IM 7.3.5 Lesson: Circumference and Wheels
Han says that you can wrap a 5-foot rope around a wheel with a 2-foot diameter because is less than pi. Do you agree with Han? Explain your reasoning.
Explore the app below where you will roll a circle on a line. Then you will mark how far the circle travels and the length of its diameter.
What do you notice?
Use your ruler to measure each distance. Record these values in the first row of the table.
If you wanted to trace two complete rotations of your object, how long of a line would you need?
Share your results with your group and record all of your groups measurements in one table.
If each person in your group rolled their object along the entire length of the classroom, which object would complete the most rotations? Explain or show your reasoning.
A car wheel has a diameter of 20.8 inches.
About how far does the car wheel travel in 1 rotation? 5 rotations? 30 rotations?
Using the same car wheel as above, write an equation relating the distance the car travels in inches, , to the number of wheel rotations, .
About how many rotations does the car wheel make when the car travels 1 mile? Explain or show your reasoning.
A bike wheel has a radius of 13 inches.
About how far does the bike wheel travel in 1 rotation? 5 rotations? 30 rotations?
Using the same bike wheel as above, write an equation relating the distance the bike travels in inches, , to the number of wheel rotations, .
About how many rotations does the bike wheel make when the bike travels 1 mile? Explain or show your reasoning.
Here are some photos of a spring toy.
If you could stretch out the spring completely straight, how long would it be? Explain or show your reasoning.
The circumference of a car wheel is about 65 inches.
If the car wheel rotates once per second, how far does the car travel in one minute?
If the car wheel rotates once per second, about how many miles does the car travel in one hour?
If the car wheel rotates 5 times per second, about how many miles does the car travel in one hour?
If the car is traveling 65 miles per hour, about how many times per second does the wheel rotate?