High School Grade
Project
6 weeks
Triangle Triumph: Unlocking Real-World Symmetry
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Purpose
This project aims to immerse students in the practical applications of triangle congruence shortcuts by connecting mathematical concepts to real-world scenarios in architecture, engineering, navigation, and design. Students will explore how these principles ensure precision and functionality in various fields, while also engaging in creative expression through geometric art. By collaborating with community partners and reflecting on potential career paths, students will deepen their understanding of the significance of math in everyday life and professional contexts.
Learning goals
Students will develop a deep understanding of triangle congruence shortcuts and their practical applications in real-world contexts such as architecture, engineering, and design. They will engage in hands-on activities to create geometric art pieces and analyze everyday objects, enhancing their problem-solving and critical-thinking skills. By collaborating with peers and presenting their findings, students will refine their communication abilities and gain insights into potential career paths related to geometry and its applications.
Standards
- Common Core - CCSS.MATH.CONTENT.HSG.CO.B.7: Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
- Common Core - CCSS.MATH.CONTENT.HSG.CO.B.8: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
- Common Core - CCSS.MATH.PRACTICE.MP4: Model with mathematics by applying triangle congruence shortcuts to real-world contexts such as architecture and engineering.
Products
Students will create a series of products including digital slide presentations, physical models, and geometric art pieces. These products will demonstrate their understanding of triangle congruence shortcuts in real-world contexts such as architecture, engineering, and navigation. Additionally, students will compose essays that reflect on their learning process and the practical applications of their findings. Diagrams will be utilized to visually represent their problem-solving strategies and design improvements for everyday objects. Throughout the project, students will engage in critique and revision sessions to refine their work before presenting to classmates and administration.
Launch
Begin the project by inviting a guest speaker from the fields of architecture or engineering to discuss how triangle congruence is vital in their work. Follow this with a hands-on activity where students use simple materials to construct models of structures or objects, applying triangle congruence shortcuts. This will provide a tangible connection between abstract mathematical concepts and their practical applications, sparking curiosity and setting the stage for the project.
Exhibition
Students will present their projects in a gallery-style exhibition open to classmates and school administration, where each group showcases their models, diagrams, and geometric art pieces. Attendees will circulate through the exhibition, engaging with students who will explain how triangle congruence shortcuts were applied in their projects. This interactive setting allows for a deeper understanding of the real-world applications and invites feedback and questions from the audience, fostering a collaborative learning environment.
Plan
| Week 1 | Day 1 | Day 2 | Day 3 | Day 4 |
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| Activities |
Activity 1: Project Launch - Organize a virtual or in-person panel with professionals from architecture and engineering to discuss the relevance of triangle congruence in their work. Facilitate a Q&A session for student inquiries.
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Activity 2: Interactive Challenge - Students will participate in a hands-on activity to design and build a small-scale structure using triangle congruence principles with materials like straws, string, and cardboard to demonstrate stability and balance.
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Activity 3: Group Research and Presentation - In small groups, students will research real-world applications of triangle congruence shortcuts in architecture and engineering. They'll prepare a digital slide presentation summarizing their findings.
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Activity 4: Individual Reflection - Students will write a reflection essay on their understanding of triangle congruence in professional contexts and its impact on their career interests.
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| Deliverables |
1. Deliverable 1: Group digital slide presentation on the application of triangle congruence shortcuts in architecture and engineering.
2. Deliverable 2: Individual reflection essay on the significance of triangle congruence in real-world applications. |
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| Preparation |
1. Prep Task 1: Coordinate with professionals for the panel discussion, ensuring they are prepared to discuss relevant applications of triangle congruence.
2. Prep Task 2: Acquire and organize materials for the interactive structure-building challenge, such as straws, string, cardboard, and scissors. 3. Prep Task 3: Compile a list of reliable online resources and articles for students to use during their group research. 4. Prep Task 4: Set up a digital platform for students to create and submit their presentations. |
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| Week 2 | Day 1 | Day 2 |
|---|---|---|
| Activities |
Activity 1: Geometric Art Creation - Students will apply their understanding of triangle congruence shortcuts (SSS, SAS, ASA, SAA) to create a geometric art piece that demonstrates balance and symmetry. They will use materials such as colored paper, rulers, protractors, and compasses to design and construct their artwork.
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Activity 2: Real-World Application Analysis - In pairs, students will select an everyday object and analyze its design using triangle congruence principles. They will identify how these principles contribute to the object's functionality and propose one improvement based on their analysis. Students will create a diagram to illustrate their findings and proposed design enhancement.
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| Deliverables |
1. Deliverable 1: A completed geometric art piece that visually incorporates triangle congruence shortcuts.
2. Deliverable 2: A diagram and written analysis of an everyday object, highlighting the role of triangle congruence in its design and suggesting an improvement. |
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| Preparation |
1. Prep Task 1: Gather materials for the geometric art activity, including colored paper, rulers, protractors, compasses, scissors, and glue.
2. Prep Task 2: Prepare examples of geometric art pieces that incorporate symmetry and congruence principles to inspire students. 3. Prep Task 3: Compile a list of everyday objects for students to choose from for their analysis (e.g., bicycles, chairs, bridges). 4. Prep Task 4: Set up a digital platform for students to submit their diagrams and written analyses. |
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| Week 3 | Day 1 | Day 2 |
|---|---|---|
| Activities |
Activity 1: Model Construction - Students will use their understanding of triangle congruence shortcuts to construct a physical model of a real-world structure, such as a bridge or tower. They will work in small groups using materials like dowels, cardstock, and connectors. The model should demonstrate structural stability through the application of congruence principles.
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Activity 2: Presentation Preparation - Students will prepare a presentation on their model, highlighting how triangle congruence shortcuts contributed to the design and stability of their structure. This presentation will include digital slides and a brief oral explanation of their model's features, the importance of congruence in its design, and potential real-world applications. Students will also incorporate reflections on how this project could relate to future career interests in architecture or engineering.
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| Deliverables |
1. Deliverable 1: A completed physical model of a structure that incorporates triangle congruence principles.
2. Deliverable 2: A digital slide presentation and oral explanation of the model, discussing the role of triangle congruence in the design and potential career connections. |
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| Preparation |
1. Prep Task 1: Gather materials for model construction, including dowels, cardstock, connectors, glue, and measuring tools.
2. Prep Task 2: Arrange for a digital platform for students to create and submit their slide presentations. 3. Prep Task 3: Organize a schedule for presentation rehearsals, allowing each group time to practice their oral explanation and receive peer feedback. 4. Prep Task 4: Provide examples of real-world structures that incorporate triangle congruence for inspiration and context. |
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| Week 4 | Day 1 | Day 2 |
|---|---|---|
| Activities |
Activity 1: Final Presentation Rehearsals - Students will rehearse their presentations in front of small peer groups, receiving constructive feedback on both content and delivery. This ensures each group is prepared to present their models, art pieces, and analyses effectively during the exhibition.
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Activity 2: Exhibition Day - Host a gallery-style exhibition where students present their models, geometric art pieces, and analyses. Students will engage with classmates and school administration, explaining how triangle congruence shortcuts were applied in their projects, and answer questions about the real-world applications and career connections.
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| Deliverables |
1. Deliverable 1: A polished final presentation, including digital slides, oral explanation, and any physical models or art pieces.
2. Deliverable 2: A written reflection on the entire project, focusing on their learning experiences, the impact of peer and teacher feedback in refining their work, and insights into potential career paths. |
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| Preparation |
1. Prep Task 1: Arrange the exhibition space, ensuring there is ample room for each group's displays and that presentation technology (e.g., projectors, laptops) is set up and functioning.
2. Prep Task 2: Prepare feedback forms or digital surveys for exhibition attendees to complete, offering insights and constructive criticism for student presenters. 3. Prep Task 3: Coordinate with school administration to ensure their attendance and participation in the exhibition. 4. Prep Task 4: Provide students with a checklist and rubric for self-assessing their final presentations, ensuring all essential elements are included and polished. |
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| Week 5 | Day 1 | Day 2 |
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| Activities |
Activity 1: Community Partner Collaboration - Students will connect with professionals in the fields of architecture, engineering, or design for a virtual or in-person workshop. These professionals will provide insights into how they use triangle congruence in their work and offer real-world challenges for students to solve using their knowledge.
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Activity 2: Career Exploration and Reflection - Students will engage in a reflective activity where they compare their experiences and findings from the project to potential career paths. They will research various professions where geometry and triangle congruence are applicable and prepare a short essay discussing their interest in these fields and how the project has influenced their perspective.
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| Deliverables |
1. Deliverable 1: A set of solutions to real-world challenges provided by community partners, demonstrating the application of triangle congruence principles.
2. Deliverable 2: A reflective essay comparing project experiences to career interests and exploring potential career paths involving geometry. |
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| Preparation |
1. Prep Task 1: Coordinate with community partners to arrange the workshop, ensuring they are prepared to share relevant applications of triangle congruence and provide challenges.
2. Prep Task 2: Compile a list of career resources and profiles for students to explore potential professions, including those in architecture, engineering, navigation, and design. 3. Prep Task 3: Set up a platform for students to submit their solutions and reflective essays. 4. Prep Task 4: Prepare guiding questions and a rubric for the reflective essay to help students focus their exploration on career connections and project experiences. |
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| Week 6 | Day 1 | Day 2 |
|---|---|---|
| Activities |
Activity 1: Career Pathways Exploration - Students will conduct in-depth research on various career paths in architecture, engineering, and design that utilize triangle congruence principles. They will identify key skills required, educational paths, and potential job roles. Each student will create a career pathway map to visually organize their findings.
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Activity 2: Reflection and Future Planning - Students will write a comprehensive reflection on their learning journey throughout the project. They will address how their understanding of triangle congruence shortcuts has evolved, its real-world applications, and how this project has influenced their career interests and aspirations. Students will also outline a personal action plan to further explore these career fields, including any additional skills or knowledge they aim to acquire.
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| Deliverables |
1. Deliverable 1: A career pathway map highlighting potential careers in fields related to triangle congruence, including required skills and educational paths.
2. Deliverable 2: A detailed reflection essay discussing the learning process, real-world applications of triangle congruence, and personal career aspirations. |
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| Preparation |
1. Prep Task 1: Provide students with access to career exploration resources, including websites, articles, and videos that detail professions in architecture, engineering, design, and related fields.
2. Prep Task 2: Develop a template or guide for the career pathway map to help students organize their research effectively. 3. Prep Task 3: Set up a platform for students to submit their career pathway maps and reflection essays. 4. Prep Task 4: Prepare guiding questions and a rubric for the reflection essay to help students focus on their learning experiences and future career plans. |
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