Middle Grades Math: Comparing Pi's and Roots

Objectives

• 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.

Vocabulary

• 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.