IM: 7.3.4: Applying Circumference (Lesson)

Last updated 11 months ago

10 questions

4.1: What Do We Know? What Can We Estimate?

4.2: Using π

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 π  for you to use in this activity.

4.3: Around the Running Track

4.4: Measuring a Picture Frame

IM: 7.3.4: Applying Circumference (Lesson)

Last updated 11 months ago

10 questions

4.1: What Do We Know? What Can We Estimate?

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?

4.2: Using π

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 π  for you to use in this activity.

Complete the table.

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?

https://curriculum.illustrativemathematics.org/MS/students/2/3/4/index.html

[Scroll to the tool under "4.2: Using π"]
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” to watch the bug’s motion.

4.3: Around the Running Track

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?

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?

4.4: Measuring a Picture Frame

Kiran bent some wire around a rectangle to make a picture frame. The rectangle is 8 inches by 10 inches.

IM: 7.3.4: Applying Circumference (Lesson)

IM: 7.3.4: Applying Circumference (Lesson)

For each picture, which measurement is shown?

Based on this information, what measurement(s) could you estimate for each picture?

Complete the table.

What is the distance around the inside of the track? Explain or show your reasoning.

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.

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?

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?

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?

For each picture, which measurement is shown?

Based on this information, what measurement(s) could you estimate for each picture?

Complete the table.

What is the distance around the inside of the track? Explain or show your reasoning.

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.

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?

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?

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?