Math Focus 7
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# Fair Game

## INTRODUCTION

I know a family who has seven sons. The mom is pregnant again. Surely the eighth child must be a girl…right? When you guess the gender of a baby, or when you play a game with dice, there are actually some things you can find out for sure about the results. Instead of talking about luck, let’s talk about the mathematics of probability!

You and your partner need to design a game to play with your friends that is fair. You will explore probability, especially in games. Once you know about probability and what makes a game fair or unfair, you will be able to design a fair game that demonstrates your understanding of probability. Be prepared to present your game to the class.

## THE PROCESS

1. Visit Mrs. Glosser's Math Goodies. Read and discuss the definitions with your partner.  Learn the formula that is used for finding the probability of an event.  Participate in the probability experiments.  To see how much you have learned, answer the questions at the end of the exercise.

2. If you roll two regular dice 30 times, then add the two numbers that were rolled, what do you think would be the most common sum? Predict the sum and then conduct the experiment. Roll both dice and record the outcome on the
Probability Experiment Worksheet
. Do this 30 times. Use the results recorded on your Worksheet to figure out how many times each sum appears. Hint: there are often several outcomes that result in the same sum. How close was your prediction to what happened?

Suppose this dice experiment was a game, in which each player gets assigned a sum and only scores points when his/her sum appears. Suppose you were assigned the sum 5 and your partner was assigned the sum 7. Would this be a fair game? Explain.

3. Have you ever played Odd or Even? This ancient game is played all over the world. One player is assigned to be "odd" and the other player is assigned to be "even." On the count of three, the two players simultaneously display one hand with either one finger or two fingers pointing out. The winner of the game is determined by the total number of fingers showing. If the total number of fingers is odd, then the odd player scores a point and the same would go for even. To analyze the game, make a chart of all of the possible outcomes. How many different outcomes are possible? How many ways can Player 1 win? How many ways can Player 2 win? Are any outcomes a draw?

4. What makes a game fair or unfair?  In a fair game, each player plays by the rules and has an equal chance of winning. With your partner, think of ways in which one player can have an unfair advantage in a game. For example, a basketball game in which the hoops are set at different heights is an unfair game. Think about the Odd or Even game. Is it a fair game?  Look back at your outcomes to explain your answer.
5. Design a game of probability.  Be sure to include the following elements: title of your game, game components, detailed directions so others can play, a list of rules, and an explanation of how you know your game is fair.

Websites:

Materials:

Paper and pencil

## ASSESSMENT

 Level 1 Level 2 Level 3 Level 4 Understanding Concepts (Probability) The student demonstrates insufficient understanding of probability. Major errors and/or misconceptions are apparent in the game design or in the results of the dice experiment. The student demonstrates a basic understanding of probability. There are some errors or misconceptions in the game design or in the results of the dice experiment. And/or the game is too simple to demonstrate probability knowledge. The student demonstrates solid understanding of probability. The game design and the results of the dice experiment demonstrate knowledge of probability. The student demonstrates thorough understanding of probability. Results of the dice experiment are correct and the game design is complex, fair, and demonstrates knowledge of probability.