Going to college can be expensive. It can also set you up to get a better job and make more money. So how much more do graduates earn, and is college worth the cost?
In this lesson, students use systems of linear equations to compare how much people with different degrees will earn. Should you pursue an MBA, or take a full-time job right after high school? And is income what matters most, anyway? Students will discuss these questions and more.

Students will

Use tuition costs and median incomes to determine net income over time for various educational paths

Use strategies to solve systems of equations to determine when two paths will yield same net income

Use data points on a graph to calculate tuition costs and median income for an Associate’s Degree and an MBA

Compare lifetime earnings for various degree types (including high school diploma)

Discuss how and even whether income potential should affect decision of whether to attend college

Before you begin

Students should be able to calculate the slope between two points on a graph, and interpret its meaning for a given real-world context. Students should also be able to solve systems of linear equations using various strategies, including algebraic and graphical.

What's an acceptable dating range? Students use linear equations and linear inequalities to examine the May-December romance, and ask whether the Half Plus Seven rule of thumb is a good one.

Topic:
Building Functions (BF), Creating Equations (CED), Expressions and Equations (EE), Functions (F), Interpreting Functions (IF), Reasoning with Equations and Inequalities (REI)

How much does Domino's charge for pizza? Students use linear functions — slope, y-intercept, and equations — to explore how much the famous pizzas really cost.

Topic:
Expressions and Equations (EE), Functions (F)

How far away from the TV should you sit? Students use right triangle trigonometry and a rational function to explore the percent of your visual field that is occupied by the area of a television.

Topic:
Building Functions (BF), Creating Equations (CED), Interpreting Functions (IF), Reasoning with Equations and Inequalities (REI), Similarity, Right Triangles, and Trigonometry (SRT)

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 much can you trust your memory? Students construct and compare linear and exponential models to explore how much a memory degrades each time it's remembered.

Topic:
Interpreting Functions (IF), Linear, Quadratic, and Exponential Models (LE)

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)

How has the iPod depreciated over time? Students compare linear and exponential decay, as well as explore how various products have depreciated and what might account for those differences.

How much Tylenol can you safely take? Students use exponential functions and logarithms to explore the risks of acetaminophen toxicity, and discuss what they think drug manufacturers should do to make sure people use their products safely.

Topic:
Building Functions (BF), Interpreting Functions (IF), Linear, Quadratic, and Exponential Models (LE), Seeing Structure in Expressions (SSE)

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)

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 much Halloween candy should you eat? Students interpret graphs to compare the marginal enjoyment and total enjoyment of two siblings feasting on piles of Halloween candy and figure out how much pleasure you get (or don't) from eating more and more.

How has the human population changed over time? Students build an exponential model for population growth and use it to make predictions about the future of our planet.

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

How hard is it to pay off municipal fines? Students use linear equations and solve linear systems to examine what happens when people are unable to pay small municipal fines. They also discuss what can happen to the most financially vulnerable citizens when cities rely heavily on fines for revenue.

Topic:
Creating Equations (CED), Expressions and Equations (EE), 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), Linear, Quadratic, and Exponential Models (LE), Seeing Structure in Expressions (SSE)

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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)