## Wheeling Around

### April JacksonEscambia County Schools

#### Description

This activity is a fun way to use real-life examples to introduce circles. This lesson explores the characteristics of a circle and the formulas to find circumference. The student uses a bicycle wheel to determine the circumference around a wheel.

#### Objectives

The student applies formulas for finding rates, distance, time and angle measures.

#### Materials

-Transparency markers or chalk
-Example Problems (See Associated File)
-Vocabulary handout (See Associated File)
-Pencils
-Bicycle wheel
-Characteristics of a Circle (See Associated File)
-Answers to Example Problems (See Associated File)
-Formulas (See Associated File)

#### Preparations

1. Gather materials for the activity.
2. Make student copies of the Vocabulary and Example Problems. (See Associated File)
3. Print out the Characteristics of a Circle, Answers to Example Problems, and Formulas pages for teacher's use. (See Associated File)

#### Procedures

Note: This lesson addresses only applying formulas for finding distance around a circle (circumference).

1. Gain attention by placing the bicycle wheel in front of the class and then drawing a circle on the board or overhead projector.

2. List the objectives of the lesson on the board or overhead:
Locate the center of the circle.
Locate the diameter of the circle.
Locate the radius of the circle.
Use the circumference formulas to calculate the distance around the circle.

3. Tell the students that we will be studying circles today.

4. Talk about the characteristics of a circle. (See Associated File)

5. Estimate and label the center of the circle with the letter A. Also, for visual learners, write the word center by the letter A.

6. Draw a line segment from one side of the circle, through the center, to the other side of the circle.

7. Label the line segment B on one end and C on the other end. Write the word diameter on the line and define the word diameter using the Vocabulary handout. (See Associated File)

8. Draw a line segment from point A to the outside of the circle.

9. Label the outside of the new segment with a D. Write the word radius on the segment and define the word radius using the Vocabulary handout. (See Associated File)

10. Go back to the original circle. Switching back and forth from the radius, to diameter, to center, have the students name each of them.

11. Pull out the bicycle wheel that you brought to the classroom.

12. Have the students identify the wheel as a circle.

13. Ask the students to identify the center of the wheel.

14. Ask the students to identify the diameter of the wheel. (The diameter is any two spokes that go from side to side on the wheel and pass through the center.)

16. Ask the students what happens when the wheel or circle turns. Wait for student feedback.

17. Guide students to tell you that when the circle turns it goes all the way around one time. Prompt students to tell you that one time around refers to the distance around the circle (circumference).

18. Ask students if they think we can determine the distance around the outside of the circle. We measure the distance of a line segment with a ruler. Guide students to discover that there is a way we can determine the distance around the circle.

19. Tell students that we can determine the distance around the circle and give them the formula. Talk about the two formulas for circumference. (See Associated File)

20. Explain to the students that pi and the symbol for pi is (3.14) and r is (radius) and d is (diameter).

21. Show the bicycle wheel again. Give the students a radius measurement of 10 inches of the wheel and ask them to determine the circumference. (2)(3.14)(10)=62.8 inches. Put all the answers given on the board. Work the problem out to arrive at the correct answer.

22. Show the bicycle wheel again. Give the student a diameter measurement of 20 inches of the wheel and ask them to determine the circumference. (3.14)(20)=62.8 inches. Put all the answers on the board. Work the problem out to arrive at the correct answer.

23. WOW! The kids got the same answer on the radius and diameter problem. Help students make the connection that the two circumference formulas give you the same answer because the diameter is made up of two radii.

24. Make the connection that the one time around the wheel is the circumference. The distance around the wheel is the circumference.

25. Provide five circles for the students and ask them determine the distance around the circles using one of the circumference formulas. Use the Example Problems handout if desired. (See Associated File)

#### Assessments

NOTE: This lesson addresses circumference only. This lesson is based on prior knowledge of the shape of a circle. This lesson assumes prior knowledge of basic mathematical computational skills.

1. Given a circle with points and line segments labeled, the student uses these labeled segments to determine the circumference of the circle by using the formulas for circumference.

2. To determine if the student understands the concept of using the circumference formulas for finding the distance around a circle, they need to correctly find the circumference of four out of the five Example Problems given in the associated file. Students who do not successfully complete four out of the five problems should receive additional instruction.