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CCSS.Math.Content.7.G.B.4: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle
Materials: jump ropes, chalk, rulers (yardsticks or measuring tape work well too), outdoor space on asphalt, graph paper
Preparation: Prepare materials by having pre-measured ropes of varying lengths available for students (one for each group to use as a “radius"), and long ropes for students to measure circumference of their circles. You will need a clipboard with a pre-made chart to write down the radius and circumference as measured by each group during the outside portion of the lesson.
Students should be familiar with the basic parts of a circle (radius and diameter) and should have some previous exposure to the concept of pi.
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Step One: Introduction
Take your class outside and ask students to get into groups of five. Direct students to form circles with their groups by joining hands, pointing out that the students represent the circumference of a circle. Lead the class in a discussion of situations where people might need to know the circumference of real-life circular objects.
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Step Two: Modeling Radius and Circumference
Once students are standing in their group circles, each group will send one member to the middle of the circle with a pre-measured rope. Assist students in stretching the rope from the person in the center to one of the group members on the outer edge of the circle, representing the radius.
While holding the rope, the student on the outer edge will walk around the circle, using chalk to draw the circle’s circumference. Once the circle is drawn, students will lay the rope down on the ground. Have your students use chalk to draw a line from the center of the circle to the outer edge (using the rope as a guide). After drawing the radius, students will measure the radius using yardsticks, measuring tape or rulers, writing the measurement down along the radius.
Ask students to then measure the circumference of the circles by laying the longer jump ropes along the outer edge of the circles, and picking those jump ropes up and using their yardsticks (or similar measuring tools) to measure the length of the rope used to find the circumference of the circles. Students will note the measurement of the circumference along the outer edge of the circle in chalk.
Walk around and collect data from each group, noting the radius and circumference of each circle. After all data has been collected, return to the classroom.
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Step Three: Discussion and Connection
Lead the class in a discussion of their experiences using the ropes and chalk to measure the parts of a circle. After students have shared their observations, make a chart on the board, sharing the data collected during the experiment.
At their desks, students will use graph paper to make simple charts to show the relationship between the radius and circumference of a circle. Students should plot the measurement of the radius and the circumference of each circle from the outside experiment, noting that as the size of the radius increases, so does the circumference of the circle.
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Step Four: Reflection and Assessment
Ask students to spend a few minutes writing about their experiences with measuring the parts of a circle. Students should address the following topics in their writing:
- What would have happened to their circles if the ropes they were given to demonstrate radius had been shorter? Longer?
- What are some real-life situations in which it would be important to know a circle’s circumference?
- In addition to ropes, what are some other objects or methods that could have been used to find the length of the radius and measurement of the circumference of each group’s circles?
Check or collect student writings to determine the level of understanding they reached during the experiment.