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 pir2.

   Use A = pi*r2 to calculate area of whole circle.

   Compare area of parallelogram to formula calculations.

   Use A = pi*r2 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