Lesson 4Applying Circumference
Learning Goal
Let’s use
Learning Targets
I can choose an approximation for
based on the situation or problem. If I know the radius, diameter, or circumference of a circle, I can find the other two.
Lesson Terms
- circle
- circumference
- diameter
- pi (π)
- radius
Warm Up: What Do We Know? What Can We Estimate?
Problem 1
Here are some pictures of circular objects, with measurement tools shown. The measurement tool on each picture reads as follows:
Wagon wheel: 3 feet
Plane propeller: 24 inches
Sliced Orange: 20 centimeters
For each picture, which measurement is shown?
Based on this information, what measurement(s) could you estimate for each picture?
Activity 1: Using
Problem 1
In the previous activity, we looked at pictures of circular objects. One measurement for each object is listed in the table.
Your teacher will assign an approximation for
If you choose to, you can change the settings in the applet and enter your calculation in the box at the bottom to check your work.
Just for fun, use the slider marked “turn,” and the other one that will appear, to watch the bug’s motion.
Complete the table.
object
radius
diameter
circumference
wagon wheel
airplane propeller
orange slice
A bug was sitting on the tip of a wind turbine blade that was 24 inches long when it started to rotate. The bug held on for 5 rotations before flying away. How far did the bug travel before it flew off?
Print Version
In the previous activity, we looked at pictures of circular objects. One measurement for each object is listed in the table.
Your teacher will assign you an approximation of
Complete the table.
object
radius
diameter
circumference
wagon wheel
airplane propeller
orange slice
A bug was sitting on the tip of the propeller blade when the propeller started to rotate. The bug held on for 5 rotations before flying away. How far did the bug travel before it flew off?
Activity 2: Around the Running Track
Problem 1
The field inside a running track is made up of a rectangle that is 84.39 m long and 73 m wide, together with a half-circle at each end.
What is the distance around the inside of the track? Explain or show your reasoning.
The track is 9.76 m wide all the way around. What is the distance around the outside of the track? Explain or show your reasoning.
Are you ready for more?
Problem 1
This size running track is usually called a 400-meter track. However, if a person ran as close to the “inside” as possible on the track, they would run less than 400 meters in one lap. How far away from the inside border would someone have to run to make one lap equal exactly 400 meters?
Activity 3: Measuring a Picture Frame
Problem 1
Kiran bent some wire around a rectangle to make a picture frame. The rectangle is 8 inches by 10 inches.
Find the perimeter of the wire picture frame. Explain or show your reasoning.
If the wire picture frame were stretched out to make one complete circle, what would its radius be?
Lesson Summary
The circumference of a circle,
If the diameter of a car tire is 60 cm, that means the radius is 30 cm and the circumference is
If the radius of a clock is 5 in, that means the diameter is 10 in, and the circumference is
If a ring has a circumference of 44 mm, that means the diameter is