Source: Cyberchase: “R-Fair City”
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 wants to see a movie but she can’t decide which of the two movies she should see. To help her decide, she flips a coin. The coin comes up “heads” three times in a row. This surprises Bianca, so she does some research to find out the probability of landing on heads or tails when flipping a coin.
Download and ShareInvestigations/Scott Foresman (2006)
Between Never and Always (complete)
Data: Kids, Cats, and Ads (complete)
Investigation 3, Sessions 1-4, pp. 44-67
Investigation 4, Sessions 1-3, pp. 68-81
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: If you roll a pair of dice and add them together, you might get a sum of “2” on your first roll. Does that mean that “2” is the most likely sum to come up? Why or why not? How many times do you think you would have to roll the dice to get some accurate data about which sum comes up the most?
Focus: Bianca does some research on what a “50-50 chance” means when flipping a coin. What does she find out? After she reads that she must make “many” coin flips, what does she do? How many coin flips does she perform in order to get more accurate results?
Follow Up: When Bianca was flipping a coin, could she accurately predict which side would come up next? Why or why not? When we say that the chances of something happening are “even-steven” or “50-50,” what do we mean?
BIANCA: I’m just in time. I really don’t like it when I miss the start of a movie. There were two films that I really wanted to see. One is this new dinosaur movie and the other stars Giovanni, my favorite actor. So when I got to the box office…
BIANCA: I don’t know which one to pick? I’ll flip a coin: heads “dinosaurs,” tails “Giovanni.” (Flips coin) “Heads.” I wonder what will happen if I try that again? (Flips coin) “Heads.” Again. (Flips coin) “Heads”. It doesn’t seem fair. Poor Giovanni didn’t come up once! Is it fair? Even steven? Fifty fifty? (Flips coin) Finally! But that’s three heads to one tail. It doesn’t seem fair. So I decided I wanted to do some research on why Giovanni didn’t win half the time.
BIANCA: “Fred’s Encyclopedia of Probability!” Let’s see. One in a million, one in a thousand, one in a hundred… Here we go, fifty fifty. When flipping a fair coin about half the time it will be heads and about half the time tails. See note, see note… Note. This will only happen if you flip the coin many times. Well I flipped the coin four times but I got three heads to one tail, and that’s not half and half. (reads book) You have to flip a lot more than four times.
BIANCA: Hey do you remember I asked you to hold my place?
GIRL IN LINE: Yes.
BIANCA: Okay, great. Thanks. Wait a minute! Flipping ten coins one time is the same as flipping one coin ten times. Excuse me, I’m trying to find out if I flip a coin a lot of times, will the results really be fifty fifty? Heads about half the time and tails about half. Will you help me? C’mon, it will only take a minute.
BIANCA: How many heads raise your hands? Hmm… only three heads and seven tails. With ten coin flips, that’s still not very close to fifty fifty. I need to try this with a lot more people.
BIANCA: This better work. Can I borrow that for a second?
MAN: Sure.
BIANCA: Thank you. Hello, I need everyone to flip a coin to see if heads really does come up about half the time. Just the people who got heads, raise your hands.
BIANCA: How many people here?
MAN: Three hundred and fifty paid at the gate.
BIANCA: Wow! Then it is true. I think I could say that’s pretty much fifty fifty. Thanks. Fred’s encyclopedia was right. If you flip a coin just a few times it might not be close to fifty fifty. But if you flip lots of times, like three hundred and fifty, then it will be closer to heads about half the time and tails about half.
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