revenues for consumers and providers under both the bundled and à la carte pricing schemes to determine which would be better for U.S. companies and customers.

How accurate are police speed guns? Students use rates and the Pythagorean Theorem to examine the accuracy of LiDAR guns used to catch speeding drivers.

How should sports teams spend their money to win more games? Students look at data for four major pro sports leagues to find out whether it's possible to buy wins.

How does two people's love for one another change over time? Students investigate the effect of coefficients on recursive functions, and explore whether or not romance can be modeled with mathematics.

How much should theaters charge for movie tickets? Students apply operations on whole numbers to figure out how much money theaters could make by charging different ticket prices, and come up with strategies theaters might use to earn more from people willing to pay more.

How many people should you date before you settle down? Students use modeling with probability distributions to come up with a rule to try to maximize their relationship happiness.

How has the length of popular movies changed over time? Students use scatterplots to examine linear and nonlinear patterns in data and make predictions about the future.

What’s the best strategy for creating a March Madness bracket? Students use probability to discover that it’s basically impossible to correctly predict every game in the tournament. Nevertheless, that doesn’t stop people from trying.