An Introduction to Pi and the Area of a Circle

Edwina R. Justice              Gunsaulus Scholastic Academy
4420 South Sacramento Ave.
Chicago IL   60632
(312) 535-7215

Objectives (Staff):

* Demonstrate a phenomenological approach to teaching mathematics

* Inspire others to use the approach

* Observe and discuss the relationship between circumference & diameter and
how that relationship, called pi, is used in the formula for the area of a
circle.

Materials:

round container lids with varying circumferences
4-column math table (label: circumference, diameter, c/d, & lid #)
graph (label - horizontal axis: diameter; vertical axis: circumference)
small circle drawn on centimeter grid
small circles
metric tape measures
calculators
glue

Recommended Strategy:

* Count square centimeters inside circle and estimate the area.

* Draw a square outside the circle. Calculate the area of the square.

* Draw a square inside the circle. Calculate the area of the square.

* Estimate the area of the circle by relating it to areas of the outer and
inner circles.

* Cut a small circle into 16 equal pie-shaped pieces. Arrange these
pieces to form a parallelogram and glue them on centimeter grid.

* Calculate the area of the parallelogram made with the pie-shaped pieces.

* Measure circumference and diameter of lids and record on 4-column math
table.

* Divide circumference by diameter and record.

* Plot ordered pairs (diameter, circumference).

* Discuss graph.

* Discuss results of C/D.

* Roll large lid or trundle wheel on board and mark circumference. Show
how diameter relates to it.

* Show how the area of the parallelogram, made from 16 pieces, is equal to
(pi)r2:

Area = base x height Note: c/d = (pi)

= 1/2 circumference x radius c = (pi) x d

= 1/2 [(pi) x 2r] r d = 2 x r

= (pi)r2 c = (pi) x 2r

* Use formula to calculate area of initial circle. Compare to estimates.

* Estimate areas of other circles and then calculate actual areas and
compare to estimates.

Performance Assessment:

This is an introductory lesson. It is not necessary to assess usage of
area of circle formula at this time.

"What mathematical relationship does pi represent?"

Students should write responses on paper. Collect, read, and assign a
rating to each.

Expected responses:

The circumference of a circle is 3.14 times its diameter. This
relationship is called pi.

Pi represents the circumference of a circle divided by its diameter.

Pi = c/d.

Also see the file guests/edwina1.html