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Hacker's Four-Zergen Game

Media Type:
Video

Running Time: 3m 02s
Size: 8.2 MB

or

Source: Cyberchase: “R-Fair City”

Collection Developed by:

Collection Credits

Collection Funded by:

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, the CyberSquad is testing various games to decide if they are fair or not. Matt, Jackie and Lucky play a game called The Squares Game. They play it and then analyze the outcome to decide whether the game is fair.

Connections

Everyday Math (2004)
Teacher Lesson Guide, pp. 104-109, 876-882
Student Reference, pp. 47, 58, 109, 119, 121-124
Math Journal, pp. 43-45, 410-413
Math Master, pp. 16, 168-169, 232, 367

Investigations/Scott Foresman (2006)
Between Never and Always (complete)
Data: Kids, Cats, and Ads (complete)

Teaching Tips

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: Let’s say you roll a pair of dice. Then, after you roll, you add up the results to get the sum. Will a sum of two come up very often? Why or why not? How about a sum of seven? Why or why not? What determines how often a certain sum will come up?

Focus: In this video segment, Jackie and Inez analyze the possible results for the Four Zergens in a Hat Game. Write down the combinations that they come up with. How did they decide that the game was unfair?

Follow Up: How many different outcomes were possible in the Four-Zergen Game? What were the chances of the CyberSquad winning? How do we know when a game is fair?

Transcript

MATT: We're looking for a very...special kind of game.

HACKER (MADAME N): Hey, watch it! I mean watch Madame N show you special game. Game is called Four Zergens in Hat. Four Zergens. Number one, two, three four. See? No tricks. Pick two Zergens from hat at same time. Multiply the two numbers. If answer is even number, keedies lose. Odd number, keedies win - and Katrina take dip in water.

JACKIE: Euw! That water's disgusting!

MATT: What if we lose?

HACKER (MADAME N): Then you take dip in water. You play?

INEZ: Hold on a sec. What do you think, Lucky?

LUCKY: I've never played this game before.

MATT: Well someone has to! I'll play!

HACKER (MADAME N): Splendid! Take seat by charming assistant.

HACKER (MADAME N): Get odd number... this cutey hat is yours. Ah-ah-ah-ah! No peeking!

MATT: No problem! Oh, no! One times four is four - an even number!

DIGIT: Matty??!

MATT: Digit!

INEZ: We want our friend back. Now!

HACKER (MADAME N): Ohhhh, keedies upset. You vant to play again?

JACKIE (SOFTLY): We should've given this game a fairness check before Matt played.

INEZ: We'll be right back.

JACKIE: The only way to find out if this game is really fair is to figure out if everyone's chance of winning is the same.

LUCKY: While you do that, I'll nose around for Matt.

INEZ: We need to know how many pairs turn out odd, and how many turn out even.

JACKIE: Let's say we pick a one. That means the other number could be a two - a three - or a four. The 1 is paired with a 2 - and 3 - and 4, making three pairs of numbers in a row.

INEZ: Cool! Now What?

JACKIE: Well, if we pick a two, what other numbers go with it? A two and a one. We've already got that.

INEZ: So the other pairs are a two/three and a two/four. And what if we picked a three first.

JACKIE: Then the only pair we don't have is a three and a four. 1, 2, 3, 4, 5... there are only 6 different combinations.

INEZ: So like in the game, let's multiply the pairs of numbers and see how many come out odd - and how many come out even.

JACKIE: 2, 3, 4, 6, 8, 12. Look! Five of the six pairs come out even!

INEZ: And only one pair comes out odd! Since we win when the answer's odd - we only have one chance out of six of winning!

JACKIE: And Madame has five chances out of six of winning!

INEZ: That's not only unfair - it sounds like a trick!

JACKIE: And that means...Hacker!

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