Source: Cyberchase: “Fortress of Altitude”
Funding for the VITAL/Ready to Teach collection was secured through the United States Department of Education under the Ready to Teach Program.
In this video segment from Cyberchase, Bianca is getting ready to run in a race on a 200 meter track. She notices that the starting positions in the six lanes are at different points along the track. She believes this is unfair and sets out to measure the distance between the starting point and the finish line in both the outside and the inside lanes.
Grade 5: Measurement Benchmarks
Investigation 1, Sessions 1-8: pp. 2-41
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 you run a race, how do you make sure it is fair for all the participants? Many races are run on tracks. Why do you think most tracks have a curved, oval-like shape? If you were running on an oval, would you want to be in the lane closest to the center or farthest away, or in one of the lanes in the middle? Why?
Focus: Bianca measures two of the lanes on the track that she is about to run on. Does she find that the distances are equal? How can that be when she is starting so much further back?
Follow Up: What measuring tools did Bianca use to determine if the two lanes were equal in distance? What shape was the track? Would it have been different if the race was on a straight course instead of a curved track?
BIANCA: I gotta get to the track. Today is my first official race since I unofficially ran in the New York Marathon.
BIANCA: I'm really excited. I feel like a winner today!
BIANCA: Hi. I'm Banca. Is this your first time, too?
GIRL #1: No. We've been competing for about three years.
ANNNOUCER: Lane One: Degroat; Two, Johnson; Three, Wright; Four, Hakim; Five, Armstrong; Six, Washington.
GIRL #3: Hey, you need to move back to your starting position. That's in lane one, back there.
BIANCA: Back there? That's not fair!
GIRL #1: Yes it is.
BIANCA: You guys have the advantage.
BIANCA: If I'm starting way back there, then the rest of you will have a head start.
GIRL #3: No. We're all running the same distance.
BIANCA: I'll prove it's not true. I'll just measure the distance from start to finish around lane one and compare it to the distance from start to finish around lane six. Now what can I use to measure the distance? Great!
BIANCA: One, Two, Three, Four, . . .
GIRL #1: Come on!
BIANCA: I just need a minute. Now where was I? There's got to be a better way than this.
BIANCA: A tape measurer! This measures up to 20 feet! It's much better than a one foot ruler!
BIANCA: Would you please step on this?
GIRL #2: Forget about it. Here comes the official.
STARTER/OFFICIAL: It's time for the race to start. What are you doing?
BIANCA: I'm trying to prove that it's unfair for me to start further back than the other runners.
STARTER/OFFICIAL: It is fair. If you and the person in the outside lane both started at the same place, she would have to run a longer distance. That's because the track curves less on the outside than it does on the inside. The starting points in each lane are staggered, so all athletes run the same distance.
BIANCA: With all due respect, I find that hard to believe.
STARTER/OFFICIAL : I've got something that will work better than a tape measurer.
STARTER/OFFICIAL: This is a trundle wheel. The perfect measuring tool for this situation. With every rotation of the wheel, it travels a meter, and the counter advances by one.
BIANCA: The distance from the starting point to the finish line . . . in lane one . . . is 200 meters.
OTHER RACERS: Bianca!
BIANCA: Please? I just need to measure lane 6.
BIANCA: So the distance . . . from the starting point to the finish line in lane six is 200 meters!
BIANCA: It is fair. The distances in the lanes are equal. I was wrong!
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