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 much should Nintendo charge for a video game console? In response to a sales slump, in 2013 Nintendo dropped the price of the Wii U video game console. The following month, they sold three times as many units, which suggests their plan worked. However, Nintendo may have gotten the price wrong.
In this lesson, students use linear and quadratic models to analyze and discuss the relationship between the price of a Wii U console and profits for Nintendo.
REAL WORLD TAKEAWAYS
Just because a company sells more of an item, though, doesn’t mean it’ll make more money. There are also costs to consider.
The profit a company makes is equal to the profit it makes per item times the number of items sold.
Video game companies may price consoles at a lower-than-profit-maximizing-price in order to sell more games.
MATH OBJECTIVES
Use real data to create and interpret a linear model for demand as a function of price
Use real data to create and interpret a quadratic model for total profit as a function of price
Multiply two linear functions to create a quadratic function
Find and interpret the maximum and intercepts of a parabola
Great anytime, including at the beginning of a unit before students have any formal introduction to the topic.
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.IF.7
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. (a) Graph linear and quadratic functions and show intercepts, maxima, and minima. (b) Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. (c) Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. (d) (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. (e) Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
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.
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.
