In the fall of 2024, Citizen Math released updated versions of every lesson in our library, plus a few new ones! We know you may have already prepped an earlier version or planned a repeat of last year, so we're continuing to make these earlier versions available through Thursday December 5, 2024.
You can find the new lessons through the regular search, and we hope you love them as much as we do. You can read more about these updates in Our Community.
How should pharmaceutical companies decide which drugs to develop? There are plenty of medications for conditions like seasonal allergies and athlete’s foot, but treatments for critical conditions such as Ebola are often non-existent. Even though treatments like these may be more important, they’re also less profitable for drug companies.
In this lesson, 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.
REAL WORLD TAKEAWAYS
Pharmaceutical companies sell many different kinds of medications.
The revenue that a company generates from a certain medication depends on a number of factors. These include the size of the market and the price that customers are willing to pay for the medication.
Pharmaceutical companies will often set a price that maximizes their revenue. The upside of this is that it incentivizes companies to develop medications, including life-saving ones. The downside is that it means that some customers may not be able to afford the medications.
MATH OBJECTIVES
Write an equation for a linear functions; interpret the meaning of the y-intercept and slope for a real-world situation
Write an equation for a quadratic function
Identify the key points of a parabola, including the min, max, and vertex; interpret the meaning of these for a real-world situation
Appropriate most times as students are developing conceptual understanding.
Algebra 1
Parabolas & Quadratics
Algebra 1
Parabolas & Quadratics
Content Standards
A.CED.2
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
F.IF.4
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
F.BF.1
Write a function that describes a relationship between two quantities. (a) Determine an explicit expression, a recursive process, or steps for calculation from a context. (b) Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. (c) (+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.
F.BF.4
Find inverse functions. (a) Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2 x<sup>3</sup> or f(x) = (x + 1)/(x — 1) for x = ‐1. (b) (+) Verify by composition that one function is the inverse of another. (c) (+) Read values of an inverse function from a graph or a table, given that the function has an inverse. (d) (+) Produce an invertible function from a non-invertible function by restricting the domain.
F.LE.1
Distinguish between situations that can be modeled with linear functions and with exponential functions. (a) Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. (b) Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. (c) Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
F.LE.2
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
F.LE.5
Interpret the parameters in a linear or exponential function in terms of a context.
Mathematical Practices
MP.1
Make sense of problems and persevere in solving them.
MP.2
Reason abstractly and quantitatively.
MP.3
Construct viable arguments and critique the reasoning of others.
MP.4
Model with mathematics.
MP.5
Use appropriate tools strategically.
MP.6
Attend to precision.
MP.7
Look for and make use of structure.
MP.8
Look for and express regularity in repeated reasoning.
