March Madness. The Big Dance. The annual NCAA basketball tournament goes by many names, and has millions of devoted fans. Every year, basketball prognosticators try to predict the outcome of the tournament. But how likely is it for someone to produce a perfect prediction?

In this lesson, 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. Students close out the lesson by analyzing geometric and arithmetic sequences commonly used to score March Madness predictions, and discuss what makes a prediction the “best.”

Students will

Calculate the probability of randomly predicting every result in the NCAA tournament correctly

Estimate the probability of creating a perfect bracket given the probability of correctly predicting a single game

In the event that no prediction is perfect, analyze different ways to score predictions to find the “best” one

Discuss the pros and cons of different scoring systems

Before you begin

Students should have some previous exposure to probability concepts. In particular, if A and B are independent events, students should know that P(A and B) = P(A)P(B).

What's an acceptable dating range? Students use linear equations and linear inequalities to examine the May-December romance, and ask whether the Half Plus Seven rule of thumb is a good one.

Topic:
Building Functions (BF), Creating Equations (CED), Expressions and Equations (EE), Functions (F), Interpreting Functions (IF), Reasoning with Equations and Inequalities (REI)

What's the ideal size for a soda can? Students use the formulas for surface area and volume of a cylinder to design different cans, calculate their cost of production, and find the can that uses the least material to contain a standard 12 ounces of liquid.

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)

How far away from the TV should you sit? Students use right triangle trigonometry and a rational function to explore the percent of your visual field that is occupied by the area of a television.

Topic:
Building Functions (BF), Creating Equations (CED), Interpreting Functions (IF), Reasoning with Equations and Inequalities (REI), Similarity, Right Triangles, and Trigonometry (SRT)

Why hasn't everyone already died of a contagion? And, if vampires exist, shouldn't we all be sucking blood by now? Students model the exponential growth of a contagion and use logarithms and finite geometric series to determine the time needed for a disease to infect the entire population. They'll also informally prove that vampires can't be real.

Topic:
Creating Equations (CED), Linear, Quadratic, and Exponential Models (LE), Seeing Structure in Expressions (SSE)

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 much do you really pay when you use a credit card? Students develop an exponential growth model to determine how much an item really ends up costing when purchased on credit.

Topic:
Building Functions (BF), Creating Equations (CED), Linear, Quadratic, and Exponential Models (LE)

Could Inspector Javert have survived the fall? Students use quadratic models to determine how high the bridge was in Les Misérables, and explore the maximum height from which someone can safely jump.

Topic:
Building Functions (BF), Creating Equations (CED), Interpreting Functions (IF)

How has the iPod depreciated over time? Students compare linear and exponential decay, as well as explore how various products have depreciated and what might account for those differences.

In which Major League Baseball stadium is it hardest to hit a home run? Students find the roots and maxima of quadratic functions to model the trajectory of a potential home-run ball.

Topic:
Creating Equations (CED), Interpreting Functions (IF), Reasoning with Equations and Inequalities (REI)

How much should Nintendo charge for the Wii U? Students use linear functions to explore demand for the Wii U console and Nintendo's per-unit profit from each sale. They use those functions to create a quadratic model for Nintendo's total profit and determine the profit-maximizing price for the console.

Topic:
Creating Equations (CED), Building Functions (BF), Interpreting Functions (IF), Reasoning with Equations and Inequalities (REI)

Which size pizza should you order? Students apply the area of a circle formula to write linear and quadratic formulas that measure how much of a pizza is actually pizza, and how much is crust.

Topic:
Building Functions (BF), Creating Equations (CED), Interpreting Functions (IF), Reasoning with Equations and Inequalities (REI)

Sign In

Like the jacket, this lesson is for Members only.

Mathalicious lessons provide teachers with an opportunity to teach standards-based math through real-world topics that students care about.

How have video game console speeds changed over time? Students write an exponential function based on the Atari 2600 and Moore's Law, and see whether the model was correct for subsequent video game consoles.

Topic:
Building Functions (BF), Interpreting Categorical and Quantitative Data (ID), Interpreting Functions (IF), Linear, Quadratic, and Exponential Models (LE)