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Relationship between Diameter and Circumference

Resource for Grades 3-5

Media Type:
Video

Running Time: 3m 40s
Size: 10.2 MB

or

Source: Cyberchase: "Spheres of Fears"

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Collection Credits

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The CyberSquad is trapped in one of the Spheres of Fears, and they are trying to get through a gate to escape. The key to the gate is locked inside a can, and in order to access the key they must attach the correct label to the can. After guessing incorrectly on the first try, the CyberSquad decides to take some measurements to find the correct label. Using two circles nearby, they compare the diameter of each circle to its circumference. They realize there is a special relationship between the circumference of a circle and the length of its diameter.

Alternate Media Available:

Transcript (Document)

Frame/Focus

Here are some Frame, Focus and Follow-up suggestions for using this video in a math lesson.

What is Frame, Focus and Follow-up?

Frame: Circles have a radius, a diameter, an area and a circumference. Sometimes it's helpful to know the diameter of a circle—like with a bicycle tire or a pizza. Other times it's more helpful to know the circumference—like when you want to make a circular fence around a trampoline or swimming pool. What is the relationship between the circle's radius and its diameter? Can you think of other things that are measured by their radius or diameter?

Focus: Pay attention to how the CyberSquad figures out the circle's circumference based on its diameter. Note what the relationship is that exists between the diameter and the circumference.

• What did the CyberSquad find the relationship between the circumference and the diameter to be?
• How did they know when they had the correct label for the can?
• Using the approximations from the video, if you have a 10" pizza and and18" pizza, approximately what is the length of crust on each pizza?

Transcript

MATT: I don’t know what Hacker’s up to, but we gotta get outta here fast!

JACKIE: How? We can’t even get through the gate to get to the code book!

DIGIT: Yes we can!

DIGIT: First you put in a cyber-coin. Then you get a can. All the cans in here have a key to open the gate! All ya do is pick the label that fits the can - ya know, the one that goes all the way around the can just right.

INEZ!/JACKIE/DIGIT: How about this one?/Uh-uh, I think it’s this one?/No, the long one!

MATT: Let’s just try this one!

MATT: Nope, too short!

MATT: Sorry...

JACKIE: Didge, we need another coin!

DIGIT: Right. Last one. So no guessing this time.

INEZ: We need to figure out for sure which label fits the can. How do we do that?

MATT: I’ve got it! I can measure around the can with this licorice.

MATT: No I can’t, it keeps slipping. But wait! I can measure the diameter. Does that help?

INEZ: Dunno... Do you think there’s a way to use the diameter to figure out the circumference?

JACKIE: Worth a try! Let’s measure some circles and see. Let’s try this round rock.

MATT: First the diameter.

JACKIE: And now the circumference.

JACKIE: Man, the circumference is a lot longer than the diameter!

JACKIE: About one...two...three times longer!

DIGIT: So it takes a little more than three diameters to equal the circumference of this circle!

INEZ: Let’s see if the same is true for this bigger circle!

INEZ: The diameter...and the circumference.

MATT : Huh! Different size circle, but same result: the circumference is still a little more than three times the diameter. We’re good to go!

JACKIE: What was that?!

DIGIT: The most terrifying Creeper of all--the King Creeper!

JACKIE: We gotta get through that gate NOW!

MATT: Okay, the diameter is this long!

INEZ: And we know the rule: to reach all the way around, the length of the label has to be a little more than three times the diameter!

MATT: Whoa!

DIGIT: Hurry...measure it already!

MATT: One diameter, two diameters, three diameters...and a little bit more!

MATT: Now we need the label that matches this length! Touchdown!

JACKIE: All right!

JACKIE: It fits just right!

JACKIE: Yes! I got the key!

DIGIT: Open the gate! Open the gate!

INEZ: Hurry! Hurry!

Standards

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