Unit 3, Lesson 3
Exploring Circumference
Grade 7
Preparation
Lesson Narrative
In this lesson, students discover that there is a proportional relationship between the diameter and circumference of a circle. They use their knowledge from the previous unit on proportionality to estimate the constant of proportionality. Then they use the constant to compute the circumference given the diameter (and vice versa) for different circles. Students learn that pi (
Determining that the relationship between the circumference and diameter of circles is proportional is an example of looking for and making use of structure and repeated reasoning (MP7, MP8).
- Comprehend the word “pi” and the symbol
to refer to the constant of proportionality between the diameter and circumference of a circle. - Create and describe (in writing) graphs that show measurements of circles.
- Generalize that the relationship between diameter and circumference is proportional and that the constant of proportionality is a little more than 3.
Required Materials
Activity 1
Required Preparation
Activity 1
The empty toilet paper roll is for optional use as a demonstration tool.
Activity 2
Household items: collect circular or cylindrical objects of different sizes, with diameters from 3 cm to 25 cm. Each group needs 3 items of relatively different sizes. Examples include food cans, hockey pucks, paper towel tubes, paper plates, CD’s. Record the diameter and circumference of the objects for your reference during student work time.
Provide one measuring tape per group of 2--4 students. Alternatively, use rulers and string.
To get a good spread of points on the graph, it is important to use circles with a wide variety of diameters, from 3 cm to 25 cm.
For the digital version of the activity, acquire devices that can run the applet.