Triangular Innovations: Building Stronger Structures Together

High School Grade

Project
8 weeks

Triangular Innovations: Building Stronger Structures Together

Angela Torres

CCSS.Math.Content.HSG-CO.B.7

CCSS.Math.Content.HSG-CO.B.8

CCSS.Math.Content.HSG-CO.C.10

CCSS.Math.Content.HSG-SRT.C.8

CCSS.Math.Content.HSG-SRT.C.7

Purpose

This project invites high school students to explore the critical role of triangles in engineering and architecture by designing and constructing a scale model of a building using only triangular shapes. Through hands-on activities and collaboration with community partners, students will apply geometry and trigonometry principles to create stable and functional structures. The project culminates in a seismic simulation test at UCSD, allowing students to evaluate the integrity of their designs and reflect on the real-world applications of their learning.

Learning goals

The learning goals for this project include understanding and applying the principles of triangle similarity and congruence, mastering the use of trigonometric ratios and the Pythagorean Theorem to solve real-world problems, and exploring the role of triangles in architectural stability and design. Students will also develop skills in critical thinking, collaboration, and effective communication through the design and presentation of their scale models. Additionally, they will gain insights into professional architectural processes by engaging with community partners and reflecting on their learning journey.

Standards

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.
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.
CCSS.Math.Content.HSG-CO.C.10 - Prove theorems about triangles.
CCSS.Math.Content.HSG-SRT.C.8 - Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
CCSS.Math.Content.HSG-SRT.C.7 - Explain and use the relationship between the sine and cosine of complementary angles.

Products

Throughout the project, students will create detailed sketches and calculations that demonstrate their understanding of geometric and trigonometric principles. They will also develop a comprehensive portfolio documenting their design process, including reflections and insights gained from community partner interactions. By the end of the project, students will present a precise scale model of their chosen structure, showcasing their ability to apply mathematical concepts to real-world architectural challenges.

Launch

Begin the project with an interactive 'Triangular Challenge Day,' where students collaborate in teams to construct the tallest freestanding structure using only triangular shapes and a limited set of materials. This engaging activity will spark curiosity and set the stage for exploring the role of triangles in architecture, while fostering teamwork and creative problem-solving. Students will reflect on their designs, discussing the stability and functionality of their structures, and drawing connections to real-world architectural principles.

Exhibition

Host a "Geometry in Architecture Showcase" where students present their scale models and portfolios to friends, family, and community partners. Set up interactive stations where attendees can engage with the seismic simulation and see the impact of different designs on structural stability. Encourage students to explain their design process and the role of triangles in their structures, fostering an environment of inquiry and dialogue.

Week 1	Day 1	Day 2	Day 3	Day 4	Day 5
Activities	Kick off with 'Triangular Challenge Day', where students work in teams to build the tallest freestanding structure using only triangular shapes and limited materials such as straws, tape, and paper. This activity promotes teamwork and introduces the concept of structural stability.	Introduce the essential question: 'In what ways do triangles contribute to the stability and functionality of architectural structures?' Facilitate a group discussion to explore initial ideas and perspectives.	Conduct a workshop on the basic properties of triangles, including different types of triangles (isosceles, equilateral, scalene) and their properties, to establish a foundational understanding.	Engage students in a hands-on activity where they use manipulatives to explore the concept of triangle congruence, focusing on the criteria of ASA, SAS, and SSS.	Assign research tasks where students individually explore historical and modern architectural examples that utilize triangular designs for stability. Encourage them to document their findings in their project journals.
Deliverables	1. A reflection piece on 'Triangular Challenge Day' where students analyze the stability and design of their structures and discuss what they learned about triangles. 2. A project journal entry summarizing their research on architectural examples that use triangles, along with initial thoughts on their importance in design.
Preparation	1. Gather materials for 'Triangular Challenge Day', including straws, tape, paper, and any other necessary construction supplies. 2. Prepare a presentation or resource sheet on the basic properties and types of triangles to support the foundational workshop. 3. Organize manipulatives, such as geometric shapes or software tools, for the triangle congruence activity. 4. Compile a list of architectural examples and resources (books, articles, websites) for student research on triangles in architecture. 5. Set up a space for students to record and share their reflections and research findings, such as a digital platform or physical display area.

Week 2	Day 1	Day 2	Day 3	Day 4
Activities	Conduct a hands-on workshop where students construct various types of triangles using materials such as cardboard, string, and protractors. This will help them understand the properties of different triangles, including angles and side lengths.	Facilitate a collaborative problem-solving session where students work in small groups to apply the triangle congruence criteria (ASA, SAS, SSS) to determine if given sets of triangles are congruent.	Introduce a real-world case study on an architectural structure that primarily uses triangles in its design. Students will analyze the structure's stability and functionality, taking notes on key observations.	Guide students in a brainstorming session to select a specific building or structure that they will replicate as a scale model. Ensure they consider the use of triangles in their design choice.
Deliverables	1. A detailed sketch and description of a chosen architectural structure, highlighting the use of triangles and explaining the reasons for their choice. 2. A group report on their findings from the problem-solving session, demonstrating their understanding of triangle congruence and its application.
Preparation	1. Prepare materials for the hands-on workshop, including cardboard, string, protractors, and rulers. 2. Develop a presentation or resource packet on the architectural case study, including images, diagrams, and historical context. 3. Compile a list of potential buildings or structures for students to consider for their scale model, ensuring a variety of architectural styles and complexity levels. 4. Set up a collaborative digital platform where groups can share their sketches and reports, allowing for peer feedback and reflection.

Week 3	Day 1	Day 2	Day 3	Day 4
Activities	Facilitate a workshop on the application of trigonometric ratios (sine, cosine, tangent) to solve real-world problems involving right triangles. Use interactive simulations to visualize these concepts.	Guide students in calculating the necessary dimensions for their scale model using trigonometric ratios and the Pythagorean Theorem. Encourage collaboration as they apply these calculations to the chosen architectural structure.	Organize a guest speaker session with a local architect or engineer to discuss the role of triangles in structural stability and how they incorporate mathematical principles in their designs.	Host a group critique session where students present their preliminary calculations and sketches, receiving feedback from peers and mentors to refine their designs.
Deliverables	1. A set of calculations using trigonometric ratios to determine the dimensions of their scale model. 2. A revised sketch of the chosen structure, incorporating feedback and demonstrating the application of trigonometric principles.
Preparation	1. Prepare resources for the trigonometry workshop, including interactive software, example problems, and calculators. 2. Coordinate with a local architect or engineer for the guest speaker session, ensuring alignment with project goals. 3. Set up a digital or physical space for students to share their calculations and sketches during the critique session. 4. Compile a list of guiding questions and criteria for students to use during peer feedback, focusing on mathematical accuracy and design feasibility.

Week 4	Day 1	Day 2	Day 3	Day 4
Activities	Conduct a workshop on the principles of structural load distribution, focusing on how triangular shapes contribute to the stability of structures. Use physical models to demonstrate these concepts.	Facilitate a hands-on activity where students test different triangular configurations to assess their load-bearing capabilities. Encourage experimentation with materials and angles to explore the impact on stability.	Organize a virtual or in-person field trip to UCSD or a local architecture firm where students can observe the application of triangles in real-world structures and learn from professionals about the importance of these shapes in engineering.	Host a collaborative design session where students refine their scale model plans based on insights gained from the week's activities, focusing on optimizing triangle usage for stability.
Deliverables	1. A report summarizing the findings from the load distribution workshop, including observations on how different triangular configurations affect stability. 2. A refined design plan for the scale model, incorporating feedback and new insights on load distribution and stability.
Preparation	1. Prepare materials and models for the structural load distribution workshop, such as small weights, varied materials for constructing triangles, and measuring tools. 2. Coordinate with UCSD or a local architecture firm to arrange the field trip, ensuring alignment with the project goals and logistical considerations. 3. Set up a virtual or physical space for students to share and discuss their refined design plans, facilitating peer feedback and collaboration. 4. Develop a resource packet that includes diagrams and case studies of real-world structures that utilize triangles for load distribution, to support student understanding.

Week 5	Day 1	Day 2	Day 3	Day 4
Activities	Facilitate a workshop on the principles of dynamic forces and how they affect architectural stability, particularly focusing on how triangles can help withstand seismic forces. Use interactive tools or simulations to illustrate these concepts.	Guide students in a collaborative design challenge where they modify their existing scale model plans to improve seismic resilience. Encourage them to think critically about material choices and triangular configurations.	Conduct a peer review session where students present their updated designs, focusing on the strategies they've implemented to enhance stability against dynamic forces. Facilitate constructive feedback and discussion.	Organize a mentorship session with community partners, such as architects or engineers, who specialize in earthquake-resistant design. Allow students to ask questions and receive expert advice on their models.
Deliverables	1. An updated design plan that incorporates strategies for seismic resilience, with annotations explaining the reasoning behind each modification. 2. A reflection piece on the peer review session, detailing the feedback received and how it influenced their design choices.
Preparation	1. Prepare interactive tools or software for the dynamic forces workshop, ensuring students can visualize the impact of seismic activity on structures. 2. Coordinate with community partners to arrange the mentorship session, providing them with an overview of the project and student progress. 3. Set up a platform for the peer review session, allowing students to present their designs and receive feedback from classmates and mentors. 4. Develop guiding questions and criteria for the peer review session, focusing on the effectiveness of design modifications for seismic resilience.

Week 6	Day 1	Day 2	Day 3	Day 4
Activities	Facilitate a workshop on the principles of triangulation and how these principles can be applied to enhance the rigidity and stability of architectural models. Use hands-on experiments with scale models to demonstrate these concepts.	Guide students in applying triangulation strategies to their scale models, focusing on optimizing for both aesthetic design and structural integrity. Encourage students to test and adjust their models based on these strategies.	Organize a collaborative feedback session where students present their models and triangulation strategies to peers and community partners. Emphasize constructive critique and sharing of best practices.	Host a reflective circle where students discuss the challenges they faced in applying triangulation principles and how they overcame them, fostering a deeper understanding and peer learning.
Deliverables	1. A revised scale model that incorporates triangulation principles for enhanced stability and aesthetics. 2. A written reflection on the triangulation process, detailing the adjustments made to the model and the rationale behind them.
Preparation	1. Prepare materials for the triangulation workshop, including sample models, construction materials, and measurement tools. 2. Coordinate with community partners to participate in the feedback session, providing them with a brief on student progress and project objectives. 3. Set up a space for the feedback session, ensuring it is conducive to presentation and discussion, whether virtual or physical. 4. Develop guiding questions for the reflective circle to help students articulate their learning experiences and insights.

Week 7	Day 1	Day 2	Day 3	Day 4
Activities	Conduct a hands-on session where students finalize the construction of their scale models, ensuring all triangular components are accurately assembled and aesthetically presented.	Facilitate a testing phase where students simulate various environmental conditions on their models, such as wind or minor seismic activity, using fans or vibration tables to assess stability.	Organize a feedback loop session where students present their completed models to peers and community partners for final critiques and suggestions for improvement.	Host a reflection circle focused on the design process and the application of geometric and trigonometric principles, encouraging students to articulate their learning experiences and challenges.
Deliverables	1. A fully constructed and tested scale model ready for the exhibition. 2. A final portfolio documenting the entire design process, including sketches, calculations, reflections, and feedback received.
Preparation	1. Ensure availability of all necessary materials for model completion, including adhesives, cutting tools, and measuring equipment. 2. Set up testing stations with equipment to simulate environmental conditions for model testing. 3. Coordinate with community partners to participate in the feedback loop session, briefing them on the student projects and objectives. 4. Prepare prompts and guiding questions for the reflection circle to facilitate meaningful discussion and introspection.

Week 8	Day 1	Day 2	Day 3	Day 4
Activities	Organize an exhibition setup session where students prepare their display areas for the 'Geometry in Architecture Showcase,' ensuring their scale models and portfolios are presented clearly and professionally.	Facilitate a rehearsal presentation session where students practice explaining their design process and the role of triangles in their structures, receiving feedback from peers to refine their delivery.	Host the 'Geometry in Architecture Showcase' exhibition for friends, family, and community partners. Encourage students to engage attendees with interactive demonstrations of their models' stability and to explain the geometric and trigonometric principles applied.	Conduct a final reflection circle where students share their overall learning experiences, challenges faced, and how the project has influenced their understanding of geometry in architecture.
Deliverables	1. A polished exhibition setup showcasing the scale model and portfolio. 2. A presentation script or outline, refined based on rehearsal feedback. 3. A comprehensive reflection piece summarizing the project journey, personal growth, and future applications of the learned principles.
Preparation	1. Arrange the exhibition space, ensuring adequate tables, display boards, and areas for interactive demonstrations are available. 2. Prepare a schedule and guidelines for the rehearsal presentations, offering constructive feedback templates for peer reviews. 3. Coordinate logistics for the 'Geometry in Architecture Showcase,' including invitations for community partners and ensuring necessary equipment (e.g., projectors, microphones) is available. 4. Develop reflection prompts to guide students in their final reflection circle, focusing on personal growth and real-world applications of their learning.