In 2004, the social network Facebook launched to little fanfare. Today, over 10% of the world’s population has a Facebook account, and the company is worth billions of dollars. But where, exactly, does the value of a social network come from?

In this lesson, students will come up with a quadratic function to model how a network’s value (measured in terms of the number of connections between users) grows with the number of people using the network. They’ll also discuss who gets the most value out of a social network: the users themselves, or the advertisers vying for likes, comments, and greenbacks.

Students will

  • Calculate the number of connections that can be formed in a small group of people
  • Derive a general formula for the number of connections in a network with p people in it, and use this as a proxy for a network’s value
  • Estimate Facebook’s value over time based on the growth of its user base
  • Discuss whether a large social network is better for users or advertisers
  • Explore an alternative to Facebook’s social network model, and discuss which approach is more valuable

Before you begin

Students should be able to write and evaluate quadratic functions. The beginning of the lesson can be used to introduce some basic concepts from graph theory (such as edges and vertices), though the lesson can also be used without making any explicit mention of these ideas.

Common Core Standards

Content Standards
Mathematical Practices


Chris Robinson, Mark Zuckerberg, the dudes who started Path