Canalysis
What’s the ideal size of a soda can?
In this lesson, students create rational functions to explore the relationship between volume, surface area, and cost to determine the optimal size of a soda can.
Students will
- Write, graph, and solve rational equations to describe geometric relationships
Before you begin
Student will calculate the volume of cylinders in this lesson. If this formula or concept is not familiar, you'll need to build in extra time for development.Common Core Standards
Content Standards
Mathematical Practices
Downloads
Related Lessons
Cheese That Goes Crunch
Which is better: crunchy or puffy Cheetos? Students calculate the surface area : volume ratio for each snack to determine which one tastes cheesier.
Carpe Donut
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.
Sofa Away From Me
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.
Fall of Javert
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.
Sharper Image
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.
Siren Song
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.
Green Acres
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.
Driving Question
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.
Wiibates
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.
Pizza Pi (HS)
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.
The Sound of Silence
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.
Prescripted
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.
You're So Fined
How do municipal fines affect people with different incomes? Students write, solve, and graph systems of linear equations to determine how long it takes to pay off a ticket and debate the fairest ways for cities to raise revenues without harming their poorest residents.
Connected
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.
Going Once, Going Twice
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.
Rise and Shine
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.
Opportunities Cost
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.
Billions & Billions
How has the human population changed over time? Students develop exponential models to analyze human population growth and explore the impact this growth will have in areas around the world.
Second Degree
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.
Mercury Rising
How have temperatures changed around the world? Students use periodic functions to compare long-term average monthly temperatures to recorded monthly temperatures, evaluate evidence of climate change, and discuss possible consequences.
Wage War
Should the government increase the minimum wage? Students use systems of linear equations to explore the relationship between wage and labor, analyze the economics of fast-food restaurants, and debate whether the federal government should increase the minimum wage.
Datelines
How much does age matter in a relationship? Students use a system of linear inequalities to explore the popular dating rule-of-thumb, ‘half plus seven’, and debate how important age -- and other factors -- are in healthy relationships.
