House of Pain
Why are so many Americans dying from opiate overdoses?
Students will
- Describe the deterioration of pain relief from a standard dosage of opioids using an exponential decay function.
- Construct a rational function to model the increased dosage a patient would need to maintain complete pain relief
- Discuss and debate the role that pharmaceutical companies, doctors, patients, and society at large can and should have in addressing the opioid epidemic in America.
Before you begin
Adjust timing as needed depending on students' familiarity with exponential decay. Students don't need to have mastered writing exponential decay functions -- they can reason intuitively about the functions they write -- but it will be helpful to have explored some functions that model decay previously.Common Core Standards
Content Standards
Mathematical Practices
Related Lessons
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.
Pyramid of Sleaza
How can you make money in a pyramid scheme? Students learn about how pyramid schemes work (and how they fail), and use geometric sequences to model the exponential growth of a pyramid scheme over time.
Loan Ranger
How much do you really pay when you use a credit card? Students develop an exponential growth model to determine how much an item really ends up costing when purchased on credit.
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.
I Remember
How much can you trust your memory? Students construct and compare linear and exponential models to explore how much a memory degrades each time it's remembered.
Going Once, Going Twice - Legacy Version
How much should you bid in an auction? Students use probability, expected value, and polynomial functions to develop a profit-maximizing bidding strategy.
iPod dPreciation
How has the iPod depreciated over time? Students compare linear and exponential decay, as well as explore how various products have depreciated and what might account for those differences.
It's a Date
How can we improve our calendar? Students examine some other ways to keep track of dates, and use number sense and function concepts to convert between different calendars.
Pounding Headache
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.
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 the Wii U? Students use linear functions to explore demand for the Wii U console and Nintendo's per-unit profit from each sale. They use those functions to create a quadratic model for Nintendo's total profit and determine the profit-maximizing price for the console.
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 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.
Wage War
How much should companies pay their employees? Students graph and solve systems of linear equations in order to examine the effects of wage levels on labor and consumer markets, and they discuss the possible pros and cons of increasing the minimum wage.
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.
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.
XBOX Xponential
How have video game console speeds changed over time? Students write an exponential function based on the Atari 2600 and Moore's Law, and see whether the model was correct for subsequent video game consoles.
Pandemic
Why hasn't everyone already died of a contagion? And, if vampires exist, shouldn't we all be sucking blood by now? Students model the exponential growth of a contagion and use logarithms and finite geometric series to determine the time needed for a disease to infect the entire population.
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.
