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The story of Rapunzel and her long, golden hair has been told for centuries. But just how long is her hair, and how long did it take to grow?

In this lesson, students will explore these questions with the help of a real-life Rapunzel named Ida Pedersen, who hasn’t cut her hair in over a decade. They’ll use linear equations to model how her hair has grown over time, and will use their model to estimate a person’s hair growth rate. Based on this, they’ll be able to see whether or not Rapunzel’s story is true to life, or whether there must be something more magical going on.

Students will

  • Construct a scatterplot from empirical data of hair length over time
  • Estimate a line of best fit, or calculate one using linear regression
  • Make predictions about hair length at a given time using proportional reasoning
  • Given hair length and time, calculate the unit rate of growth
  • Construct graphs that model hair growth in different scenarios

Before you begin

Students should be able to solve proportions and calculate unit rates. They should also know how to plot points on a scatterplot. The scatterplot in the lesson suggests a linear fit, so students should either know how to perform a linear regression, or be able to write the equation of a line that they informally fit to the data.

Common Core Standards

Content Standards
Mathematical Practices

Additional Materials

  • Rulers


Ida Pedersen, Rapunzel