Project Introduction and Essential Questions - Introduce the 'Game Theory Carnival' and 'Game Design Hackathon,' discussing essential questions around predicting outcomes and optimizing game mechanics using mathematical principles. (15 min)

Game Theory Carnival Station Rotations - Participate in interactive game stations that explore probability, geometry, and quadratic equations, encouraging critical thinking about mathematical models in games. (40 min)

Reflection and Digital Portfolio Setup - Begin creating a digital portfolio to document project progress, with a focus on reflections from the Game Theory Carnival experience. (25 min)

Introduction to Geometric Shapes in Games - Explore the role of geometric shapes in game design, including constructing shapes like equilateral triangles, squares, and hexagons. (30 min)

Game Design Hackathon Brainstorming Session - Collaborate in small groups to brainstorm simple game concepts that incorporate probability and geometric principles. (30 min)

Concept Sketching and Sharing - Sketch initial ideas for game designs and share with peers for feedback, focusing on mathematical application and creativity. (25 min)

Introduction to Quadratic Equations in Game Scoring - Explore how quadratic equations can be used to model scoring systems and probabilities in games. (25 min)

Hands-On Workshop: Digital Game Simulation Tools - Work with software tools to begin creating simple digital simulations of game concepts. (30 min)

Game Prototype Development - Start designing and building physical prototypes of board games using geometric shapes and quadratic-based scoring systems. (35 min)

Peer Feedback Session - Share prototype progress with classmates and gather constructive feedback based on essential questions. (20 min)

Game Mechanics Exploration - Students analyze different game mechanics and identify how geometry and quadratic equations can influence game outcomes. (30 min)

Introduction to Digital Simulation Tools - Hands-on workshop where students are introduced to software tools for creating digital game simulations. (25 min)

Geometry in Game Design - Students work in groups to brainstorm how different geometric shapes can be integrated into game designs and how these shapes affect gameplay. (30 min)

Quadratic Equations Workshop - Interactive session where students solve problems involving quadratic equations to model probabilities in games. (25 min)

Game Prototype Sketching - Students begin sketching their initial game design ideas, focusing on integrating geometric shapes and quadratic-based scoring systems. (30 min)

Peer Feedback Session - Students present their sketches to peers for feedback, focusing on the clarity and mathematical integration of their designs. (25 min)

Digital Portfolio Setup - Students create digital portfolios to document their project progress, including reflections on design challenges and strategies. (20 min)

Simulation Software Deep Dive - Students receive guided practice in using simulation tools to create digital game elements, emphasizing how geometry and quadratics are used. (35 min)

Prototype Refinement - Students refine their game prototypes based on peer feedback, ensuring that geometric and quadratic elements are accurately represented. (30 min)

Reflection and Documentation - Students update their digital portfolios with reflections on the week’s activities and their evolving game designs. (25 min)

Geometric Construction Challenge - Construct an equilateral triangle, square, and regular hexagon inscribed in circles using geometric tools, fostering precision and understanding of geometric principles. (30 min)

Digital Simulation Enhancement - Expand digital game simulations by integrating constructed geometric shapes to explore their influence on game dynamics. (25 min)

Quadratic Probability Analysis - Analyze how quadratic equations can model probabilities in games, focusing on fairness and strategic outcomes. (30 min)

Collaborative Game Design - Collaborate in groups to apply quadratic equations and geometric shapes in refining game rules and scoring systems. (25 min)

Prototype Testing Session - Conduct tests on physical game prototypes to assess functionality and balance, utilizing geometric and quadratic elements. (25 min)

Peer Evaluation Workshop - Participate in peer reviews of prototypes, providing feedback on mathematical accuracy and game mechanics based on essential questions. (30 min)

Digital Portfolio Update - Document reflections and insights from testing and peer evaluations in digital portfolios, focusing on growth and strategy adjustments. (20 min)

Game Mechanics Optimization - Use feedback to optimize game mechanics, ensuring geometric precision and quadratic accuracy for fair play. (35 min)

Virtual Showcase Preparation - Prepare for the upcoming virtual showcase by finalizing prototypes and rehearsing explanations of mathematical concepts applied in designs. (30 min)

Reflection and Strategy Session - Reflect on the project journey and strategize final improvements in design and presentation, updating digital portfolios accordingly. (25 min)

Advanced Game Mechanics Workshop - Delve deeper into complex game mechanics, focusing on integrating advanced geometric shapes and quadratic equations to enhance gameplay. (30 min)

Peer Collaboration Session - Pair up with classmates to exchange ideas and strategies on incorporating mathematical principles into game mechanics, offering feedback and suggestions. (25 min)

Digital Game Simulation Development - Utilize software tools to further develop digital simulations, incorporating peer feedback and advanced mathematical models. (35 min)

Reflection and Documentation Update - Add new insights and progress into the digital portfolio, focusing on how advanced mechanics were integrated into designs. (20 min)

Physical Prototype Iteration - Continue refining physical board game prototypes, focusing on the accuracy of geometric constructions and scoring systems. (25 min)

Peer Review & Feedback - Conduct a structured peer review session where students play each other’s games and provide detailed feedback on design and mathematics. (30 min)

Quadratic Scoring System Refinement - Focus on perfecting the scoring systems of games using quadratic equations, ensuring fairness and balance. (30 min)

Digital Portfolio Enhancement - Document the refinement process in the digital portfolio, reflecting on challenges and solutions in scoring system development. (25 min)

Game Prototype Presentation Prep - Prepare a brief presentation overview of the game, highlighting the mathematical principles applied and the design process. (25 min)

Peer Presentation and Feedback - Present game prototypes to peers, articulating the design and mathematical applications, and gather feedback for final adjustments. (30 min)

Final Prototype Testing - Conduct thorough tests on both digital and physical game prototypes, focusing on functionality, fairness, and engagement. (30 min)

Peer Feedback Session - Engage in structured peer reviews, providing detailed feedback on game mechanics and mathematical integration based on essential questions. (25 min)

Game Mechanics Refinement - Use peer feedback to refine and optimize game mechanics, ensuring accurate geometric and quadratic applications. (30 min)

Digital Portfolio Update - Document the refinement process and insights gained from feedback in digital portfolios, reflecting on growth and strategy adjustments. (25 min)

Virtual Showcase Preparation - Finalize prototypes and rehearse presentations, focusing on explaining mathematical principles and demonstrating game designs. (30 min)

Reflection and Strategy Session - Reflect on the project journey, strategize final improvements, and update digital portfolios with reflections on challenges and achievements. (25 min)

Mock Virtual Showcase - Conduct a mock showcase where students present their games to peers, practicing explanations and receiving last-minute feedback. (30 min)

Final Presentation Preparation - Make final adjustments to presentations based on feedback, ensuring clarity and confidence in articulating design and mathematical concepts. (25 min)

Virtual Showcase Event - Host the virtual showcase where students present their completed game prototypes to peers, educators, and family members. (35 min)

Reflection and Portfolio Completion - Reflect on the showcase experience and complete digital portfolios with final reflections on the project journey and personal growth. (20 min)

Final Prototype Testing and Iteration - Conduct thorough testing on both digital and physical game prototypes, focusing on the precision of geometric and quadratic elements. Make final adjustments based on test results to ensure fairness and engagement. (30 min)

Portfolio Reflection and Completion - Reflect on the entire project journey in digital portfolios, highlighting key insights and growth. Ensure all reflections, strategies, and documentation are complete and organized for presentation. (25 min)

Showcase Rehearsal - Practice presenting game prototypes, focusing on articulating the mathematical concepts and design process. Peer feedback will help refine presentation skills and content. (30 min)

Final Design Adjustments - Make any last-minute tweaks to game designs and presentations based on rehearsal feedback to ensure clarity and impact. (25 min)

Virtual Showcase Presentation - Present game prototypes in a virtual showcase to peers and educators, explaining mathematical principles and design choices. Engage in Q&A to demonstrate understanding and application of concepts. (40 min)

Showcase Feedback Session - Participate in a feedback session, receiving constructive feedback from attendees on both the game design and presentation. Document this feedback for future reference. (15 min)

Peer Review and Reflection - Conduct a peer review session to discuss showcase experiences and share feedback. Reflect on how peer insights can be incorporated into future projects. (30 min)

Digital Portfolio Finalization - Finalize digital portfolios, ensuring all project phases are documented with reflections, challenges, and solutions. Prepare portfolios for submission. (25 min)

Project Debrief and Celebration - Participate in a class debrief to highlight successes, challenges, and learning outcomes. Celebrate the completion of the project and recognize individual and group achievements. (30 min)

Future Planning and Goal Setting - Reflect on skills developed and set personal goals for future projects that incorporate mathematical principles and creative design. Document these goals in portfolios. (25 min)