In this video segment from Cyberchase Inez competes in a rollerblading competition against Rimm, a skater for Team Hacker. Just before Inez skates, Hacker changes the shape of the field. It still has the same perimeter, but it is much narrower. The CyberSquad decides to compare the perimeter and area of the three different fields they've had to skate on to make sure it is a fair competition.
Investigations/Scott Foresman (2006)
Flips, Turns, and Area (3rd Grade)
Investigation 1, Session 4: pp. 23-26
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: When we measure the distance around a football field we are finding its perimeter. When we measure the inside space of the football field, where the players actually play, we are measuring something totally different – the area. Do you think differently shaped fields can still have the same area? How is that possible?
Focus: As you watch this segment, look carefully at the pictures of the fields on the Skwak pad. Notice what measurements the CyberSquad chooses to make. What do the fields have in common? How are they different?
Follow Up: In this video segment, did the fields have the same perimeter? Did they have the same area? How did Hacker change the field before Inez had to skate? Can you draw two rectangles that have the same perimeter but different areas?
OLLIE: Totally more at stake now, dudes and dudettes. It’s time to skate the third and final round. And the team that’s losing skates first in the final round! Inez...you’re up!
HACKER: Not so fast! Since my team is in the lead, I’m changing the shape of the field!
INEZ: Not again!
HACKER: Yes, again! Ha ha ha!
DIGIT Look at the field! There’s less room inside than last time!
JACKIE: But it’s still twenty-six fence pieces around - I just counted ‘em! So it’s legal.
MATT: Time out! Time out! Something besides the shape is changing every time Hacker switches the field, and if we don’t figure it out fast, Radopolis will belong to Hacker!
INEZ: And so will I!
DIGIT I got a plan. Skwak it!
INEZ: Here, take the Skwak pad.
JACKIE: Ok, here’s the picture of the field I skated on. Four fence pieces this side and this side...
INEZ: And nine fence pieces here and here.
MATT: For a grand total of 26 pieces around - the legal perimeter.
INEZ: Now, let’s check Matt’s field. You know, it looks like maybe you did have less room inside than Jackie.
MATT: How can there be less room inside?
JACKIE: Room inside? That’s it! What’s inside is the area. We need to check the areas!
INEZ: And areas mean squares. Try adding squares to the pictures.
JACKIE: Oh man, look at that. 1, 2, 3, 4 times 9. My field has 36 squares inside.
MATT: 28, 29, 30! Hey, my field has 30 squares inside. No wonder I ran out of room!
DIGIT: This is unbelievable. Change the shape and the room inside changes too. Even though the distance around the outside stays the same.
MATT: It’s pretty amazing but the pictures don’t lie. Different shapes with the same perimeter can have different areas inside.
INEZ: Come on! We have to figure out how much room I have to skate on.
JACKIE: Yours is two by eleven... still 26 for the perimeter. What’s the new area inside?
INEZ: 22 squares! That’s 8 less than Matt - and 14 less than you had to bike on, Jackie!
DIGIT: I’m afraid Hack’s changes don’t give you much area to compete in, Inez.
JACKIE: No way Inez can win with so little room inside! She’s bound to go out! Bound to get a low score! Bound to be cheering on Hacker for the rest of her life!
INEZ: Coach, what do I do?
DIGIT: Well, let’s see, you got a smaller field ...less room inside, I dunno...keep your tricks small?
OLLIE: We’re back and ready for round three! Inez vs. Rim! Does Inez totally have her work cut out for her or what?! Not only is her team losing 19 to 10 but she has to skate against Rim, the top ranked skater in all of cyberspace!
DIGIT: Okay, now remember, less area, less room, smaller tricks!
INEZ: Got it!
JACKIE: You can do it, Inez!
MATT: Go get ‘em, Nezzie!
INEZ: Don’t call me Nezzie!
MATT: She’s ready.
OLLIE: And Inez starts off with a nice minibackscratcher!
INEZ: Keep it small... don't go wide...
OLLIE: The mini-sow cow! Controlled, and away from the fence. Wicked! A mini-whirlwind 720! A mini-tucked Nollie!
MATT:/JACKIE:/DIGIT: Go Inez, go! You’re the girl! She’s running out of steam! Oh, but she finishes the move! A totally heroic skate!
JACKIE: Way to go, Inez!
DIGIT You’re the best!
MATT: Totally awesome!
INEZ: Totally small!
OLLIE: It’s a perfect score of 10! A 10! A 10! Motherboard’s All-Stars lead 20 to 19 with Rim to skate!
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