**The Area of a Circle (Version 2.0)**

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.

**Objectives (Grade 8)**:

Review areas of plane figures.

Determine the relationship between the circumference and diameter of a

circle.

Show the geometric representation of the area of a circle as the shape of

a parallelogram.

Derive and use the formula for computing the area of a circle.

Participate in group activity.

**Materials**:

Tape measures

Round container lids with varying circumference measurements

Paper circles (equal circumferences)

Paper circles with varying circumference measurements

Centimeter grids

Transparencies:

Table with 4 columns labeled - lid number, circumference, diameter, and

circumference/diameter

Graph: Label x-axis as diameter and y-axis as circumference

Several blank transparencies

Worksheet:

Draw four circles of unequal radii on a cm. grid

**Recommended Strategy**:

Form small groups and measure circumference and diameter of several lids.

Divide circumference by diameter for each lid.

Record data on table (transparency).

Graph ordered pairs (diameter, circumference).

Discuss constant (pi) that results when circumference is divided by

diameter.

Cut paper circles with equal circumferences into 16 equal pie-shaped pieces.

Arrange 16 pieces (on cm. grid) to form a parallelogram.

Calculate area of parallelogram.

Label base of parallelogram as 1/2c and height as r.

Review c = (pi)d c = 2(pi)r.

Show that area of the parallelogram is 1/2(2pi*r)r or pir^{2}.

Use A = pi*r^{2} to calculate area of whole circle.

Compare area of parallelogram to formula calculations.

Use A = pi*r^{2} to calculate areas of 4 circles (worksheet).

Cut circles into 1/16's and form parallelograms.

Calculate areas and compare to formula calculations.

**Extension**:

Make a cylinder and show how the surface area is the total areas

of two circles (the ends) and one rectangle (the side).

Also see the file guests/edwina1.html

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