In most places, fines for speeding are calculated according to how many miles-per-hour over the speed limit a driver is moving. But does that make sense? Is driving 80 in a 60 really the same as driving 40 in a 20? If not, is there a better way to determine speeding penalties?
In this lesson, students learn how speeding tickets are calculated and use linear functions in order to compare a few different proposals and figure out the fairest way to keep the highways safe.
Students will
Given the recorded speed and speed limit, evaluate a linear function to calculate a fine
Using the fine amount and speed limit, solve for how fast the fine recipient must have been driving
Create graphical representations from verbal descriptions of a linear relationship
Compare models for speeding fines, and determine when each would be favorable for drivers
Before you begin
Students should have a basic understanding of linear relationships, including how to move back and forth among verbal descriptions, equations, and graphical representations of those relationships. Some of the driving scenarios presume that students will be able to use percent change as a basis of comparison.
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 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.
Which crops should farmers grow? Students use linear relationships and proportional reasoning to explore comparative advantage and the risks and benefits of trade.
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.
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 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)
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.
Topic:
Creating Equations (CED), Expressions and Equations (EE), Reasoning with Equations and Inequalities (REI), Functions (F)
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)
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Mathalicious lessons provide teachers with an opportunity to teach standards-based math through real-world topics that students care about.
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Topic:
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