As the name suggests, a pyramid scheme is rarely a sound investment. In spite of this, every few years there’s an article in the news about people who have been duped by such a scheme. So what exactly is a pyramid scheme, and do people actually make money from them?

In this lesson, students learn about how pyramid schemes work, and use geometric sequences to model the (exponential!) growth of a pyramid scheme over time. While these investments may look appealing, a more detailed analysis will reveal why most people who put money into a pyramid scheme never recoup their investment. Pyramids may be fun for archaeologists or geometers, but when it comes to your finances, they’re a shape that’s best avoided.

Students will

Understand how pyramid schemes work using concrete examples

Determine how much money a person can make from a pyramid scheme in various scenarios

Determine the number of people required to sustain a pyramid scheme

Explore what happens when a pyramid scheme collapses, including who makes money and who doesn’t

Discuss whether or not it ever makes sense to invest in a pyramid scheme

Before you begin

Students will be calculating finite sums of geometric sequences several times in this lesson. Some prior experience with these sums will be useful. In particular, they’ll have an easier time if they know the formula for the finite sum of a geometric sequence, but this knowledge isn’t required. You can either omit the formula entirely, or use this lesson as an opportunity to introduce the formula.

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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 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)

Do social networks like Facebook make us more connected? Students create a quadratic function to model the number of possible connections as a network grows, and consider the consequences of relying on Facebook for news and information.

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