Unit: Apple Pi - Using estimation and measurement skills, students will determine the
ratio of circumference to diameter and explore the meaning of pi.
Students will discover the circumference and area formulas based on
their investigations. (6-8)
Lesson: 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: Discovering the Area Formula for Circles - Using a circle that has been divided into congruent sectors, students discover the area formula by using their knowledge of parallelograms. Students then calculate the area of various flat circular objects that they have brought to school. Finally, students investigate various strategies for estimating the area of circles.
Related Activity: A Circle Tool - How do the area and circumference of a circle compare to its radius and diameter? This activity allows you to investigate these relationships in the Intro and Investigation sections and then hone your skills in the Problems section. (3-8)
Lesson: Square Circles- Students use a variety of units when measuring the side length and perimeter of squares and the diameter and circumference of circles. From these measurements, students will discover the constant ratio of 1:4 for all squares and the ratio of approximately 1:3.14 for all circles. (6-8)
Lesson: Pi Line - Students measure the diameter and circumference of various circular objects, plot the measurements on a graph, and relate the slope of the line to pi, the ratio of circumference to diameter. (9-12)
||Unit: Pi filling, Archimedes Style! In the spirit of Archimedes’ method of approximating pi, students inscribe and circumscribe regular polygons in and around the unit circle, which is known to have an area of pi. Students then consider the area of the polygons, using either an applet or a graphing calculator. The area of the n‑gons approaches pi as n increases. (9-12)
Activity: Computing Pi - The Greek mathematician Archimedes approximated pi by inscribing and circumscribing polygons about a circle and calculating their perimeters. Similarly, the value of pi can be approximated by calculating the areas of inscribed and circumscribed polygons. This activity allows for the investigation and comparison of both methods. (6-12)