Lessons in Units

CCSS UnitsIs *Wheel of Fortune* rigged? Students use percents and probabilities to compare theoretical versus experimental probabilities, and explore whether the show is legit, or whether there might be something shady going on!

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.

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.

How do vehicles turn so smoothly? Students calculate the circumferences of circles to determine how far vehicles travel during a turn and explore the engineering that allows cars to turn so smoothly.

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.

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.

What’s the ideal size of a soda can? Students create rational functions to explore the relationship between volume, surface area, and cost to determine the optimal size of a soda can.

How should police departments address excessive use of force? Students compare the distributions of excessive force of two police departments and explore how the shape of the distribution affects the effectiveness of different solution attempts.

Should you ever buy an extended warranty? Students use percents and expected value to determine whether product warranties are a good deal.

Which size pizza should you order? Students apply the area of a circle formula to write linear and quadratic formulas that measure how much of a pizza is actually *pizza*, and how much is crust.

Why do manmade objects look the way they do? Students analyze the symmetry of objects, use geometric reflections to construct symmetrical images of their own, and debate the nature of beauty and perfection.

How were free states and slave states represented in Congress? In this lesson, students use census data and fraction multiplication to explore the effects of the Three-Fifths Compromise on the balance of power between free and slave states in early America.

Who should buy health insurance? Students use percents and expected value to explore the mathematics of health insurance from a variety of perspectives.

How do noise-canceling headphones work? In this lesson, students use transformations of trigonometric functions to explore how sound waves can interfere with one another, and how noise-canceling headphones use incoming sounds to figure out how to produce that sweet, sweet silence.

How much of what we see is advertising? Students decompose irregular polygons into triangles and rectangles, find their areas to estimate the fraction of a scene that’s advertising, and discuss the pros and cons of living in an ad-free world.