Carnival Games
CARNIVAL.JPG





Your school is planning a school carnival as a fundraiser. You and your group must create a game to run at the carnival. You need to prepare a report about your game to the carnival planning committee. Your report should include how to play the game, how to win, the materials needed, the possible outcomes, and the theoretical probability of each outcome. You should also play your game 50 times and record the experimental probabilities. Your report should also include a fundraising component that includes how much you would charge for each play of the game, what the prizes would be and how much they would cost, and how much money you would expect to raise after 100 plays of your game.






ACTIVITIES:
Activity
Due Date
Date Completed
Exploring Fair and Unfair Games Activity


Game Description and Rules


List of Possible Outcomes in a Table and a Tree Diagram


Theoretical Probabilities of each possible outcome listed as a decimal, fraction, and percent


Game was played 50 times and Results are Displayed in a Table


Experimental Probabilities are correctly written as a fraction, decimal and percent


Fundraising Report




Exploring Fair and Unfair Games



A game is fair if each player has the same chance of winning. In other words, a game is fair if the probabilities of each player winning are the same.
Play these three games with a partner. Choose who will be Player A and who will be Player B




Game 1 - Place 1 red cube and 1 blue cube in a bag. Draw 1 cube from the bag without looking. If the cube is red, player A wins. If the cube is blue, player B wins.


Before you play the game, decide if the game is fair or not. If it is unfair, tell which player is more likely to win. Create a chart like the one below and fill in the data as you play.
Play the game 20 times and record your results in this table.
Tally
Total
Player A wins


Player B wins


Number of times played

20
Find the experimental probabilities for both players.
P(A wins) = _ P(B wins) = _

List the sample space for this game.

What‘s the theoretical probability that player A wins?

What’s the theoretical probability that player B wins?

How do the experimental probabilities compare to the theoretical probabilities?

Game 2 – Place 2 red cubes and 2 blue cubes in a bag. Draw 2 cubes from the bag without looking. If the cubes are the same color, player A wins. If the cubes are different colors, player B wins.


Before you play the game, decide if the game is fair or not. If it is unfair, tell which player is more likely to win. Create a chart like the one below and fill in the data as you play.


Play the game 20 times and record your results in this table.
Tally
Total
Player A wins


Player B wins


Number of times played

20
Find the experimental probabilities for both players.

P(A wins) = _ P(B wins) = _

List the sample space for this game.

What‘s the theoretical probability that player A wins?

What’s the theoretical probability that player B wins?

How do the experimental probabilities compare to the theoretical probabilities?

Game 3 – Place 3 red cubes and 1 blue cube in a bag. Draw 2 cubes from the bag without looking. If the cubes are the same color, player A wins. If the cubes are different colors, player B wins.

Before you play the game, decide if the game is fair or not. If it is unfair, tell which player is more likely to win. Create a chart like the one below and fill in the data as you play.
Play the game 20 times and record your results in this table.
Tally
Total
Player A wins


Player B wins


Number of times played

20

Find the experimental probabilities for both players. P(A wins) = _
P(B wins) = _

List the sample space for this game.

What‘s the theoretical probability that player A wins?

What’s the theoretical probability that player B wins?

How do the experimental probabilities compare to the theoretical probabilities?



Reflection Questions

1. Does a fair game always seem fair? Give examples why or why not.

2. If you and your partner played the same games tomorrow, will the experimental probabilities be the same that they are today? Explain why or why not.

3. If you and your partner played the same games tomorrow, will the theoretical probabilities be the same as they are today? Explain why or why not.

4. Fred and Julie played game 1. Fred won 7 times and Julie won 13 times. How can this happen if the game is fair?

5. Jamie and Jenny also played game 1. The first 3 cubes drawn were blue. Is the fourth cube more likely to be red or blue? Explain your answer.

Brainstorm ideas for fair and unfair games. Use coins, dice, spinners, cubes in a bag, or whatever you want.

RESOURCES:


§Introduction to Probability Lesson Online http://www.mathgoodies.com/lessons/vol6/intro_probability.html

· Explore probability concepts online with the following website http://nlvm.usu.edu/en/nav/category_g_3_t_5.html





ASSESSMENT RUBRIC: You will be graded according to the following rubric.







Novice
Apprentice
Practitioner
Expert
Game Description
  • includes how to play the game
  • includes the materials needed
  • includes how to play the game
  • includes the materials needed
  • game uses compound events
  • includes how to play the game

  • includes the materials needed
  • uses compound events
  • explains if events are independent or dependent
all of Practitioner plus explains whether or not the game is fair and your reasons for choosing the game
Theoretical Probabilities
  • possible outcomes are listed or shown in a tree diagram
  • possible outcomes are listed and shown in tree diagram
  • all possible outcomes are listed and shown in a tree diagram
  • probability of each outcome is correctly written as a fraction, decimal and percent
all of Practitioner plus includes the odds of each outcome
Experimental
Probabilities
  • includes a table of game results after 50 plays
  • includes a table of game results after 50 plays probabilities are written as a fraction, decimal or a percent
  • includes a table of game results after 50 plays
  • probabilities are correctly written as a fraction, decimal, and percent
all of Practitioner plus game results are shown in graphs
Fundraising Report
  • includes price to play
  • describes game prizes
  • includes price to play
  • describes game prizes and prices for prizes
  • includes price to play
  • describes game prizes and prices for prizes
  • correctly predicts how much would be raised after 100 plays based on data
all of Practitioner plus compares the game to a common carnival game
Mathematical Computations
  • all work is neatly shown
  • work contains more than 5 errors
  • all work is neatly shown work
  • contains 2 to 5 errors
  • all work is neatly shown
  • work contains 1 or 2 errors
  • work is neatly typed
  • work contains no errors
Mathematical Content/
Mechanical Criteria
  • contains more than 5 spelling or grammar mistakes
  • explanation shows limited understanding of the mathematical concepts
  • contains 4 – 5 spelling or grammar mistakes
  • explanation shows some understanding of the mathematical concepts
  • accurate use of math vocabulary
  • contains only a few spelling or grammar mistakes
  • explanation shows complete understanding of the mathematical concepts
  • accurate use of math vocabulary
  • complete accuracy in spelling and grammar
  • vivid writing style