Project Pathways: Quadratics in Motion Exploration

10th Grade

Project
10 weeks

Project Pathways: Quadratics in Motion Exploration

Angela Torres

Purpose

The purpose of this project is to engage 10th-grade students in a deeper understanding of quadratic equations through hands-on, real-world applications. By investigating projectile motion, students will explore how quadratic functions model the paths of objects in motion, enhancing their comprehension of mathematical concepts and their relevance in everyday life. This project aims to foster critical thinking and analytical skills as students record, graph, and analyze projectile motion, ultimately creating a digital portfolio that showcases their learning process and growth. Through peer review and digital feedback, students will refine their work, gaining insights into the iterative nature of problem-solving and the importance of collaboration and communication. The project culminates in an interactive digital map, making their analyses accessible and demonstrating the practical applications of math in predicting and understanding motion in the natural world.

Learning goals

In this project, students will delve into the world of quadratic functions and their applications in real-life scenarios, particularly focusing on projectile motion. They will explore different forms of quadratic equations, including vertex form, standard form, and factored form, to understand how each can model the path of a projectile. Students will develop problem-solving skills by learning to solve quadratic equations through various methods such as factoring, completing the square, and using the quadratic formula. Additionally, they will enhance their analytical skills by recording and analyzing projectile motions, plotting these on coordinate grids, and interpreting the results. This project will also foster critical thinking and collaboration as students engage in peer reviews and digital feedback loops, refining their work based on constructive feedback. Through creating a digital portfolio and an interactive digital map, students will not only showcase their mathematical understanding but also improve their digital literacy and communication skills. Finally, students will reflect on the broader applications of quadratic equations, considering their relevance in various careers and everyday life, thereby deepening their appreciation for the role of mathematics in the natural world.

Standards

Common Core - CCSS.MATH.CONTENT.HSF.IF.B.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
Common Core - CCSS.MATH.CONTENT.HSF.IF.C.7.A: Graph linear and quadratic functions and show intercepts, maxima, and minima.
Common Core - CCSS.MATH.CONTENT.HSA.REI.B.4: Solve quadratic equations in one variable.

Products

In this project, students will create a comprehensive digital portfolio that documents their exploration of quadratic equations through the lens of projectile motion. This portfolio will include video recordings of projectile motions they choose to analyze, detailed graphs plotted on coordinate grids, and thorough mathematical analyses that demonstrate their understanding of quadratic functions. Additionally, students will develop an interactive digital map that showcases various projectile scenarios they have studied, with clickable features that provide access to their videos, graphs, and analyses. This map will serve as an engaging tool for sharing their findings with a wider audience, highlighting the real-world applications of quadratic equations in predicting projectile paths. Through this project, students will accomplish a deeper understanding of quadratic functions and their relevance, as well as enhance their skills in mathematical analysis, digital literacy, and collaborative feedback.

Launch

To launch the project, organize an outdoor demonstration where students witness a live projectile motion event, such as a water balloon catapult or a model rocket launch. Begin with a brief discussion on how quadratic equations are used to predict the paths of these projectiles. Then, have students make initial predictions about the projectile's path using basic observations. This hands-on experience will spark curiosity and provide a tangible context for the mathematical concepts they will explore throughout the project. Encourage students to brainstorm different types of projectile motions they might want to record and analyze for their projects.

Exhibition

To culminate the project, organize a "Projectile Motion Fair" where students can showcase their interactive digital maps to peers, teachers, and family members. Set up stations for each group where attendees can explore different projectile scenarios, watch the recorded videos, and engage with the students' analyses and graphs. Encourage students to prepare short presentations explaining their process, findings, and reflections on the real-world applications of quadratic equations. Additionally, invite local professionals from fields such as engineering, sports, or physics to provide real-world insights and feedback, enhancing the authenticity and relevance of the learning experience. This exhibition not only celebrates students' work but also fosters a deeper appreciation for the practical applications of mathematics.

Week 1	Day 1	Day 2	Day 3	Day 4	Day 5
Activities	Activity 1: Introduction to Quadratic Equations - The teacher will introduce the concept of quadratic equations, focusing on their relevance in projectile motion. Students will participate in a class discussion to share their prior knowledge and questions about quadratic functions.	Activity 2: Outdoor Demonstration - Organize an outdoor demonstration of a live projectile motion event (e.g., water balloon catapult or model rocket launch). Students will observe and make initial predictions about the path of the projectiles.	Activity 3: Brainstorming Session - In small groups, students will brainstorm different types of projectile motions they would like to record and analyze for their projects. They will list potential objects and scenarios.	Activity 4: Introduction to Digital Tools - Provide an overview of the digital tools and platforms students will use to create their digital portfolios and interactive maps. Conduct a brief tutorial on how to use these tools.	Activity 5: Initial Research and Planning - Students will conduct initial research on their chosen projectile scenarios, gathering information that will help them understand the physics and mathematics involved. They will create a project plan outlining their objectives and the steps they will take.
Deliverables	1. Deliverable 1: Reflection Journal Entry - Students will submit a reflection journal entry summarizing their observations from the outdoor demonstration and their initial thoughts on the project. 2. Deliverable 2: Project Plan - Each student or group will submit a project plan outlining their chosen projectile scenario, objectives, and a timeline for their work.
Preparation	1. Teacher Preparation Task 1: Organize and set up the outdoor demonstration, ensuring all necessary safety measures are in place. 2. Teacher Preparation Task 2: Prepare a presentation introducing quadratic equations and their applications in projectile motion. 3. Teacher Preparation Task 3: Familiarize with the digital tools and platforms that students will use, ensuring the ability to provide guidance and troubleshoot any issues. 4. Teacher Preparation Task 4: Gather and prepare materials for students to use during the brainstorming and research activities, such as reference books, articles, and video resources.

Week 2	Day 1	Day 2	Day 3	Day 4	Day 5
Activities	Activity 1: Review of Quadratic Equations - Conduct a review session on the different forms of quadratic equations (vertex form, standard form, factored form). Students will solve example problems and discuss their applications in projectile motion.	Activity 2: Hands-On Experimentation - In small groups, students will conduct a simple experiment to gather data on projectile motion. They will use tools such as protractors and stopwatches to measure angles and times of their chosen projectiles.	Activity 3: Data Collection and Organization - Students will organize the data collected from their experiments into tables and charts. They will begin to identify patterns and key features that relate to quadratic functions.	Activity 4: Introduction to Graphing - Provide a tutorial on graphing quadratic functions using coordinate grids. Students will practice plotting their collected data and identifying intercepts, maxima, and minima.	Activity 5: Peer Collaboration - Facilitate a session where students share their initial findings and graphs with peers. They will provide and receive constructive feedback to refine their analyses.
Deliverables	1. Deliverable 1: Experiment Report - Students will submit a report detailing their experimentation process, data collected, and initial analyses. This report will include tables, charts, and a preliminary graph of their data. 2. Deliverable 2: Reflection Journal Entry - A reflective journal entry where students describe their learning experiences during the hands-on experimentation and data collection activities.
Preparation	1. Teacher Preparation Task 1: Prepare materials for the hands-on experimentation, including protractors, stopwatches, and any other necessary equipment. 2. Teacher Preparation Task 2: Develop a review session plan covering the key concepts of quadratic equations and their forms. 3. Teacher Preparation Task 3: Create graphing tutorials and resources to assist students in plotting their data accurately on coordinate grids. 4. Teacher Preparation Task 4: Set up the classroom for peer collaboration, ensuring a conducive environment for discussion and feedback.

Week 3	Day 1	Day 2	Day 3	Day 4	Day 5
Activities	Activity 1: In-depth Exploration of Vertex Form - Students will learn about the vertex form of quadratic equations. The teacher will provide examples and students will practice converting quadratic equations to vertex form and interpreting the significance of the vertex in projectile motion.	Activity 2: Graphing Vertex Form - Conduct a session where students graph quadratic equations in vertex form using their collected data. They will focus on identifying the vertex and axis of symmetry.	Activity 3: Real-World Application Analysis - Students will research and present examples of real-world applications of quadratic equations in vertex form, focusing on sports, architecture, or physics.	Activity 4: Interactive Digital Tool Workshop - Guide students in using digital tools to create dynamic graphs of their projectile data in vertex form. Students will begin to integrate these graphs into their digital portfolios.	Activity 5: Peer Review and Feedback - Facilitate a session where students present their vertex form analyses to peers. They will give and receive feedback, focusing on accuracy and clarity of their interpretations.
Deliverables	1. Deliverable 1: Vertex Form Analysis Report - Students will submit a report that includes their interpretations of vertex form quadratic equations, graphs of their projectile data, and real-world application examples. 2. Deliverable 2: Reflection Journal Entry - Students will write a journal entry reflecting on their learning experience with vertex form, including insights gained from peer feedback.
Preparation	1. Teacher Preparation Task 1: Develop instructional materials and examples for the vertex form of quadratic equations, including a presentation and practice worksheets. 2. Teacher Preparation Task 2: Prepare digital graphing tools and ensure students have access to devices and software needed for dynamic graph creation. 3. Teacher Preparation Task 3: Create a rubric for peer review sessions, outlining criteria for effective feedback and areas of focus. 4. Teacher Preparation Task 4: Compile a list of resources (articles, videos) that showcase real-world applications of quadratic equations in vertex form.

Week 4	Day 1	Day 2	Day 3	Day 4	Day 5
Activities	Activity 1: Exploration of Standard Form - Students will delve into the standard form of quadratic equations. The teacher will provide examples and guide students in transforming quadratic equations into standard form and identifying the significance of coefficients in projectile motion.	Activity 2: Graphing Standard Form - Conduct a session where students graph quadratic equations in standard form using their collected data. They will learn to identify key features such as intercepts and the axis of symmetry.	Activity 3: Problem Solving with Quadratic Formula - Introduce the quadratic formula as a method for solving quadratic equations. Students will practice solving equations to find the roots and relate these solutions to their projectile data.	Activity 4: Digital Portfolio Development - Guide students in integrating their standard form graphs and analyses into their digital portfolios. Students will begin to organize their work, ensuring clarity and coherence in presentation.	Activity 5: Collaborative Work Session - Facilitate a session where students work together to refine their standard form analyses and digital portfolio entries. Encourage peer feedback and collaborative problem-solving.
Deliverables	1. Deliverable 1: Standard Form Analysis Report - Students will submit a report that includes their interpretations of standard form quadratic equations, graphs of their projectile data, and solutions using the quadratic formula. 2. Deliverable 2: Reflection Journal Entry - Students will write a journal entry reflecting on their learning experience with standard form and the quadratic formula, including insights from peer collaboration.
Preparation	1. Teacher Preparation Task 1: Develop instructional materials and examples for the standard form of quadratic equations, including a presentation and practice worksheets. 2. Teacher Preparation Task 2: Prepare graphing resources and ensure students have access to tools and software needed for graphing and solving quadratic equations. 3. Teacher Preparation Task 3: Create guidelines for digital portfolio entries, outlining expectations for clarity and coherence. 4. Teacher Preparation Task 4: Organize a collaborative work session layout that encourages student interaction and effective feedback exchange.

Week 5	Day 1	Day 2	Day 3	Day 4	Day 5
Activities	Activity 1: Exploration of Factored Form - Students will explore the factored form of quadratic equations. The teacher will present examples and guide students in converting quadratic equations to factored form, emphasizing the significance of the roots in projectile motion.	Activity 2: Graphing Factored Form - Conduct a session where students graph quadratic equations in factored form using their collected data. They will focus on identifying the roots and how they relate to the projectile's path.	Activity 3: Problem Solving with Factored Form - Students will practice solving quadratic equations in factored form to find the roots, applying these solutions to their projectile data.	Activity 4: Digital Portfolio Enhancement - Guide students in adding their factored form graphs and analyses to their digital portfolios. Emphasize the importance of clear and thorough documentation of their work.	Activity 5: Peer Feedback and Refinement - Facilitate a session where students review each other's factored form analyses and digital portfolio entries. Encourage constructive feedback and collaborative problem-solving to refine their work.
Deliverables	1. Deliverable 1: Factored Form Analysis Report - Students will submit a report that includes their interpretations of factored form quadratic equations, graphs of their projectile data, and solutions using the roots found. 2. Deliverable 2: Reflection Journal Entry - Students will write a journal entry reflecting on their learning experience with factored form, including insights gained from peer feedback and collaboration.
Preparation	1. Teacher Preparation Task 1: Develop instructional materials and examples for the factored form of quadratic equations, including a presentation and practice worksheets. 2. Teacher Preparation Task 2: Prepare graphing resources and ensure students have access to tools and software needed for graphing and solving quadratic equations in factored form. 3. Teacher Preparation Task 3: Create guidelines for digital portfolio enhancement, outlining expectations for thorough documentation and clarity. 4. Teacher Preparation Task 4: Organize a peer feedback session layout that encourages effective feedback exchange and collaborative problem-solving.

Week 6	Day 1	Day 2	Day 3	Day 4	Day 5
Activities	Activity 1: Introduction to Data Interpretation - The teacher will introduce key concepts of data interpretation and analysis, focusing on how to extract meaningful information from projectile motion data.	Activity 2: Data Refinement and Analysis - Students will revisit their collected data, refining it to ensure accuracy and consistency. They will perform deeper analyses to identify trends and anomalies in their projectile motion data.	Activity 3: Advanced Graphing Techniques - Conduct a session where students learn advanced graphing techniques to represent their refined data visually. Emphasize the use of digital tools to enhance the clarity and presentation of graphs.	Activity 4: Interpretation and Presentation Workshop - Students will practice interpreting their graphs and data, developing skills to effectively communicate their findings and insights to others.	Activity 5: Peer Review and Feedback Session - Facilitate a session where students present their refined data analyses and graphs to peers. Encourage constructive feedback and discussions to enhance their interpretations.
Deliverables	1. Deliverable 1: Refined Data Analysis Report - Students will submit a comprehensive report including their refined data, advanced graphs, and interpretations. This report should demonstrate a clear understanding of the data's implications. 2. Deliverable 2: Reflection Journal Entry - Students will write a journal entry reflecting on their experiences with data refinement and advanced analysis techniques, including insights gained from peer feedback.
Preparation	1. Teacher Preparation Task 1: Develop instructional materials and examples for data interpretation and analysis, including presentations and practice datasets. 2. Teacher Preparation Task 2: Prepare tutorials and resources on advanced graphing techniques, ensuring students have access to necessary digital tools and software. 3. Teacher Preparation Task 3: Create guidelines for the data analysis report, outlining expectations for clarity, accuracy, and depth of analysis. 4. Teacher Preparation Task 4: Organize a peer review session layout that encourages effective feedback exchange and collaborative discussions on data interpretations.

Week 7	Day 1	Day 2	Day 3	Day 4	Day 5
Activities	Activity 1: Introduction to Interactive Digital Mapping - The teacher will introduce students to the concept of digital maps and their applications in presenting data visually. Students will explore examples of interactive maps to understand how they can be used to share their findings.	Activity 2: Interactive Map Design Workshop - Conduct a workshop where students brainstorm and plan the design of their interactive digital maps. They will outline the features they want to include, such as clickable elements, descriptions, and multimedia components.	Activity 3: Map Creation Using Digital Tools - Guide students in using digital mapping tools to start creating their interactive maps. They will begin by adding basic elements like location markers, labels, and links to their data analyses.	Activity 4: Integration of Multimedia - Students will enhance their maps by integrating multimedia elements such as videos, images, and audio narrations related to their projectile motion analyses. This will add depth and engagement to their presentations.	Activity 5: Peer Review and Iteration - Facilitate a session where students present their initial interactive maps to peers. Encourage constructive feedback focusing on usability, clarity, and engagement. Students will iterate on their designs based on the feedback received.
Deliverables	1. Deliverable 1: Initial Interactive Digital Map - Students will submit an initial version of their interactive digital map, showcasing their projectile motion analyses with integrated multimedia elements. 2. Deliverable 2: Reflection Journal Entry - Students will write a journal entry reflecting on their experiences with interactive map design and multimedia integration, including insights gained from peer feedback.
Preparation	1. Teacher Preparation Task 1: Develop instructional materials and examples for interactive digital mapping, including presentations and case studies of effective maps. 2. Teacher Preparation Task 2: Prepare tutorials and resources on digital mapping tools, ensuring students have access to necessary software and platforms. 3. Teacher Preparation Task 3: Create guidelines for the interactive digital map, outlining expectations for functionality, clarity, and multimedia integration. 4. Teacher Preparation Task 4: Organize a peer review session layout that encourages effective feedback exchange and collaborative discussions on map design and usability.

Week 8	Day 1	Day 2	Day 3	Day 4	Day 5
Activities	Activity 1: Refinement of Interactive Maps - Students will focus on refining their interactive digital maps, ensuring that all elements are accurate, clear, and effectively integrated. This includes revisiting their multimedia components, adjusting layouts, and enhancing user experience.	Activity 2: Advanced Multimedia Integration - Conduct a session where students explore advanced multimedia integration techniques. They will learn how to add interactive elements such as quizzes or interactive timelines to their maps.	Activity 3: User Testing and Feedback - Students will conduct user testing sessions where peers and other students interact with their maps. They will gather feedback on usability, engagement, and clarity.	Activity 4: Iterative Map Improvement - Based on the feedback from user testing, students will make iterative improvements to their maps. This process will involve problem-solving to address any issues identified during testing.	Activity 5: Presentation Skills Workshop - Provide a workshop on effective presentation skills. Students will prepare to present their interactive maps, focusing on how to clearly convey their analyses and insights.
Deliverables	1. Deliverable 1: Refined Interactive Digital Map - Students will submit an updated version of their interactive digital map, incorporating changes based on user feedback and advanced multimedia integration. 2. Deliverable 2: Reflection Journal Entry - Students will write a journal entry reflecting on their experiences with user testing, iterative design, and the skills gained in multimedia integration.
Preparation	1. Teacher Preparation Task 1: Develop instructional materials on advanced multimedia integration techniques, including examples and tutorials. 2. Teacher Preparation Task 2: Organize resources for user testing, such as feedback forms and guidelines for constructive criticism. 3. Teacher Preparation Task 3: Prepare a workshop on presentation skills, including tips on engaging an audience and effectively communicating complex information. 4. Teacher Preparation Task 4: Set up a schedule for user testing sessions, ensuring a smooth process for feedback collection and iteration.

Week 9	Day 1	Day 2	Day 3	Day 4	Day 5
Activities	Activity 1: Finalization of Interactive Maps - Students will focus on finalizing their interactive digital maps, ensuring all elements are cohesive and well-integrated. They will conduct a final review to check for any errors or areas that need improvement.	Activity 2: Presentation Rehearsal - Students will rehearse their presentations in small groups, receiving feedback from peers on clarity, engagement, and effectiveness. This rehearsal will help them refine their delivery and address any potential issues.	Activity 3: Reflection and Self-Assessment - Students will participate in a reflection session where they assess their own learning and growth throughout the project. They will identify key takeaways and areas for further improvement.	Activity 4: Final Peer Review Session - Facilitate a session where students present their final interactive maps to a new set of peers. This session will focus on providing constructive feedback before the final exhibition.	Activity 5: Exhibition Preparation - Students will prepare materials and practice their setups for the upcoming "Projectile Motion Fair." They will ensure all digital components function correctly and rehearse their explanations for visitors.
Deliverables	1. Deliverable 1: Final Interactive Digital Map - Students will submit the final version of their interactive digital map, demonstrating their understanding and application of quadratic functions in projectile motion. 2. Deliverable 2: Presentation Outline - Students will submit a detailed outline of their presentation, highlighting the key points they will cover during the "Projectile Motion Fair." 3. Deliverable 3: Reflection Journal Entry - Students will write a comprehensive journal entry reflecting on their overall project experience, including personal growth, challenges faced, and skills developed.
Preparation	1. Teacher Preparation Task 1: Review and provide feedback on students' final interactive maps and presentation outlines, ensuring alignment with project goals and expectations. 2. Teacher Preparation Task 2: Organize and schedule the final peer review session, ensuring a supportive environment for constructive feedback exchange. 3. Teacher Preparation Task 3: Prepare materials and logistical arrangements for the "Projectile Motion Fair," including setting up stations and coordinating with any invited guests or professionals. 4. Teacher Preparation Task 4: Develop a checklist for students to use during exhibition preparation, ensuring all technical and presentation elements are ready for the fair.

Week 10	Day 1	Day 2	Day 3	Day 4	Day 5
Activities	Activity 1: Final Exhibition Setup - Students will arrive early in the week to set up their stations for the 'Projectile Motion Fair.' They will ensure their interactive digital maps are correctly displayed and all multimedia components function smoothly.	Activity 2: Presentation Finalization - Students will fine-tune their presentations, practicing their delivery and ensuring they can confidently explain their analyses, findings, and the real-world applications of quadratic equations.	Activity 3: Exhibition Day - Host the 'Projectile Motion Fair,' where students present their interactive digital maps to peers, teachers, family members, and invited professionals. Students will engage with attendees, answer questions, and demonstrate their understanding of projectile motion.	Activity 4: Feedback and Reflection Session - After the exhibition, students will gather to discuss their experiences, share feedback on each other's presentations, and reflect on the entire project's process and outcomes.	Activity 5: Project Closure and Celebration - Conclude the project with a celebration of students' achievements. Recognize outstanding work and encourage students to reflect on their growth and future applications of the skills learned.
Deliverables	1. Deliverable 1: Exhibition Presentation - Students will present their interactive digital maps and analyses during the 'Projectile Motion Fair.' 2. Deliverable 2: Final Reflection Journal Entry - Students will submit a comprehensive reflection on their project experience, highlighting their learning journey, challenges faced, and the skills they have developed.
Preparation	1. Teacher Preparation Task 1: Coordinate the logistics for the 'Projectile Motion Fair,' including setting up the venue, arranging for necessary equipment, and confirming the attendance of invited guests. 2. Teacher Preparation Task 2: Provide students with a checklist for their exhibition setup, ensuring each student is prepared and aware of what they need to bring and display. 3. Teacher Preparation Task 3: Prepare feedback forms for guests to fill out during the exhibition, allowing students to receive diverse perspectives on their work. 4. Teacher Preparation Task 4: Organize a post-exhibition feedback and reflection session, creating a supportive environment for students to share their experiences and insights. 5. Teacher Preparation Task 5: Plan a celebratory event to acknowledge students' hard work and achievements, fostering a sense of accomplishment and closure for the project.