In this student centered lesson, the teacher relates the skill of finding the circumference of a circle to everyday life circular objects. In order to do this, the teacher takes the students down to the gymnasium and they are asked to find or calculate the radius, diameter, and circumference of a frisbee, bottom of a water bottle, hula hoop, and the circle in the center of the gymnasium. Also, the idea for this lesson was based off of a research article that explained effective methods for teaching this concept to students.
Lesson: Radius, Diameter, and Circumference of a Circle (8.3)
New Jersey Core Curriculum Content Standards
4.2E Measuring Geometric Objects
1. Develop strategies for finding the circumference of a circle
Focus: Connections and Problem-Solving
Learning Objectives
· Given a circle with any radius or diameter, students will correctly calculate its circumference.
· Given a circle with any circumference, students will correctly calculate its radius and diameter.
Lesson Strategy
In order to introduce today’s lesson, the teacher will talk to students about sports and ask how many participate in them. Then, the teacher will explain to students today’s activity and take the class down to the gym where the basketball court is located. Once in the gym, there will be stations set up. Students will complete Radius, Diameter, and Circumference of a Circle (1) worksheet in their groups. Students will use string, meter sticks, rulers, and calculators to help them complete the worksheet. This activity gives the students practice in finding the radius, diameter, and circumference of everyday, different-sized circular objects. After the activity, the students will return to the classroom and the teacher will facilitate a class discussion.
This lesson accommodates all three different types of learners. The kinesthetic learners will learn by actually measuring objects to find the radius, diameter, and circumference. The auditory learners will benefit by talking with their group members and discussing what they have found for the different measurements. Finally, the visual learners will like the worksheet created by the teacher so they can visually see their data and keep it organized.
Adaptations: If students are having difficulty measuring the circumference, diameter, and radius using a piece of string and a ruler, the teacher can show students several demonstrations. In addition, the teacher should walk around the gym and aid students if they are having trouble. Once students have returned to the classroom, the teacher will facilitate a class discussion about the activity. If there is not enough time for a discussion, the teacher will collect the worksheet and review it to see if students understand the material.
Materials
· Pencils
· Rulers
· Calculators
· Meter Sticks
· Scissors
· String (about 20 pieces cut at appropriate lengths, extra should be prepared)
· Worksheets: Radius, Diameter, and Circumference of a Circle (1, 2)
Preparation
The teacher needs to prepare worksheets Radius, Diameter, and Circumference of a Circle (1, 2). In addition, he or she must reserve the gym and the appropriate equipment (frisbees and hula hoops) if necessary. Also, the teacher must have string cut at appropriate lengths, as well as a few water bottles for one of the stations. Before class, the teacher needs to set up the stations in the gym. The stations should already have the equipment set up as well as string for students to use to help them measure. The activity should be performed ahead of time by the teacher, so that he/she has all of the correct measurements and calculations. The teacher should know in advance which students will be working together (there will be approximately four students per group).
The students should have completed Circumference of a Circle (3) worksheet, which will be discussed at the beginning of class.
Procedure
Before
· Review homework: Circumference of a Circle (3) worksheet
- Ask students to volunteer answers
- Answer any questions
· Introduce today’s lesson
- Ask students if they like to play sports
- If so, which sports do they participate in?
- Tell students that we are going to the gym to measure the radius, diameter, and circumference of different objects (circle in center of the gym, frisbee, water bottle, and hula hoop)
- Tell students that they will measure the radius, diameter, and circumference of the objects the same way that was done the previous class period (using a string and a ruler/meter stick)
- Tell students which groups they will be working in (heterogeneous groups of four)
- Tell students that they must complete Radius, Diameter, and Circumference of a Circle (1) worksheet
· Ask students to help hand out materials
- Radius, Diameter, and Circumference of a Circle (1) worksheet (one per student)
- Ruler (one per group)
- Meter Stick (one per group)
- Calculator (one per student)
- Scissors (one per group)
· Read directions on the worksheet and answer any questions
· Take students to the gym
Activity
· Once in the gym, show students the different stations
- There will be one station for Circle in the Center of the Gym
- There will be two stations for Water Bottles
- There will be two stations for Frisbees
- There will be two stations for Hula Hoops
- Groups will be assigned which station to begin at
- After a group has completed a station, they should move to a new one
- If students have to wait for a station, they can do calculations for questions 2 and 3 for each object while they wait
· The teacher should walk around the gym to observe and help students if necessary
· After students are finished, students should return to the classroom
Summary and Reinforcement
· The teacher will facilitate a class discussion about the lesson and what students have found
· Students will be asked to share what they found for the radius, diameter, and circumference of the different objects
· If there is not enough time for a class discussion, the worksheet will be collected
· Instruct students to complete Radius, Diameter, and Circumference of a Circle (2) worksheet for homework
Assessment
During the activity, the teacher will be able to listen to what the students are talking about and discovering as he or she walks around the gym. The teacher will also evaluate whether or not students understand radius, diameter, and circumference and how they are related by the class discussion. If there is not enough time for the discussion, the teacher will be able to see students’ work by collecting the worksheet. Also, the teacher will be able to assess students understanding according to their homework assignments.
Resource
Tent, Margaret T. “Circles and the Number Pi”. Mathematics Teaching in the Middle School. Vol. 6, April 2001.
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