In the popular game show Wheel of Fortune, contestants spin a wheel and make money based on where it lands; the higher the dollar amount, the more they can make. If contestants land on Bankrupt, though, they lose everything. So how often should the wheel land on each amount…and is it possible that the show is rigged?
In this lesson, students use percents and probabilities to explore whether the show is legit, or whether there might be something shady going on!
Students will
Use the Wheel of Fortune wheel to calculate how often each value should come up as a percent (theoretical probability)
Watch an episode of Wheel of Fortune to determine how often each value actually came up (experimental probability)
Create bar graph comparing theoretical vs. experimental probabilities, and discuss why they may be different
Discuss whether results indicate that Wheel of Fortune is rigged
Understand that a single episode (27 spins) is insufficient to definitely determine whether show is rigged
Before you begin
Students should be able to calculate a percent given a part and a whole, and explain that this value means "out of 100." Students should also be able to compare quantities by creating a bar graph.
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Topic:
Geometry (G), Ratios and Proportional Relationships (RP)
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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)
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.
Who should buy health insurance? Students use percents and expected value to explore the mathematics of health insurance from a variety of perspectives.
Topic:
Number System (NS), Ratios and Proportional Relationships (RP), Statistics and Probability (SP)
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.
How much should vowels cost on Wheel of Fortune? Students use ratios and percents to explore what would happen if Wheel of Fortune charged prices for vowels based on how often they come up.
Topic:
Ratios and Proportional Relationships (RP), Statistics and Probability (SP)
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)
Should shoe companies sell left and right shoes separately? Students collect survey and measurement data, construct bar graphs, and discuss distributions and measures of central tendency in order to figure out whether shoe companies should necessarily be selling their products in same-size pairs.
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.
Why do different jobs pay so differently? 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.
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.
What does a fair wealth distribution look like? Students use mean, median, histograms, and box-and-whisker plots to compare how wealth is distributed in different countries and debate the pros and cons of their ideal distribution.
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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