How much would it cost to get all the toys in a Happy Meal? The McDonald’s Happy Meal is a cultural phenomenon. Parents like it because it’s a quick and easy meal, and kids like it because it comes with a toy (typically part of a larger set).
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.
Students will
Create frequency distribution from experimental data and interpret the results
Use theoretical and experimental probability to reason about real-world decisions
Calculate expected value and use it to evaluate decisions in a real-world context
Before you begin
Students should be familiar with theoretical and experimental 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 chance that PRISM ensnares an innocent person? Students use conditional probabilities to examine some of the implications of a program like PRISM. Specifically, if someone has been identified as a threat, what’s the probability that person actually is a threat?
Topic:
Conditional Probability and the Rules of Probability (CP)
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)
What’s the best strategy for creating a March Madness bracket? Students use probability to discover that it’s basically impossible to correctly predict every game in the tournament. Nevertheless, that doesn’t stop people from trying.
Topic:
Conditional Probability and the Rules of Probability (CP), Creating Equations (CED), Linear, Quadratic, and Exponential Models (LE)
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 states spend on schools and police? Students analyze histograms and use mean and median to explore state spending habits. Then, they discuss how much they think states should be spending.
Topic:
Interpreting Categorical and Quantitative Data (ID)
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)
Is there evidence of racial bias in death penalty sentencing? Students analyze almost thirty years’ worth of data summarized in frequency tables and discuss whether they see evidence of racial bias in who receives the death penalty and who doesn’t.
Topic:
Conditional Probability and the Rules of Probability (CP), Interpreting Categorical and Quantitative Data (ID)
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)
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)
What’s the best way to play roulette? Students use probabilities and odds to analyze roulette payouts and debate the optimal strategy for winning the game (including not playing at all).
Topic:
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)