7-3.5 How Far is it Around?! (Alternative)

This activity is an alternative to OUR lesson 7-3.5 Circumference and Wheels. In making this alternative I am attempting to clarify that the circumference of a circle is about 6 times the radius. I think it should be striking to the students that it is a lot further around around a circle than across. I want the students to feel this. The idea about how far a wheel rolls was addressed earlier in another alternative lesson. Additionally the students will get more practice with moving between the radius of a circle and the circumference. Here are the original goals and narrative from OUR 7-3.5 Circumference and Wheels Student Facing Goals If I know the radius or diameter of a wheel, I can find the distance the wheel travels in some number of revolutions. This lesson is optional. The goal of this lesson is to apply students’ understanding of circumference to calculate how far a wheel travels when it rolls a certain number of times. This relationship is vital for how odometers and speedometers work in vehicles. In previous lessons, students saw that the relationships between radius, diameter, and circumference of different circles are proportional relationships. In this lesson, they 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 also a proportional relationship between the number of times a wheel rotates and the distance the wheel travels. 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. Students make use of the structure of a proportional relationship as they work toward describing the relationship between the number of rotations of a wheel and the distance the wheel travels with an equation (MP7).

By Jeff Holcomb