Created byLynn Parker

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Create Your Own Game of Chance

Grade 6Math7 days

In the 'Create Your Own Game of Chance' project, 6th-grade students are tasked with applying their understanding of probability to design fun and fair games. Through various activities and experiments, such as simulating games with marbles and coin flips, students explore both theoretical and experimental probabilities. They collect, summarize, and analyze data to improve game mechanics, ensuring fairness and enjoyment. The project fosters critical thinking, data visualization, and reflective reasoning, aligned with Common Core Math Standards.

ProbabilityGame DesignData AnalysisFairnessMathematical ConceptsExperimentation

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Inquiry Framework

Question Framework

Driving Question

The overarching question that guides the entire project.How can we apply our understanding of probability to design a fun and fair game of chance?

Essential Questions

Supporting questions that break down major concepts.

What is probability and how is it used in games of chance?
How can understanding probability help in creating fair games?
What are the key components needed to design a game of chance?
How does probability impact the outcome of a game?
What strategies can be used to ensure that a game is both fun and fair?
How can data be collected and analyzed to improve game design?
In what ways do theoretical and experimental probabilities differ?

Standards & Learning Goals

Learning Goals

By the end of this project, students will be able to:

Students will understand and apply the principles of probability in the context of games.
Students will design and evaluate their own game of chance using mathematical concepts of probability.
Students will be able to collect, summarize, and interpret data related to their games to determine fairness and enjoyment.
Students will analyze the role of theoretical versus experimental probability in predicting game outcomes.
Students will develop strategies to ensure that the games they create are both engaging and fair, utilizing statistical data.

Common Core Standards

CCSS.MATH.CONTENT.6.SP.B.5

Primary

Summarize numerical data sets in relation to their context, such as by: reporting the number of observations; describing the attribute under investigation, including how it was measured and its units of measurement.Reason: Students will collect and analyze data related to their games of chance, summarizing their findings which aligns with summarizing numerical data sets in relation to their games' context.

CCSS.MATH.CONTENT.6.SP.A.3

Secondary

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.Reason: Understanding probability requires recognizing how data can be summarized and how variation can affect outcomes, which is central to this project's goals.

CCSS.MATH.CONTENT.6.SP.B.4

Secondary

Display numerical data in plots on a number line, including dot plots, histograms, and box plots.Reason: Students might display their game's outcome data using various plots to analyze fairness and randomness, directly aligning with this standard about data representation.

Entry Events

Events that will be used to introduce the project to students

Casino Day Mystery

Transform the classroom into a casino for a day, where students participate in various games of chance. Each station poses a unique challenge related to probability, enticing students to dive deeper into the math behind the games.

Chance Carnival

Host a classroom carnival where traditional games of chance are played. Students are tasked with investigating the fairness of each game, enabling them to ask critical questions and propose improvements that involve calculating probabilities.

Real-Life Probability Scenarios

Present students with real-life scenarios—such as weather predictions, board games and sports analytics—where probability plays a crucial role. Students explore these scenarios and develop their game using insights gained.

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Portfolio Activities

These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.

Activity 1

Probability Primer Puzzle

Students will solve puzzles and engage in small experiments to grasp the basic concepts of probability and its applications in everyday life, including gaming.

Steps

Here is some basic scaffolding to help students complete the activity.

1. Introduce the concept of probability through simple examples like coin tosses or dice rolls, and discuss where they may see probability at work in real life scenarios such as weather forecasts.

2. Have students partake in simple random experiments like drawing colored marbles from a bag, and record the outcomes to illustrate basic probability principles.

3. Use puzzles like predicting the next card in a shuffled deck to solidify understanding.

Final Product

What students will submit as the final product of the activityA reflective journal entry summarizing the student's initial understanding of probability and how they see it applied in their everyday lives.

Alignment

How this activity aligns with the learning objectives & standardsCCSS.MATH.CONTENT.6.SP.A.3 - Introduces the basic notion of probability and its relevance by discussing how a center or variation may summarize multiple data points.

Activity 2

Theoretical vs. Experimental Elucidation

Students will explore the difference between theoretical and experimental probabilities by conducting hands-on investigations and comparing their results.

Steps

Here is some basic scaffolding to help students complete the activity.

1. Explain the difference between theoretical probability (what should happen) vs. experimental probability (what actually happened).

2. Have groups of students conduct a simple experiment, such as flipping a coin 50 times, and record their results.

3. Calculate theoretical probability (e.g., 50% for heads/tails) and compare it with experimental results, prompting a class discussion on observed discrepancies and potential reasons behind them.

Final Product

What students will submit as the final product of the activityA report detailing the students' findings, reflections on theoretical vs. experimental probability, and an explanation of any discrepancies observed.

Alignment

How this activity aligns with the learning objectives & standardsCCSS.MATH.CONTENT.6.SP.B.4 - Uses data collection and representation, including plots, to explore quantitative data related to probability.

Activity 3

Data Detective Workshop

Students delve into data analysis as they gather in-depth results from their games, summarizing findings and improving game fairness.

Steps

Here is some basic scaffolding to help students complete the activity.

1. Have students play their games in several rounds, meticulously recording game outcomes and related probability data.

2. Utilize statistical tools to graph outcomes and pinpoint fairness measures, creating histograms or dot plots where necessary.

3. Instruct on interpretation of data variations to suggest plausible adjustments to game mechanics, ensuring enhanced fairness and fun.

Final Product

What students will submit as the final product of the activityAn analyzed dataset of game outcomes with summarizing visual graphs and proposed amendments based on data interpretations.

Alignment

How this activity aligns with the learning objectives & standardsAligns with CCSS.MATH.CONTENT.6.SP.B.5 - Emphasizes summarizing and interpreting numerical data sets in direct relation to the student games' probabilistic outcomes.

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Rubric & Reflection

Portfolio Rubric

Grading criteria for assessing the overall project portfolio

Probability Game Creation and Analysis Rubric

Category 1

Understanding and Application of Probability

Assesses the students' comprehension and practical application of probability concepts in their game design.

Criterion 1

Understanding of Probability Concepts

Evaluates the depth of students' understanding of probability concepts such as theoretical and experimental probability.

Exemplary

4 Points

Demonstrates a sophisticated understanding of theoretical and experimental probability, with clear explanations and nuanced insights into their differences and applications in games.

Proficient

3 Points

Shows thorough understanding of theoretical and experimental probability, and explains their differences and applications accurately.

Developing

2 Points

Exhibits basic understanding of theoretical and experimental probability, with some inaccuracies in explanations and applications.

Beginning

1 Points

Shows minimal understanding of probability concepts, with significant misconceptions and incorrect applications.

Criterion 2

Application of Probability in Game Design

Assesses how well students apply probability principles to create a fair and engaging game.

Exemplary

4 Points

Applies probability concepts innovatively to create a highly fair and engaging game, showing leadership in design thinking.

Proficient

3 Points

Effectively applies probability concepts to create a fair and engaging game.

Developing

2 Points

Applies probability concepts inconsistently, resulting in a game that shows varying degrees of fairness and engagement.

Beginning

1 Points

Struggles to apply probability concepts, resulting in a game that lacks fairness and engagement.

Category 2

Data Collection and Analysis

Evaluates the students' ability to collect, visualize, and interpret data related to their games' probabilistic outcomes.

Criterion 1

Data Collection

Measures the thoroughness and accuracy with which students collect data during their game activities.

Exemplary

4 Points

Collects data meticulously with comprehensive records that are highly accurate and relevant to the game's probabilistic analysis.

Proficient

3 Points

Collects data accurately with some attention to detail and relevance to the game's analysis.

Developing

2 Points

Collects data with some inaccuracies and gaps, showing limited relevance to the game's analysis.

Beginning

1 Points

Collects data with significant inaccuracies and gaps, showing little relevance to the game's analysis.

Criterion 2

Data Visualization and Interpretation

Evaluates the quality of students' visual data representations and their interpretations regarding game fairness and engagement.

Exemplary

4 Points

Produces exceptional visual data representations that are clear and insightful. Provides comprehensive interpretations that suggest innovative improvements.

Proficient

3 Points

Produces quality visual data representations with clear interpretations, offering plausible improvements.

Developing

2 Points

Produces basic visual data representations with limited interpretations and few improvements suggested.

Beginning

1 Points

Produces poor visual data representations with minimal interpretations and lacks suggestions for improvement.

Category 3

Reflective Reasoning and Improvement Strategies

Assesses the quality of students' reflections on their learning process and the strategies they propose for improving their games.

Criterion 1

Reflective Reasoning

Evaluates students' ability to reflect on their learning experiences and insights gained from the project.

Exemplary

4 Points

Exhibits sophisticated reflective reasoning with deep insights into learning experiences and their impact on game design.

Proficient

3 Points

Demonstrates thorough reflective reasoning with clear insights into learning experiences.

Developing

2 Points

Offers basic reflections with limited insights into learning experiences.

Beginning

1 Points

Provides minimal reflections with little insight into learning experiences.

Criterion 2

Improvement Strategies

Assesses the creativity and feasibility of the strategies proposed by students to enhance game design.

Exemplary

4 Points

Proposes innovative and highly feasible strategies for improving the game's design, showing advanced problem-solving skills.

Proficient

3 Points

Proposes feasible strategies for improving the game's design with clear problem-solving.

Developing

2 Points

Proposes limited strategies for game improvement, with basic problem-solving.

Beginning

1 Points

Proposes minimal or unfeasible strategies for game improvement with little problem-solving.

Reflection Prompts

End-of-project reflection questions to get students to think about their learning

Question 1

Reflect on how your understanding of probability has evolved from the beginning of the project to now. What were some key insights you gained?

Text

Required

Question 2

How confident are you in your ability to apply probability concepts to real-world situations and game design?

Scale

Required

Question 3

Which activity or experiment in this project helped you most in understanding the difference between theoretical and experimental probability?

Multiple choice

Required

Options

Probability Primer Puzzle

Theoretical vs. Experimental Elucidation

Data Detective Workshop

Question 4

What strategies did you find most effective in designing a fun and fair game of chance?

Text

Required

Question 5

On a scale from 1 to 5, how would you rate the fairness of the game you designed, based on the data collected?

Scale

Required