In the Constitutional Convention of 1787, there was a debate about how to count states’ slave populations for the purposes of determining representation in Congress. One result of that convention was the Three-Fifths Compromise, which counted each slave as three-fifths of a person.

In this lesson, students use census data and fraction multiplication to explore the effects of the Three-Fifths Compromise on the balance of power between free and slave states in early America.

Students will

  • Given the free and slave populations of various states in the 1790 census, calculate the fraction of each state’s total population represented by slaves
  • Based on a fixed number of representatives per unit of population, use census data to calculate each state’s representation in Congress
  • Discuss the impact the Three-Fifths Compromise had on the “population” numbers for the purposes of congressional representation
  • Discuss the effects of the compromise from a historical perspective

Before you begin

Students should be able to multiply whole numbers by fractions.

Note: Clearly slavery is a sensitive topic in the American conversation, particularly for those who continue to experience personal and systemic racism as a daily reality. While this lesson focuses on the mathematical nature of the Three-Fifths Compromise as a mechanism for determining congressional representation, that is obviously not its only feature, or even its primary feature. If you’re not sure whether you’re prepared to discuss the implications of and circumstances surrounding the compromise, it might be helpful to collaborate with colleagues in other departments before beginning, or before extending the lesson further.

Common Core Standards

Content Standards
Mathematical Practices


Rafranz Davis