Math Masters: Community Problem Solvers!

High School Grade

Project
8 weeks

Math Masters: Community Problem Solvers!

WMaier

Communication

Connections

Problem Solving

Reasoning & Proof

Representation

Purpose

The purpose of this project is to engage high school students in applying mathematical functions and equations to real-world problems within their community. Through this hands-on experience, students will develop a deep understanding of mathematical concepts and improve their problem-solving, reasoning, and communication skills. By writing a comprehensive PBAT paper and presenting their findings to a Math PBAT Panel, students will demonstrate their ability to accurately use mathematical language, make connections between concepts, and represent solutions effectively.

Learning goals

Students will develop the ability to accurately use mathematical language and notations while clearly explaining their mathematical thinking. They will demonstrate an in-depth understanding of the relationships between mathematical concepts and apply efficient strategies to solve non-routine problems. Through this project, students will create sophisticated mathematical representations to model and solve real-world problems, making valid arguments and justifying their solutions thoroughly.

Standards

Communication - Always uses mathematical language and notations accurately. Always clearly explains mathematical thinking in an organized and detailed way.
Connections - Demonstrates an in-depth understanding of the relationships between mathematical concepts, procedures, and/or strategies.
Problem Solving - Selects appropriate and efficient strategies to solve non-routine problems. Provides in-depth analysis of strategies. Executes conceptually sound mathematical procedures accurately.
Reasoning & Proof - Makes valid conceptual/theoretical argument(s) and mathematically justifies it logically and thoroughly.
Representation - Creates an accurate and sophisticated mathematical representation(s), inherent to the task, to solve problems or portray solutions.

Products

Students will collaboratively develop a comprehensive PBAT paper and presentation, showcasing their ability to use mathematical functions and equations to address a real-world problem identified in their community. Throughout the project, students will create detailed mathematical models and representations that illustrate their problem-solving process and solutions. These products will be refined through peer feedback and one-on-one teacher critiques, culminating in an exhibition before a Math PBAT Panel.

Launch

Begin the project by inviting students to identify and discuss various real-world issues within their community that can be modeled using mathematical functions and equations. Facilitate a brainstorming session where students collaborate in small groups to generate a list of potential problems, such as optimizing public transportation routes or analyzing local business trends. Encourage students to select a problem that resonates with them, fostering a sense of ownership and relevance as they embark on their mathematical exploration.

Exhibition

Students will present their findings and solutions to a Math PBAT Panel composed of teachers, peers, and community members. Each student will deliver a presentation that includes a detailed explanation of their mathematical reasoning, supported by accurate representations and visual aids. The exhibition will feature interactive stations where students can demonstrate how their mathematical models address real-world problems, allowing for audience engagement and discussion. This format will encourage students to articulate their understanding and receive constructive feedback from a diverse audience.

Week 1	Day 1	Day 2	Day 3	Day 4	Day 5
Activities	Launch the project with an introduction session where students discuss the essential question: 'How can mathematical functions and equations be used to model and solve real-world problems in our community?'	Facilitate a brainstorming session in small groups where students identify various real-world issues within their community that can be analyzed through mathematical functions and equations. Encourage creative and diverse thinking.	Guide students to select a specific problem from the brainstormed list that resonates with their interests. Ensure students understand the significance and relevance of their chosen problem.	Conduct a workshop to review mathematical functions and equations, emphasizing their application in real-world contexts. Use examples that relate to the problems identified by students during brainstorming.	Assist students in forming project teams based on shared interest areas or complementary skills. Encourage collaboration and initial planning discussions within teams.
Deliverables	1. A list of at least three potential real-world problems identified by each student or group, along with a brief rationale for why these problems are relevant and interesting. 2. A selected problem statement by each group, clearly defined and supported by an explanation of its significance within the community.
Preparation	1. Prepare a presentation that introduces the essential question and outlines the project goals and expectations. 2. Gather examples of real-world problems that can be solved using mathematical functions and equations to inspire students during brainstorming. 3. Create a guide on effective brainstorming techniques and provide it to students to facilitate their discussions. 4. Develop a short workshop on mathematical functions and equations, including practical examples and applications relevant to community issues. 5. Prepare guidelines for forming effective project teams, including tips on collaboration and communication skills.

Week 2	Day 1	Day 2	Day 3	Day 4
Activities	Guide students in conducting preliminary research on their chosen problem to gather data and identify variables that can be mathematically modeled.	Facilitate a workshop on how to translate real-world problems into mathematical functions and equations, using examples from students' selected topics.	Support students in drafting initial mathematical models that represent their chosen problems, encouraging exploration of different types of functions and equations.	Organize peer feedback sessions where students present their initial models to their peers and receive constructive feedback for refinement.
Deliverables	1. A research summary outlining key data and variables related to the chosen problem, along with potential mathematical approaches for modeling. 2. An initial draft of mathematical models, including functions and equations, that represent the chosen problem.
Preparation	1. Compile resources and examples of mathematical modeling in real-world contexts related to students' chosen problems. 2. Prepare a workshop on translating real-world problems into mathematical models, including examples and practice exercises. 3. Develop guidelines for effective peer feedback, including a rubric or checklist to help students provide and receive constructive critiques. 4. Arrange access to research tools and databases that students can use to gather information on their chosen problem.

Week 3	Day 1	Day 2	Day 3	Day 4
Activities	Facilitate a workshop on refining mathematical models, focusing on accuracy and sophistication in representation. Provide examples of advanced mathematical representations.	Guide students in revising their initial models based on peer feedback and research findings. Encourage the use of visual aids and technology tools to enhance their representations.	Organize sessions for one-on-one meetings with students to provide personalized feedback on their revised mathematical models and discuss potential improvements.	Conduct a peer review session where students present their refined models and receive feedback on clarity and accuracy of mathematical language and notation.
Deliverables	1. A revised and refined mathematical model that accurately represents the chosen problem, including functions, equations, and visual representations. 2. A reflection document from each student or group summarizing the feedback received and how it was incorporated into their revisions.
Preparation	1. Prepare a workshop on refining mathematical models, including advanced representation techniques and examples. 2. Compile a list of technology tools and software that students can use to create sophisticated mathematical representations. 3. Develop a feedback checklist to guide one-on-one meetings and peer review sessions, focusing on accuracy and clarity of mathematical language. 4. Set up a schedule for one-on-one feedback meetings with students, ensuring all groups have dedicated time for personalized guidance.

Week 4	Day 1	Day 2	Day 3	Day 4
Activities	Facilitate a session on developing mathematical arguments and proofs, emphasizing logical reasoning and justification techniques.	Guide students in creating a comprehensive outline for their PBAT paper, detailing their mathematical models, problem-solving approaches, and justifications.	Organize a peer feedback workshop where students share their outlines and receive input on the clarity and structure of their arguments.	Conduct one-on-one meetings with students to provide targeted feedback on their outlines, focusing on the depth and coherence of their mathematical reasoning.
Deliverables	1. A detailed outline of the PBAT paper, including sections on the mathematical models used, problem-solving strategies, and reasoning and proof. 2. A reflection document summarizing feedback received from peers and teachers, noting planned revisions to enhance clarity and coherence.
Preparation	1. Prepare materials for a session on mathematical arguments and proofs, including examples of strong justifications and logical reasoning. 2. Develop a guide for structuring a PBAT paper outline, emphasizing the integration of mathematical language and reasoning. 3. Create a checklist for peer feedback sessions to help students focus on evaluating the clarity and coherence of arguments. 4. Schedule one-on-one meetings with each student or group to discuss their outlines and provide personalized feedback.

Week 5	Day 1	Day 2	Day 3	Day 4
Activities	Conduct a workshop on drafting and writing mathematical analyses, focusing on organizing mathematical reasoning, interpretations, and justifications within the PBAT paper.	Guide students in integrating feedback from previous weeks into their draft, ensuring each section of their paper logically connects mathematical concepts and solutions.	Facilitate a peer review session where students exchange drafts to receive constructive feedback on clarity, coherence, and depth of mathematical analysis.	Organize one-on-one meetings where students discuss their draft progress with teachers, focusing on enhancing mathematical language and notation accuracy.
Deliverables	1. A complete first draft of the PBAT paper, including sections that detail mathematical models, problem-solving strategies, and theoretical arguments. 2. A peer-reviewed feedback document, summarizing key insights and suggestions for improving the draft.
Preparation	1. Develop workshop materials that outline effective mathematical analysis writing techniques, including clear examples and structured approaches. 2. Create a feedback rubric for peer review sessions, focusing on evaluating the use of mathematical language, clarity, and logical flow. 3. Prepare a schedule for one-on-one meetings with students, ensuring each group receives focused guidance on their draft development. 4. Compile resources and examples of well-structured mathematical papers to provide students with reference materials.

Week 6	Day 1	Day 2	Day 3	Day 4
Activities	Facilitate a workshop on creating effective visual aids and presentations to convey mathematical findings to an audience. Discuss the integration of graphs, charts, and other visual representations to enhance understanding.	Guide students in developing a draft of their presentation, focusing on clear communication of mathematical reasoning, models, and solutions.	Organize practice presentation sessions where students present their work to peers and receive feedback on presentation skills and content clarity.	Conduct one-on-one meetings with students to provide personalized feedback on their presentation drafts and suggest improvements.
Deliverables	1. A draft of the presentation, including visual aids that effectively communicate the mathematical models and solutions. 2. A reflection document summarizing peer and teacher feedback on the presentation, noting planned improvements for the final presentation.
Preparation	1. Prepare workshop materials on creating impactful visual aids and presentations, including examples of effective graphs and charts. 2. Develop a checklist for presentation feedback, focusing on clarity, engagement, and the use of mathematical language. 3. Schedule practice presentation sessions and ensure necessary equipment and resources are available for students. 4. Compile a list of best practices for public speaking and presentation skills to share with students.

Week 7	Day 1	Day 2	Day 3	Day 4
Activities	Facilitate a workshop on refining the final PBAT paper, focusing on enhancing mathematical language, coherence, and depth of analysis. Encourage students to incorporate previous feedback thoroughly.	Guide students in conducting final revisions to their papers, ensuring all mathematical models, arguments, and proofs are accurate and well-documented.	Organize a peer review session where students exchange their revised papers and provide feedback specifically targeting the use of mathematical language and clarity of explanations.	Conduct one-on-one meetings with students to provide final feedback on their PBAT papers and discuss any remaining areas for improvement before submission.
Deliverables	1. A polished final draft of the PBAT paper, ready for submission, including all mathematical models, problem-solving strategies, and theoretical justifications. 2. A peer-reviewed feedback document that highlights key suggestions incorporated into the final draft.
Preparation	1. Develop workshop materials that focus on refining the final paper, including tips for enhancing mathematical language and coherence. 2. Create a checklist for peer review sessions to guide students in evaluating the clarity and accuracy of mathematical language and reasoning. 3. Prepare a schedule for one-on-one meetings, ensuring each student or group receives targeted feedback on their final paper. 4. Compile resources and examples of exemplary PBAT papers to serve as reference materials for students.

Week 8	Day 1	Day 2	Day 3	Day 4
Activities	Conduct a rehearsal for the Math PBAT Panel presentation, where students present their findings to peers in a simulated panel setting. Encourage students to practice responding to audience questions and integrating visual aids effectively.	Facilitate a final feedback session where peers provide constructive critiques on presentation delivery, clarity, and engagement, focusing on improving any weak areas identified during rehearsal.	Guide students in making final adjustments to their presentations and papers based on rehearsal feedback, ensuring all mathematical reasoning and visual aids are clear and effective.	Host the Math PBAT Panel exhibition, where students present their final projects to a panel of teachers, peers, and community members, showcasing their solutions to real-world problems using mathematical functions and equations.
Deliverables	1. A final, polished presentation delivered to the Math PBAT Panel, showcasing the comprehensive mathematical analysis and solutions to the chosen problem. 2. A final PBAT paper submitted to the teacher, reflecting all revisions and feedback, demonstrating clear mathematical reasoning and accurate use of mathematical language.
Preparation	1. Arrange the logistics for the Math PBAT Panel exhibition, including scheduling, panel invitations, and setup of the presentation space with necessary equipment. 2. Prepare guidelines for the panel, detailing the criteria for evaluating students' presentations and providing them with a clear understanding of expectations. 3. Compile feedback forms for panel members to provide structured, constructive feedback on students' presentations and papers. 4. Ensure all technical equipment, such as projectors and computers, are functioning and available for the students' use during their presentations.