Illuminations: Apple Pi

Apple Pi
Using estimation and measurement skills, students will determine the ratio of circumference to diameter and explore the meaning of π. Students will discover the circumference and area formulas based on their investigations.

Math Content

  • Discover the ratio and meaning of π
  • Discover the formula for finding the circumference of circles
  • Discover the formula for finding the area of circles

Prerequisite Knowledge

Students should be familiar with the basic terminology association with circles, such as center, radius, and diameter.

Individual Lessons

Lesson 1 - The Ratio of Circumference to Diameter

Students measure the circumference and diameter of circular objects. They calculate the ratio of circumference to diameter for each object in an attempt to identify the value of pi and the circumference formula.

Lesson 2 - Discovering the Area Formula for Circles

Using a circle that has been divided into congruent sectors, students will discover the area formula by using their knowledge of parallelograms. Students will then calculate the area of various flat circular objects that they have brought to school. Finally, students will investigate various strategies for estimating the area of circles.

NCTM Resources

Principles and Standards for School Mathematics
National Council of Teachers of Mathematics Thinkfinity Verizon Foundation
More and Better Mathematics for All Students
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