Probability Carnival: Design a Fair Game
Inquiry Framework
Question Framework
Driving Question
The overarching question that guides the entire project.How can we design a carnival game that is both fun and fair, using probability to predict outcomes and ensure an engaging experience for all players?Essential Questions
Supporting questions that break down major concepts.- How can probability help us design a fair game?
- What makes a game fun and engaging for players?
- How can we use math to predict the outcomes of our game?
- How do we calculate the probability of winning in our game?
- How can we test our game to make sure it is fair and fun?
Standards & Learning Goals
Learning Goals
By the end of this project, students will be able to:- Students will be able to calculate probabilities of simple events.
- Students will apply probability concepts to design a carnival game.
- Students will evaluate the fairness of their game using probability.
- Students will iterate on their game design based on testing and feedback.
Entry Events
Events that will be used to introduce the project to studentsCarnival Crisis!
A local carnival owner arrives, distraught because their games are losing money. They explain that either the games are too hard, so no one wins, or too easy, so everyone wins, and they lose money. They ask the students to redesign a game using their knowledge of probability to make it fun, fair, and profitable.Portfolio Activities
Portfolio Activities
These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.Dice Roll Probability Lab
Students will learn the basics of probability by experimenting with dice rolls. They will record their results and calculate the probability of each outcome.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA probability journal with recorded dice roll data and calculated probabilities for each number.Alignment
How this activity aligns with the learning objectives & standardsLearning Goal: Students will be able to calculate probabilities of simple events.Game Design Brainstorm
Students will brainstorm and sketch out initial ideas for their carnival game, focusing on how probability can be used to make the game fair and engaging.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityInitial game design sketches with descriptions of gameplay and how probability is involved.Alignment
How this activity aligns with the learning objectives & standardsLearning Goal: Students will apply probability concepts to design a carnival game.Fairness Check: Game Testing & Analysis
Students will create a simple prototype of their game and test it to determine the probability of winning. They will analyze the results to determine if the game is fair.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA game prototype and a probability analysis report detailing the fairness of the game.Alignment
How this activity aligns with the learning objectives & standardsLearning Goal: Students will evaluate the fairness of their game using probability.Game Changer: Design Refinement & Presentation
Students will refine their game design based on the data collected during testing. They will make adjustments to improve the game's fairness and engagement, then present their final design.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA final carnival game design with a presentation explaining the game's rules, probability of winning, and design improvements made based on testing and feedback.Alignment
How this activity aligns with the learning objectives & standardsLearning Goal: Students will iterate on their game design based on testing and feedback.Rubric & Reflection
Portfolio Rubric
Grading criteria for assessing the overall project portfolioCarnival Game Design Rubric
Probability Experiment & Analysis
This category assesses the student's ability to accurately calculate probabilities, record experimental data, and summarize their findings with insightful reflections.Probability Calculation Accuracy
Accuracy of probability calculations based on dice roll data.
Exemplary
4 PointsCalculations are precise, accurate, and demonstrate a sophisticated understanding of probability. Shows all work clearly and logically.
Proficient
3 PointsCalculations are mostly accurate with minor errors. Demonstrates a thorough understanding of probability. Shows most of the work clearly.
Developing
2 PointsCalculations contain significant errors, indicating a developing understanding of probability. Work is partially shown or difficult to follow.
Beginning
1 PointsCalculations are largely inaccurate, demonstrating a beginning understanding of probability. Work is missing or incomprehensible.
Data Recording & Observations
Clarity and completeness of the recorded dice roll data and observations.
Exemplary
4 PointsData is meticulously recorded and organized, with comprehensive observations and insights noted. Demonstrates exceptional attention to detail.
Proficient
3 PointsData is clearly recorded and organized, with relevant observations included. Demonstrates thoroughness in data collection.
Developing
2 PointsData is partially recorded or disorganized, with limited observations noted. Demonstrates some effort in data collection.
Beginning
1 PointsData is incomplete, missing, or incomprehensible, with minimal or no observations. Demonstrates little effort in data collection.
Summary Quality & Insights
Quality of the summary, including insights and understanding of probability concepts.
Exemplary
4 PointsSummary demonstrates a deep understanding of probability concepts with insightful reflections and connections to real-world applications. Shows exceptional critical thinking.
Proficient
3 PointsSummary demonstrates a clear understanding of probability concepts with thoughtful reflections. Shows effective critical thinking.
Developing
2 PointsSummary demonstrates a basic understanding of probability concepts with limited reflections. Shows some critical thinking.
Beginning
1 PointsSummary demonstrates a minimal understanding of probability concepts with little to no reflection. Shows limited critical thinking.
Game Design Ideation
This category evaluates the student's ability to generate creative game ideas and clearly articulate the relationship between game mechanics and probability.Creativity & Variety
Variety and creativity of the game ideas presented.
Exemplary
4 PointsPresents a wide range of highly creative and innovative game ideas, demonstrating exceptional imagination and originality.
Proficient
3 PointsPresents a good variety of creative game ideas, demonstrating imagination and originality.
Developing
2 PointsPresents a limited variety of game ideas, showing some creativity.
Beginning
1 PointsPresents few game ideas with limited creativity or originality.
Sketch Clarity & Detail
Clarity and detail of the game design sketches.
Exemplary
4 PointsSketches are exceptionally clear, detailed, and well-labeled, providing a comprehensive visual representation of the game designs.
Proficient
3 PointsSketches are clear, detailed, and labeled, providing a good visual representation of the game designs.
Developing
2 PointsSketches are partially clear or lacking in detail, with some labeling. Provides a limited visual representation of the game designs.
Beginning
1 PointsSketches are unclear, lacking detail, and poorly labeled. Provides a minimal visual representation of the game designs.
Explanation of Game Mechanics & Probability
Explanations of how each game works and how probability is involved.
Exemplary
4 PointsProvides exceptionally clear and detailed explanations of how each game works, with a sophisticated understanding of how probability influences the outcomes.
Proficient
3 PointsProvides clear and detailed explanations of how each game works, with a thorough understanding of how probability influences the outcomes.
Developing
2 PointsProvides partially clear explanations of how each game works, with a basic understanding of how probability influences the outcomes.
Beginning
1 PointsProvides unclear or incomplete explanations of how each game works, with a minimal understanding of how probability influences the outcomes.
Game Testing & Fairness Analysis
This category assesses the student's ability to build a functional game prototype and analyze its fairness using probability calculations and critical thinking.Prototype Quality & Functionality
Quality and functionality of the game prototype.
Exemplary
4 PointsPrototype is exceptionally well-built, functional, and closely resembles the intended game design. Demonstrates advanced craftsmanship and attention to detail.
Proficient
3 PointsPrototype is well-built, functional, and resembles the intended game design. Demonstrates good craftsmanship.
Developing
2 PointsPrototype is partially functional or has some flaws in construction. Demonstrates basic craftsmanship.
Beginning
1 PointsPrototype is poorly constructed, non-functional, or does not resemble the intended game design. Demonstrates limited craftsmanship.
Probability Calculation Accuracy (Game Testing)
Accuracy in calculating the probability of winning based on game testing.
Exemplary
4 PointsCalculations are precise, accurate, and demonstrate a sophisticated understanding of probability in the context of game outcomes. Shows all work clearly.
Proficient
3 PointsCalculations are mostly accurate with minor errors. Demonstrates a thorough understanding of probability in the context of game outcomes. Shows most work.
Developing
2 PointsCalculations contain significant errors, indicating a developing understanding of probability. Work is partially shown.
Beginning
1 PointsCalculations are largely inaccurate, demonstrating a beginning understanding of probability. Work is missing or incomprehensible.
Fairness Analysis Report
Thoroughness and clarity of the analysis report on the fairness of the game.
Exemplary
4 PointsReport is exceptionally thorough, providing a detailed analysis of the game's fairness with clear justifications and insightful conclusions. Demonstrates advanced critical thinking.
Proficient
3 PointsReport is thorough, providing a clear analysis of the game's fairness with reasonable justifications. Demonstrates effective critical thinking.
Developing
2 PointsReport is partially thorough, providing a basic analysis of the game's fairness with limited justifications. Demonstrates some critical thinking.
Beginning
1 PointsReport is incomplete, providing a minimal analysis of the game's fairness with little to no justification. Demonstrates limited critical thinking.
Game Refinement & Presentation
This category evaluates the student's ability to refine their game design based on feedback and effectively communicate their final design, including the improvements made and the probability of winning.Design Improvement
Extent and quality of improvements made to the game design based on testing and feedback.
Exemplary
4 PointsDemonstrates extensive and highly effective improvements to the game design, addressing key issues identified during testing and feedback. Shows exceptional problem-solving skills.
Proficient
3 PointsDemonstrates effective improvements to the game design, addressing most issues identified during testing and feedback. Shows good problem-solving skills.
Developing
2 PointsDemonstrates some improvements to the game design, addressing some issues identified during testing and feedback. Shows basic problem-solving skills.
Beginning
1 PointsDemonstrates limited or no improvements to the game design, failing to address issues identified during testing and feedback. Shows limited problem-solving skills.
Presentation Quality
Clarity and organization of the final game design presentation.
Exemplary
4 PointsPresentation is exceptionally clear, well-organized, and engaging, effectively communicating the game's rules, probability of winning, and design improvements. Demonstrates advanced presentation skills.
Proficient
3 PointsPresentation is clear, well-organized, and engaging, communicating the game's rules, probability of winning, and design improvements. Demonstrates effective presentation skills.
Developing
2 PointsPresentation is partially clear or disorganized, with some communication of the game's rules, probability of winning, and design improvements. Demonstrates basic presentation skills.
Beginning
1 PointsPresentation is unclear, disorganized, and fails to effectively communicate the game's rules, probability of winning, and design improvements. Demonstrates limited presentation skills.
Understanding of Game Rules & Probability
Understanding and explanation of the game's rules and probability of winning.
Exemplary
4 PointsDemonstrates a deep and sophisticated understanding of the game's rules and probability of winning, providing clear, concise, and accurate explanations. Shows exceptional mastery of the concepts.
Proficient
3 PointsDemonstrates a thorough understanding of the game's rules and probability of winning, providing clear and accurate explanations. Shows strong mastery of the concepts.
Developing
2 PointsDemonstrates a basic understanding of the game's rules and probability of winning, providing partially clear explanations. Shows some understanding of the concepts.
Beginning
1 PointsDemonstrates a minimal understanding of the game's rules and probability of winning, providing unclear or inaccurate explanations. Shows limited understanding of the concepts.