What’s the best way to play roulette? As glamorized in casino ads around the world, the prospect of winning big on a spin of roulette can set hearts racing. And yet somehow the house always wins in the end!
In this lesson, students use probabilities and odds to analyze roulette payouts and debate the optimal strategy for winning the game (including not playing at all).
Students will
Describe the probability of an event given a sample space
Calculate expected value
Reason with probabilities to inform real-world decisions
Before you begin
Students should be familiar with basic probabilities.
In basketball, which shot should you take? Students use probability and expected value to determine how much 3-point and 2-point shots are really "worth" to different NBA players.
Topic:
Conditional Probability and the Rules of Probability (CP)
What does it mean for a playlist to be "random?" Students use probability to explore the idea of randomness, as well as the patterns that can emerge from random processes like shuffles.
Topic:
Conditional Probability and the Rules of Probability (CP), Interpreting Categorical and Quantitative Data (ID)
What is the likelihood of winning at craps? Students learn the rules of the popular casino game, and use probabilities to determine how likely players are to win big (or go broke).
Topic:
Congruence (CO), Modeling with Geometry (MG)
How many people should you date before you settle down? Students use modeling with probability distributions to come up with a rule to try to maximize their relationship happiness.
Topic:
Conditional Probability and the Rules of Probability (CP), Making Inferences and Justifying Conclusions (IC)
When is it worth buying a Powerball ticket? Students count combinations and apply basic rules of probability and expected value to determine when the Powerball jackpot is large enough to justify the cost of playing the game.
Topic:
Conditional Probability and the Rules of Probability (CP)
When should NFL teams go for it on fourth down? Students use quadratic functions to develop a model of expected points. They then apply this model to determine when teams should punt the ball, and more importantly, when they shouldn’t.
Topic:
Building Functions (BF), Interpreting Functions (IF), Using Probability to Make Decisions (MD)
How much should you bid in an auction? Students create polynomial functions to model the expected value of a given bid and determine the optimal amount someone should bid in any auction.
Topic:
Building Functions (BF), Interpreting Functions (IF)
How accurate should government surveillance be? Students calculate conditional probabilities to determine the likelihood of false-positives and false-negatives, and discuss the tradeoffs between safety and accuracy.
Topic:
Conditional Probability and the Rules of Probability (CP)
How much would it cost to get all the toys in a Happy Meal? Students use trials, probabilities, and expected value to determine how many meals it takes to get a complete set of Happy Meal toys and debate whether McDonald’s should allow customers to pay a fee to choose their own figurine.
Topic:
Conditional Probability and the Rules of Probability (CP), Interpreting Categorical and Quantitative Data (ID), Making Inferences and Justifying Conclusions (IC)
Should airlines overbook their flights? Students use compound probability and expected value to determine the optimal number of tickets an airline should sell and discuss whether airlines should be allowed to overbook their flights.
Topic:
Conditional Probability and the Rules of Probability (CP), Creating Equations (CED), Using Probability to Make Decisions (MD)
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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 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)