Why do different jobs pay so differently? top-paid teacher earns in a year. On one hand, this seems unfair. On the other hand...it still seems unfair. But there’s a reason some jobs pay so much better than others.
In this lesson, students use unit rates to compare how much different professions make per year/day/hour and discuss ways to possibly equate compensation with social contribution.
Students will
Use ratio and rate reasoning to solve real world problems
Calculate daily and hourly unit rates
However, in other professions that generate value for society at large – e.g. a teacher increases students’ future earnings, the President boosts economic performance – that value is often not reflected in compensation.
Before you begin
Students will find rates throughout this lesson. If they aren't familiar with the concept of a unit rate, they can reason their way through answers; simply adjust the timings to allow for lots of discussion of the mathematical reasoning.
How hard is it to steal second base in baseball? Students use the Pythagorean Theorem and proportions to determine whether a runner will successfully beat the catcher's throw.
Topic:
Geometry (G), Ratios and Proportional Relationships (RP)
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)
Why do certain pairs of notes sound better than others? Students use ratios and fraction division to explore what makes two notes sound good or bad when played together.
Topic:
Number System (NS), Ratios and Proportional Relationships (RP)
Is Wheel of Fortune rigged? Students use percents and probabilities to compare theoretical versus experimental probabilities, and explore whether the show is legit, or whether there might be something shady going on!
Topic:
Ratios and Proportional Relationships (RP), Statistics and Probability (SP)
How many calories does a body burn? Students interpret and apply the formula for resting metabolic rate (RMR) in order to learn about how calories consumed from food, calories burned from exercise, and calories burned automatically contribute to a body's weight.
Topic:
Expressions and Equations (EE), Ratios and Proportional Relationships (RP)
How much of your life do you spend doing different activities? Students use proportional reasoning and unit rates to calculate how much of their total lifespan they can expect to spend sleeping, eating, and working...and discuss how they'd like to spend the time that's left over.
How fast is the Earth spinning? Students use unit rates to find the speed at which the planet rotates along the Equator, Tropic of Cancer, and Arctic Circle.
Topic:
Expressions and Equations (EE), Ratios and Proportional Relationships (RP)
Why do concert tickets cost so much? Students use percents to describe how much of a ticket’s price goes to various parties -- artist, venue, brokers, etc. -- and debate the fairest ways to price and sell event tickets.
How do you determine the best scorer in basketball? Students compare LeBron James and Tyson Chandler in various ways, from total points, to points per game/minute, to a new measure called net points in order to decide.
Topic:
Number System (NS), Ratios and Proportional Relationships (RP)
How do filmmakers create slow-motion and time-lapse videos? Students combine a camera's frame rate, a video player's frame rate, and proportional reasoning to explore movie magic.
What size ice cubes should you put in your drink? Students use surface area, volume, and rates to explore the relationship between the size of ice cubes and how good they are at doing their job: chilling.
Topic:
Geometry (G), Ratios and Proportional Relationships (RP)
Should fast food restaurants rewrite their menus in terms of exercise? Students write and evaluate expressions to determine how long it takes to burn off foods from McDonald’s and debate the pros and cons of including this information on fast food menus.
Topic:
Ratios and Proportional Relationships (RP), Expressions and Equations (EE)
How much should people pay for cable? Students interpret scatterplots and calculate the costs and revenues for consumers and providers under both the bundled and à la carte pricing schemes to determine which would be better for U.S. companies and customers.
Topic:
Number System (NS), Ratios and Proportional Relationships (RP)
What’s the fairest way to tip at a restaurant? Students use percents to calculate tips for different restaurant bills and debate the best ways to compensate waiters and waitresses.
How does the what we see affect our happiness? Students explore the concept of the jen ratio – the ratio of positive to negative observations in our daily lives – and use it to discuss how the content we consume and the things we observe influence our experience of the world.
How big is the White House? Students build scale models of the White House, compare scaling in one vs. two vs. three dimensions and design their ideal version of the president’s house.
Topic:
Geometry (G)
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How have video game consoles changed over time? Students create exponential models to predict the speed of video game processors over time, compare their predictions to observed speeds, and consider the consequences as digital simulations become increasingly lifelike.
Topic:
Building Functions (BF), Interpreting Categorical and Quantitative Data (ID), Interpreting Functions (IF), Linear, Quadratic, and Exponential Models (LE), Seeing Structure in Expressions (SSE)