How have temperatures changed around the world? Recent years have been the hottest on record. While some see this as evidence of a dangerous trend that merits drastic action, others find little alarming about such fluctuations.

In this lesson, students use periodic functions to compare long-term average monthly temperatures to recorded monthly temperatures, evaluate evidence of climate change, and discuss possible consequences.

- Model a periodic phenomena (monthly temperatures) with a trigonometric function.

- Transparency sheets or tracing paper.

Climate scientists

How much should people pay for donuts? Students use linear, rational, and piecewise functions to describe the total and average costs of an order at Carpe Donut.

How far away from the TV should you sit? Students use right triangle trigonometry and a rational function to explore the percent of your visual field that is occupied by the area of a television.

Could Inspector Javert have survived the fall? Students use quadratic models to determine how high the bridge was in *Les Misérables*, and explore the maximum height from which someone can safely jump.

How have video game consoles changed over time? Students create exponential models to predict the speed of video game processors over time, compare their predictions to observed speeds, and consider the consequences as digital simulations become increasingly lifelike.

Can you predict a country's Winter Olympic performance? Students analyze scatterplots and correlation coefficients to pick out the best predictive model for Olympic success.

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.

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.

How much should Nintendo charge for a video game console? Students use linear and quadratic models to analyze and discuss the relationship between the price of a Wii U console and profits for Nintendo.

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.

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 pharmaceutical companies decide which drugs to develop? Students create linear and quadratic functions to explore how much pharmaceutical companies profit from different drugs and consider ways to incentivize companies to prioritize medications that are valuable to society.

Do social networks like Facebook make us more connected? Students create a quadratic function to model the number of possible connections as a network grows, and consider the consequences of relying on Facebook for news and information.

How much should you bid in an auction? Students create polynomial functions to model the expected value of a given bid and determine the optimal amount someone should bid in any auction.

What time should school start in the morning? Students use periodic functions to compare the alertness levels of adults vs. teenagers over the course of the day and debate the merits of starting school later.

Is higher education a good investment? Students write and solve systems of linear equations to determine how long it would take to pay off various degrees and discuss the pros and cons of different educational paths.

How dangerous are heat and humidity? Students use polynomial functions to explore the heat index and discuss the life-and-death consequences that cities around the world will face in the coming years.

What’s the best way to use Instagram? Students use histograms, linear regressions, and r-squared values to debate the most effective strategies to gain Insta-fame...and the consequences of always having to smile for the camera.

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 have video game consoles changed over time? Students create exponential models to predict the speed of video game processors over time, compare their predictions to observed speeds, and consider the consequences as digital simulations become increasingly lifelike.

In basketball, should you ever foul at the buzzer? Students use probabilities to determine when the defense should foul...and when they should *not*.