How do municipal fines affect people with different incomes? Cities and towns around the country rely on parking and speeding tickets to generate much-needed revenue. Unfortunately these fines can trap the neediest residents in a cycle of debt, especially when they’re compounded by monthly late fees.
In this lesson, 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.
Students will
Write and solve a system of linear equations and interpret the intersection in a real-world context
Explore how changing the slopes and y-intercepts affects where (and if) two lines intersect
Use a unit rate to create a table, graph, and equation
Before you begin
Students should be comfortable relating a scenario to an equation to a graph. Previous experience with systems of equations is not needed.
How much is Domino’s really charging for pizza? Students use slope, y-intercept, and linear equations to explore the costs of different-sized pizzas at Domino’s and debate whether the pizza chain should be more transparent in its pricing.
Which movie rental service should you choose? Students develop a system of linear equations to compare Redbox, AppleTV, and Netflix, and determine which is the best plan for them.
Topic:
Expressions and Equations (EE), Functions (F)
How should speeding tickets be calculated? Students use linear equations to explore how police officers determine speeding fines...and whether tickets are calculated fairly.
How hard should you exercise? Students write and graph an equation for maximum heart rate in terms of age, and then calculate ideal heart rate zones for different types of workouts.
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.
Topic:
Creating Equations (CED), Seeing Structure in Expressions (SSE), Similarity, Right Triangles, and Trigonometry (SRT)
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.
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.
Topic:
Building Functions (BF), Creating Equations (CED), Interpreting Functions (IF), Linear, Quadratic, and Exponential Models (LE)
What should teacher salaries be based on? Students will use and compare linear functions to analyze how teacher pay is currently determined, and decide whether they would give merit-based pay an A+ or failing marks.
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.
Topic:
Building Functions (BF), Creating Equations (CED)
How is the homeless population changing around the country? Students write linear equations to model the homeless populations in New York City and Los Angeles and discuss what they can do to aid people experiencing homelessness in their communities.
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.
Topic:
Building Functions (BF), Interpreting Functions (IF), Linear, Quadratic, and Exponential Models (LE)
How should Arlington National Cemetery plan for its future? Students write and solve linear equations to estimate when Arlington National Cemetery will reach capacity, evaluate various proposals to prolong its lifespan, and debate the best way for Arlington to honor soldiers and their families.
Topic:
Expressions and Equations (EE), Functions (F)
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.
Topic:
Creating Equations (CED), Interpreting Functions (IF), Linear, Quadratic, and Exponential Models (LE), Reasoning with Equations and Inequalities (REI)
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.
Topic:
Creating Equations (CED), Building Functions (BF), Interpreting Functions (IF), Reasoning with Equations and Inequalities (REI)
Are hybrid cars worth the extra cost? Students use linear equations to compare the costs of driving a car with a standard engine versus a hybrid engine and debate whether new buyers should always go green
Topic:
Expressions and Equations (EE), Functions (F)
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.
Topic:
Building Functions (BF), Creating Equations (CED), Interpreting Functions (IF), Reasoning with Equations and Inequalities (REI)
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.