Education Technology

Middle Grades Math: Comparing Pi's and Roots

by Texas Instruments


  • Students will compare the circumference of a circle with the hypotenuse of a right triangle in order to compare the sizes of irrational numbers.
  • Students will use measurements, formulas and calculator computations, and formulas and exact calculations to make comparisons.


  • rational number
  • irrational number
  • real number
  • decimal approximation
  • precision

About the Lesson

This lesson involves manipulating the radius of a circle and the sides of a right triangle in an attempt to set the circumference of the circle equal to the hypotenuse of the right triangle
As a result, students will:

  • Unwrap the circle alongside the hypotenuse.
  • Use measurements to find decimal approximations of lengths in order to compare them.
  • Use the circumference formula and the Pythagorean theorem to find decimal approximations of the lengths using a calculator.
  • Use the formulas to find exact lengths.