Most students in the fifth grade have a solid grasp of how to find the area and perimeter of a quadrilateral and triangle. Learning the steps to find the circumference and area of a circle is built on that foundation. Students know that circumference, the outside edge of a circle, is similar to the perimeter of squares and triangles. Area is the space inside a boundary. This definition, which the students already understand about the of area of polygons, also applies to the area of a circle -- the space within the circumference.
Things You'll Need
- Colored paper
Give each pair of students a piece of sidewalk chalk with a string tied to it. Vary the lengths of string you give each pair. Head out to the basketball courts or other large concrete area on the campus. Each student makes a point on the courts. This is the central point of their circle. One student holds the end of the string with the chalk, the other student pins the other end of the string to the central point. The student with the chalk stretches the string. He walks around the central point, keeping the string taut, drawing the circumference of his circle. When he gets back to his starting point, he will have a perfect circle with a central point marked.
Draw a diameter -- a line that passes through the central point and is on opposite sides of the circumference -- on each large sidewalk circle. Have each student walk heel-to-toe across the diameter. The number of steps it takes for them to cross the diameter is their new unit of measure. For instance, if it took the student 10 steps to walk across the diameter, 10 steps is her unit of measure. Now, ask the students to walk heel-to-toe around the entire circumference, counting how many units it takes them to return to their starting point. Each student should make it around the circumference in a little over three of her units. When all students have calculated how many units it takes to get around the circle, return to the classroom.
Make a table on the board to record the number of units of measure it took each student to walk completely around the circumference. The students notice that everyone, no matter the size of their foot or the size of their circle, made it around the circle in a little over three units. This is the perfect opportunity to introduce pi, 3.14 -- the ratio between the circumference and the diameter of a circle. Promote discussion to see if the students discover how to find the circumference of any circle. After discussion, share with the students the formula for finding the circumference: circumference = 3.14 x diameter.
Draw a circle on heavy colored paper. Divide the circle into 16 sectors with a black marker. Outline the circumference with a heavier black outline. Copy the circle for all of your students on colored paper. After discussing with the students ways to find the area of a circle, direct them to cut out each sector. After they have cut out each sector, tell them to make a rectangle with the sectors by alternating the curved edge of the circumference on the top edge and bottom edge of the rectangle. Glue the new rectangle to a piece of colored paper.
Label the base and the height of the new rectangle. Ask the students to identify which part of the circle the base and height are. Because of the heavier outline, they will notice the base is the circumference. They will be able to see the height of the rectangle is the radius of the circle. Since circumference of a circle is the diameter times pi, the base of the rectangle made out of the circle is half of the diameter times pi. The radius is half of the diameter, which results in the base represented by 3.14 x radius. The height is the radius. Therefore, the formula to find the area of a circle is area = 3.14 x radius squared.
Tips & Warnings
- Give the student with the smallest feet a large string.
- Give the student with the largest feet a small string.
- Some students will need help keeping the string taut to make a perfect circle.
- A mnemonic trick to remember the formula for circumference, C = pi x d, is "cherry pie delight."
- A mnemonic trick to remember the formula for area of a circle, A= pi x radius squared, is "apple pies are square."
- "Teaching Student-Centered Mathematics: Grades 5-8"; John Van DeWalle; June 2005
- Worsley School: The Circle Area Formula
- Photo Credit Jupiterimages/Photos.com/Getty Images Thinkstock/Comstock/Getty Images
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