Carnival+Games


 * Carnival Games **

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. <span style="font-family: 'Arial','sans-serif'; font-size: 12pt;">Play these three games with a partner. Choose who will be Player A and who will be Player B

==__<span style="font-family: 'Arial','sans-serif';">Game 1 __<span style="font-family: 'Arial','sans-serif';"> - 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. ==

<span style="font-family: 'Arial','sans-serif';">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. <span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;">Find the experimental probabilities for both players. <span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;">P(A wins) = _ P(B wins) = _
 * = <span style="font-family: 'Arial','sans-serif'; font-size: 12pt;">Play the game 20 times and record your results in this table. ||= <span style="font-family: 'Arial','sans-serif'; font-size: 12pt;">Tally ||= <span style="font-family: 'Arial','sans-serif'; font-size: 12pt;">Total ||
 * = <span style="font-family: 'Arial','sans-serif'; font-size: 12pt;">Player A wins ||=  ||=   ||
 * = <span style="font-family: 'Arial','sans-serif'; font-size: 12pt;">Player B wins ||=  ||=   ||
 * = <span style="font-family: 'Arial','sans-serif'; font-size: 12pt;">Number of times played ||=  ||= 20 ||

<span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;">List the sample space for this game.

<span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;">What‘s the theoretical probability that player A wins?

<span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;">What’s the theoretical probability that player B wins?

<span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;">How do the experimental probabilities compare to the theoretical probabilities?

== __<span style="font-family: 'Arial','sans-serif';">Game 2 __<span style="font-family: 'Arial','sans-serif';"> – 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. ==

<span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;">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. <span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;">

<span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;">Find the experimental probabilities for both players.
 * = <span style="font-family: 'Arial','sans-serif'; font-size: 12pt;">Play the game 20 times and record your results in this table. ||= <span style="font-family: 'Arial','sans-serif'; font-size: 12pt;">Tally ||= <span style="font-family: 'Arial','sans-serif'; font-size: 12pt;">Total ||
 * = <span style="font-family: 'Arial','sans-serif'; font-size: 12pt;">Player A wins ||=  ||=   ||
 * = <span style="font-family: 'Arial','sans-serif'; font-size: 12pt;">Player B wins ||=  ||=   ||
 * = <span style="font-family: 'Arial','sans-serif'; font-size: 12pt;">Number of times played ||=  ||= 20 ||

<span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;">P(A wins) = _ P(B wins) = _

<span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;">List the sample space for this game.

<span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;">What‘s the theoretical probability that player A wins?

<span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;">What’s the theoretical probability that player B wins?

<span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;">How do the experimental probabilities compare to the theoretical probabilities? == __<span style="font-family: 'Arial','sans-serif';">Game 3 __<span style="font-family: 'Arial','sans-serif';"> – 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. == <span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;">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.
 * = <span style="font-family: 'Arial','sans-serif'; font-size: 12pt;">Play the game 20 times and record your results in this table. ||= <span style="font-family: 'Arial','sans-serif'; font-size: 12pt;">Tally ||= <span style="font-family: 'Arial','sans-serif'; font-size: 12pt;">Total ||
 * = <span style="font-family: 'Arial','sans-serif'; font-size: 12pt;">Player A wins ||=  ||=   ||
 * = <span style="font-family: 'Arial','sans-serif'; font-size: 12pt;">Player B wins ||=  ||=   ||
 * = <span style="font-family: 'Arial','sans-serif'; font-size: 12pt;">Number of times played ||=  ||= 20 ||

<span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;">Find the experimental probabilities for both players. P(A wins) = _ <span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;">P(B wins) = _

<span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;">List the sample space for this game.

<span style="font-family: 'Arial','sans-serif';">What‘s the theoretical probability that player A wins?

<span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;">What’s the theoretical probability that player B wins?

<span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;">How do the experimental probabilities compare to the theoretical probabilities?

<span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;">Reflection Questions
<span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;">1. Does a fair game always seem fair? Give examples why or why not.

<span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;">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.

<span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;">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.

<span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;">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?

<span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;">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.

<span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;">Brainstorm ideas for fair and unfair games. Use coins, dice, spinners, cubes in a bag, or whatever you want.

<span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;">RESOURCES:
<span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;"> § Introduction to Probability Lesson Online [] <span style="font-family: 'Arial','sans-serif'; font-size: 10pt; margin: 0in 0in 0pt;"> <span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;"> · Explore probability concepts online with the following website [] <span style="font-family: 'Arial','sans-serif'; font-size: 10pt; margin: 0in 0in 0pt;"> <span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;"> <span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;"> <span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;"> <span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;">

<span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;">﻿ ASSESSMENT RUBRIC: You will be graded according to the following rubric.
<span style="font-family: 'Arial','sans-serif'; margin: 0in 0in 0pt;">


 * || <span style="font-family: 'Arial','sans-serif'; font-size: 12pt;">**Novice** || <span style="font-family: 'Arial','sans-serif'; font-size: 12pt;">**Apprentice** || <span style="font-family: 'Arial','sans-serif'; font-size: 12pt;">**Practitioner** || <span style="font-family: 'Arial','sans-serif'; font-size: 12pt;">**Expert** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">**Game Description** || * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">includes how to play the game
 * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">includes the materials needed || * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">includes how to play the game
 * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">includes the materials needed
 * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">game uses compound events || * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">includes how to play the game

**<span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">Mechanical Criteria ** || * <span style="display: block; margin: 0in 0in 0pt 0.15in; mso-list: l0 level1 lfo1; tab-stops: list 0in; text-indent: -0.15in;"><span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">contains more than 5 spelling or grammar mistakes
 * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">includes the materials needed
 * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">uses compound events
 * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">explains if events are independent or dependent || <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">all of //Practitioner// plus explains whether or not the game is fair and your reasons for choosing the game ||
 * **<span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">Theoretical Probabilities ** || * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">possible outcomes are listed __or__ shown in a tree diagram || * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">possible outcomes are listed __and__ shown in tree diagram || * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">all possible outcomes are listed __and__ shown in a tree diagram
 * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">probability of each outcome is correctly written as a fraction, decimal and percent || <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">all of //Practitioner// plus includes the odds of each outcome ||
 * **<span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">Experimental **
 * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">Probabilities ** || * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">includes a table of game results after 50 plays || * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">includes a table of game results after 50 plays probabilities are written as a fraction, decimal __or__ a percent || * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">includes a table of game results after 50 plays
 * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">probabilities are correctly written as a fraction, decimal, __and__ percent || <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">all of //Practitioner// plus game results are shown in graphs ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">**Fundraising Report** || * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">includes price to play
 * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">describes game prizes || * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">includes price to play
 * <span style="display: block; margin: 0in 0in 0pt 0.15in; mso-list: l0 level1 lfo1; tab-stops: list 0in; text-indent: -0.15in;"><span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">describes game prizes and prices for prizes || * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">includes price to play
 * <span style="display: block; margin: 0in 0in 0pt 0.15in; mso-list: l0 level1 lfo1; tab-stops: list 0in; text-indent: -0.15in;"><span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">describes game prizes and prices for prizes
 * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">correctly predicts how much would be raised after 100 plays based on data || <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">all of //Practitioner// plus compares the game to a common carnival game ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">**Mathematical Computations** || * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">all work is neatly shown
 * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">work contains more than 5 errors || * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">all work is neatly shown work
 * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">contains 2 to 5 errors || * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">all work is neatly shown
 * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">work contains 1 or 2 errors || * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">work is neatly typed
 * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">work contains no errors ||
 * **<span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">Mathematical Content/ **
 * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">explanation shows limited understanding of the mathematical concepts || * <span style="display: block; margin: 0in 0in 0pt 0.15in; mso-list: l0 level1 lfo1; tab-stops: list 0in; text-indent: -0.15in;"><span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">contains 4 – 5 spelling or grammar mistakes
 * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">explanation shows some understanding of the mathematical concepts || * <span style="display: block; margin: 0in 0in 0pt 0.15in; mso-list: l0 level1 lfo1; tab-stops: list 0in; text-indent: -0.15in;"><span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">accurate use of math vocabulary
 * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">contains only a few spelling or grammar mistakes
 * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">explanation shows complete understanding of the mathematical concepts || * <span style="display: block; margin: 0in 0in 0pt 0.15in; mso-list: l0 level1 lfo1; tab-stops: list 0in; text-indent: -0.15in;"><span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">accurate use of math vocabulary
 * <span style="display: block; margin: 0in 0in 0pt 0.15in; mso-list: l0 level1 lfo1; tab-stops: list 0in; text-indent: -0.15in;"><span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">complete accuracy in spelling and grammar
 * <span style="font-family: 'Arial','sans-serif'; font-size: 11pt;">vivid writing style ||