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.

Were megalodons godfathers of the sea? Students model the bodies of different sharks using cylinders, and explore how the volume of a cylinder changes when its dimensions change. They learn that the megalodon was a massive ocean beast, but that its size may ultimately have led to its downfall.

How should the winner of *The Biggest Loser* be chosen? Students model weight loss with linear equations, and use percent change to compare absolute and relative weight loss for several contestants. They also examine historical data to determine which method produces the fairer game.

What's the best way to design a food tray? Students calculate the volumes of rectangular prisms and use that information to design a cafeteria tray that looks good and holds a balanced meal.

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.