Unit 3, Lesson 5
Circumference and Wheels (Optional)
Grade 7
Preparation
Lesson Narrative
This lesson is optional because it goes beyond grade-level expectations. The goal of this lesson is to extend students’ understanding of circumference by exploring various proportional relationships related to how far a wheel travels when it rolls. This relationship is vital for how odometers and speedometers work in vehicles.
First, students notice that the circumference of a circle is the same as the distance a wheel rolls forward as it completes one rotation. Next, they see that there is a proportional relationship between the number of times a wheel rotates and the distance the wheel travels. Students use quantitative and abstract reasoning to represent this relationship with an equation (MP2). The last activity examines the relationship between the speed a vehicle is traveling and the number of rotations of the tires in a given amount of time.
- Compare wheels of different sizes and explain (orally) why a larger wheel needs fewer rotations to travel the same distance.
- Generalize that the distance a wheel rolls in one rotation is equal to the circumference of the wheel.
- Write an equation to represent the proportional relationship between the number of rotations and the distance a wheel travels.
Let’s explore how far different wheels roll.
Required Materials
Required Preparation
The circular objects that students measured earlier can be reused for this activity. Rather than wrapping something around each circle, students will roll the circle on a flat surface in order to measure its circumference. If reusing the same set of circular objects, make sure that the groups do not get the objects that they did in the previous activity.
Prepare to distribute blank paper that is long enough for students to trace one complete rotation of their cylindrical object. For objects with a diameter greater than 4 inches, receipt tape may be better.