#1638. Finding the circumference given the radius

Mathematics, level: Middle
Posted Mon Mar 20 20:53:47 PST 2000 by Mitch (rururu@yahoo.com).
Univ. of S. Florida, USA
Materials Required: Construction paper, scissors, etc.
Activity Time: 45 min.
Concepts Taught: geometry, pi

I. Lesson Title: Finding the circumference given the radius

II. Subject: Mathematics

III. Grade Level: G6-7

IV. Goal: Develop an understanding of pi and the relationship between the diameter/radius and the circumference.

V. Objectives: The students will:
1. Define pi.
2. Find the circumference given a diameter or a radius.
3. Find a diameter or a radius given the circumference.

VI. Materials:
1. Construction paper
2. Scissors
3. Compasses
4. Yarn or thread
5. Rulers (at least 50 cm long)
6. Handout with a blank matrix. The matrix has five rows and three columns. The columns in the top row are labeled as Radius, Diameter and Circumference. The column labeled Radius has the following values from the top to the bottom rows: 6, 8, 10 and 12. One of those four numbers is randomly circled by the instructor beforehand, which is the radius assigned to a particular student.
7. Paper and pencil

VII. Procedures:
1. Distribute handouts and construction paper.
2. Explain to students the definition of radius, diameter and circumference.
(Also explain to them how to use a compass if they do not know how.)
3. Have students draw a circle using a compass with a radius assigned to them, and cut it as precisely as possible.
4. Using the yarn, let them measure the circumference of the circle, and fill in diameter and circumference for the assigned radius.
5. First, let students contemplate the relationship between the diameter and the circumference. For those who can not find it, give the following formula and let students fill in the space.
(Assigned diameter) x ( ) = (measured circumference)
6. Have students guess what the circumferences of the circles are with the non-assigned radii and instruct them to write them down in the matrix.
7. Have students compare the guessed value with those measured by the other students who were assigned to such radii.
8. Explain to students that what they have found is pi and that they can find the circumference if given the diameter/radius or the diameter/radius if given the circumference. Give some problems and have students solve them.

VIII. Assessment:
1. The handout with a matrix on it is collected at the end of class. (3 points)
2. A quiz will be given at the beginning of the next meeting. In the quiz, students will be asked to find the circumference given the diameter/radius or the diameter/radius given the circumference. (7 points)

IX. Evaluation: The lesson plan will be evaluated based on the following questions.
1. Did students cut the circle and measure its diameter precisely?
2. Did students engage in the task without being distracted?
3. Based on the assessment, did students reach the objectives?