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Opportunities' Costs (Updated!)

Is college a good investment?

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Opportunities' Costs (Updated!)

Is college a good investment?

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Opportunities Costs - Student Handout.pdf
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Opportunities Costs - Teacher Guide.pdf
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2023-2024 Versions

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.

Is higher education a good investment? One of the biggest questions students face is how much education to get. While bachelors and graduate degrees may lead to higher earnings, they can also be expensive and take years to earn.

In this lesson, students write and solve systems of linear equations to determine how long it would take to pay off various degrees and discuss the pros and cons of different educational paths.

REAL WORLD TAKEAWAYS

  • Professions have different upfront costs (both time and money) for education, and they have different median salaries after that education is attained.
  • Some professions with high median salaries require lots of time and money for education in the short run.
  • Whether someone “should” get more education depends on what’s important to them – e.g. netting more money, doing particular type of work, having a particular status – and how long they expect to work.

MATH OBJECTIVES

  • Write linear equations to model real-world scenarios
  • Solve systems of equations graphically, algebraically, and/or by reasoning with tables
This complex task is best as a culminating unit activity after students have developed formal knowledge and conceptual understanding.
Grade 8
Solving Linear Systems
Grade 8
Solving Linear Systems
Content Standards F.IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. 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.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. 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.8 Look for and express regularity in repeated reasoning.

Other Grade 8 Lessons

Domino Effect (Updated!)

How much does Domino’s charge for pizza?

Grade 8
Writing Linear Equations
Great anytime, including at the beginning of a unit before students have any formal introduction to the topic.

You're So Fined (Updated!)

How do municipal fines affect people with different incomes?

Grade 8
Solving Linear Systems
Great anytime, including at the beginning of a unit before students have any formal introduction to the topic.

Square Dancing (Updated!)

What secrets are hidden in squares?

Grade 8
Squares, Roots, Irrationals
Great anytime, including at the beginning of a unit before students have any formal introduction to the topic.

Sweet Tooth (Updated!)

How much Halloween candy should you eat?

Grade 8
Functions
Great anytime, including at the beginning of a unit before students have any formal introduction to the topic.

Timber (Updated!)

What size tree should we use for lumber?

Grade 8
Cones, Cylinders, Spheres
Appropriate most times as students are developing conceptual understanding.

Domino Effect (Updated!)

How much does Domino’s charge for pizza?

Grade 8
Writing Linear Equations
Great anytime, including at the beginning of a unit before students have any formal introduction to the topic.

You're So Fined (Updated!)

How do municipal fines affect people with different incomes?

Grade 8
Solving Linear Systems
Great anytime, including at the beginning of a unit before students have any formal introduction to the topic.

Square Dancing (Updated!)

What secrets are hidden in squares?

Grade 8
Squares, Roots, Irrationals
Great anytime, including at the beginning of a unit before students have any formal introduction to the topic.

Sweet Tooth (Updated!)

How much Halloween candy should you eat?

Grade 8
Functions
Great anytime, including at the beginning of a unit before students have any formal introduction to the topic.

Timber (Updated!)

What size tree should we use for lumber?

Grade 8
Cones, Cylinders, Spheres
Appropriate most times as students are developing conceptual understanding.