Modeling Prompt

If time is limited, the question about flipping 6 coins can be skipped. If an additional challenge is desired, students can generalize the fair games they created for flipping 5 coins and 6 coins to apply to any odd or even number of coins.

After students have completed the task, invite them to share the fair game they created in the last question, and how they know it’s fair. Groups can pair up and play each other’s games, or students can share with the whole class.

1. Here are some games:
   • The Flipper flips 3 coins. If exactly 2 are the same, then the Flipper wins, and otherwise they lose.
   • The Flipper flips 4 coins. If exactly 2 are the same, then the Flipper wins, and otherwise they lose.

   Are these games fair?

2. Design rules for a fair game for flipping 5 coins.
3. Design rules for a fair game for flipping 6 coins.
4. Design a fair game using any objects you want—for example, coins, spinners, or number cubes. Explain how you know your game is fair.

If an additional challenge is desired, students can generalize the fair games they created for flipping 4 coins and 5 coins to apply to any even or odd number of coins.

After students have completed the task, invite them to share the fair game they created in the last question, and how they know it’s fair. Groups can pair up and play each other’s games, or students can share with the whole class.

1. Here are some games:
   • The Flipper flips 3 coins. If there are more heads than tails, then the Flipper wins, and otherwise they lose.
   • The Flipper flips 4 coins. If exactly 2 are the same, then the Flipper wins, and otherwise they lose.
   1. One of the games is fair and the other one is not. Which one is fair?
   2. For the game that isn’t fair, change the rules to make it fair.
2. Design rules for a fair game for flipping 5 coins.
3. Design rules for a fair game that involves rolling two number cubes.