How do vehicles turn? In this lesson, students use the geometry of circles to understand how we get from point A to point B when the path isn’t a straight one.

How should pharmaceutical companies decide what to develop? In this lesson, students use linear and quadratic functions to explore how much pharmaceutical companies expect to make from different drugs, and discuss ways to incentivize companies to develop medications that are more valuable to society.

How long does it take to pay off municipal fines? Students use linear equations and solve linear systems to examine what happens when people are unable to pay small municipal fines. They also discuss what can happen to the most financially vulnerable citizens when cities rely heavily on fines for revenue.

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.

How much is money worth? Students apply operations on rational and decimal numbers to calculate how much the U.S. Mint spends on different coins, and discuss whether we really need all these coins.

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 should grades be calculated? Students use averages and weighted means to examine some different grading schemes and decide what other factors ought to be considered when teachers assign grades.

How can we compare similar items? Students plot points with positive and negative coordinates in order to compare items across two different attributes. They use the plots to decide which item is the “best” in different scenarios, and discuss whether or not negative numbers always represent the “opposite” of positive numbers.

What transformations do smartphones use? In this lesson, students identify and categorize the different transformations that occur when a user manipulates a smartphone screen. They also use on-screen coordinates to calculate the results of zooming within an application and to decide whether ponying up for a larger screen is worth it.

How have temperatures changed around the world? Students use trigonometric functions to model annual temperature changes at different locations around the globe and explore how the climate has changed in various cities over time.

How have temperatures changed around the world? Students compare current temperatures to historical averages, and add and subtract positive and negative numbers to explore how the climate has changed in various cities over time.

What does Earth really look like? Students approximate the areas of different landmasses by decomposing them into triangles and rectangles. They do this for two different maps, and debate whether or not the map you use affects how you see — both literally and figuratively — the world.

Should shoe companies sell left and right shoes separately? Students collect survey and measurement data, construct bar graphs, and discuss distributions and measures of central tendency in order to figure out whether shoe companies should necessarily be selling their products in same-size pairs.

How do camera settings affect the final image, and how can we use aperture and shutter speed to take better pictures? Students use the area of circles and fractions to explore how to properly expose a picture, and how photographers use depth of field and motion blur to get the perfect shot.

How much more do graduates earn, and is college worth the cost? Students use systems of linear equations to compare different educational options.