Nobody likes getting tickets. For many people they’re merely an annoyance; for people struggling to make ends meet they can be a serious burden. And since many states levy additional monthly fees when someone can’t pay off a fine in its entirety, some people get stuck in a cycle of debt that’s difficult to escape.

In this lesson, students write linear equations and solve linear systems to examine the relative difficulty of paying off a small municipal fine. They also discuss what can happen to the most financially vulnerable citizens when cities rely heavily on fines for revenue.

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.

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)

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.

Are solar panels worth the cost? Students set up and solve systems of linear equations to compare different electricity plans and determine when each option is the least expensive.

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.

Topic:
Building Functions (BF), Creating Equations (CED), Interpreting Functions (IF), Linear, Quadratic, and Exponential Models (LE)

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.

Topic:
Linear, Quadratic, and Exponential Models (LE), Reasoning with Equations and Inequalities (REI)

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)

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Mathalicious lessons provide teachers with an opportunity to teach standards-based math through real-world topics that students care about.

How do the rules of an election affect who wins? Students calculate (as a percent) how much of the electoral and popular vote different presidential candidates have received, and add with integers to explore elections under possible alternative voting systems.

Topic:
Number System (NS), Ratios and Proportional Relationships (RP), Reasoning with Equations and Inequalities (REI)

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.

Topic:
Building Functions (BF), Interpreting Categorical and Quantitative Data (ID), Interpreting Functions (IF), Linear, Quadratic, and Exponential Models (LE)