```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 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)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```