Lessons in Units

CCSS UnitsHow do you increase the horsepower of a car engine? Students calculate the volumes of different car cylinders, and explore ways to make engine even more powerful by changing the dimensions of an engine's internal geometry.

How much should states spend on schools and police? Students analyze histograms and use mean and median to explore state spending habits. Then, they discuss how much they think states should be spending.

When should NFL teams go for it on fourth down? Students use quadratic functions to develop a model of expected points. They then apply this model to determine when teams should punt the ball, and more importantly, when they shouldn’t.

What's the best way to position a car's mirrors? Students use reflections and congruent angles to determine the best orientation for rear- and side-view mirrors, and learn how to correct those dangerous blind spots.

How has the urban population changed over time, and will we all eventually live in cities? Students use recursive rules along with linear and exponential models to explore how America's urban areas have been growing over the last 200 years.

Why do tires appear to spin backwards in some car commercials? Students apply unit rates and the formula for the circumference of a circle to determine what makes a spinning wheel sometimes look like it’s moving in the opposite direction of the car sitting on top of it.

Does 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.