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
Objectives (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
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.
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.
Also see the file guests/edwina1.html
Return to Mathematics Index