Return to Mathematics IndexAn Introduction to Pi and the Area of a CircleEdwina R. Justice Gunsaulus Scholastic Academy 4420 South Sacramento Ave. Chicago IL 60632 (312) 535-7215Objectives (Staff):

* Demonstrate a phenomenological approach to teaching mathematics

* Inspire others to use the approachObjectives (Grades 5-7):

* 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

glueRecommended 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)r^{2}:

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)r^{2}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.

Ask the following question:

"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.

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