"Trigonometry Toolbox: Building with Right Angles"

High School Grade

Project
4 weeks

"Trigonometry Toolbox: Building with Right Angles"

Jeremy Hudson

Purpose

The purpose of this project is to engage high school students in understanding and applying right triangle trigonometry within a real-world context, specifically in the field of construction. Through this project, students will explore the essential question: "How can right triangle trigonometry aid construction projects?" By designing and building a product of their own creation, students will gain hands-on experience that reinforces their mathematical skills and enhances their problem-solving abilities. This project aims to bridge theoretical knowledge with practical application, fostering deeper learning and preparing students for potential careers in construction and related fields.

Learning goals

In this project, students will explore the practical applications of right triangle trigonometry in construction. They will learn to calculate angles and lengths using trigonometric ratios, such as sine, cosine, and tangent, to solve real-world problems. By designing and building a product, students will apply these mathematical concepts to create accurate and functional structures, enhancing their understanding of how trigonometry is used in construction projects. This hands-on experience will develop their problem-solving skills, critical thinking, and ability to work collaboratively in a construction setting.

Standards

Common Core - CCSS.MATH.CONTENT.HSG.SRT.C.6: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
Common Core - CCSS.MATH.CONTENT.HSG.SRT.C.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Common Core - CCSS.MATH.PRACTICE.MP4: Model with mathematics, applying the mathematics they know to solve problems arising in everyday life, society, and the workplace.

Products

In this project, students will apply their understanding of right triangle trigonometry to design and construct a model structure, such as a bridge or a roof truss, that demonstrates the practical use of trigonometric principles in construction. Students will work collaboratively to create detailed blueprints and then build a scale model using materials provided in class. The final product will showcase their ability to accurately calculate angles and dimensions using trigonometry, ensuring the structural integrity and aesthetic appeal of their design. This hands-on project will culminate in a presentation where students explain their design process, the mathematical concepts applied, and the real-world implications of their work in construction.

Launch

To kick off the project, begin with a hands-on demonstration of how right triangle trigonometry is used in real-world construction. Invite a local construction professional to the class to discuss and demonstrate how they use trigonometry in their work, such as calculating roof angles or ensuring structural integrity. Following this, engage students in a mini-challenge where they use basic trigonometry tools to measure and calculate the height of a nearby structure, like a flagpole or a building. This activity will provide a tangible connection between the mathematical concepts and their practical applications, sparking curiosity and setting the stage for the project.

Exhibition

At the end of the project, students will showcase their designs and constructions in a "Trigonometry in Construction Expo." This event will be held in the school's auditorium or gymnasium, where students will present their projects to classmates, teachers, and invited guests, including local construction professionals. Each student or group will have a booth displaying their design process, calculations, and final product. Attendees will have the opportunity to ask questions and provide feedback, allowing students to explain the practical applications of right triangle trigonometry in their projects. This exhibition not only celebrates student achievement but also connects classroom learning to real-world applications in construction.

Week 1	Day 1	Day 2	Day 3	Day 4	Day 5
Activities	Activity 1: Introduction and Project Launch - Begin with a discussion on the purpose of the project and the essential question: 'How can right triangle trigonometry aid construction projects?' Introduce the concept of trigonometric ratios and their relevance in construction.	Activity 2: Guest Speaker Session - Invite a local construction professional to the class to discuss and demonstrate the use of trigonometry in construction. Students should prepare questions to ask the professional.	Activity 3: Hands-On Demonstration - Conduct a mini-challenge where students use trigonometry tools (e.g., clinometers) to measure and calculate the height of a nearby structure (e.g., flagpole, building).	Activity 4: Trigonometry Basics Workshop - Provide a workshop on calculating angles and lengths using sine, cosine, and tangent. Focus on solving simple right triangle problems.	Activity 5: Reflection and Group Formation - Reflect on the week's learning and form student groups for the project. Discuss initial ideas for the design and construction project.
Deliverables	1. Deliverable 1: Reflection Journal Entry - Students will submit a reflection on what they learned from the guest speaker and the hands-on demonstration. 2. Deliverable 2: Mini-Challenge Report - Students will submit a report detailing their calculations and findings from the mini-challenge activity.
Preparation	1. Teacher Preparation Task 1: Coordinate with a local construction professional to schedule the guest speaker session. 2. Teacher Preparation Task 2: Prepare trigonometry tools (e.g., clinometers, measuring tapes) for the mini-challenge activity. 3. Teacher Preparation Task 3: Develop a workshop presentation on trigonometric ratios and basic problem-solving techniques. 4. Teacher Preparation Task 4: Create reflection journal prompts to guide student reflections on the week's activities.

Week 2	Day 1	Day 2	Day 3	Day 4	Day 5
Activities	Activity 1: Understanding Trigonometric Applications - Begin with a class discussion on the various applications of trigonometry in construction, reinforcing the concepts introduced in Week 1. Use examples such as calculating slopes, angles, and distances in building designs.	Activity 2: Design Blueprint Workshop - Guide students in creating detailed blueprints of their intended model structure (e.g., bridge, roof truss). Discuss the importance of precision and accuracy in construction designs.	Activity 3: Trigonometry Problem-Solving Session - Conduct a session where students solve complex right triangle problems related to their projects. Provide real-world scenarios that require the use of trigonometric ratios and the Pythagorean Theorem.	Activity 4: Peer Review - Organize a peer review session where student groups present their initial blueprints for feedback. Encourage constructive criticism and collaborative problem-solving.	Activity 5: Prototype Building - Begin the construction phase by allowing students to start building a prototype of their model structure. Focus on applying trigonometric calculations to ensure accuracy.
Deliverables	1. Deliverable 1: Blueprint Submission - Students will submit their detailed blueprints, including calculations and design plans, by the end of the week. 2. Deliverable 2: Problem-Solving Portfolio - Students will compile solved trigonometry problems related to their project into a portfolio.
Preparation	1. Teacher Preparation Task 1: Gather examples of trigonometric applications in various construction projects to discuss with the class. 2. Teacher Preparation Task 2: Prepare materials and resources for the blueprint workshop, including templates and tools for drafting. 3. Teacher Preparation Task 3: Develop a set of complex trigonometry problems that are relevant to the students' projects. 4. Teacher Preparation Task 4: Facilitate the peer review process by creating guidelines and criteria for constructive feedback. 5. Teacher Preparation Task 5: Ensure all necessary building materials and tools are available for the prototype building activity.

Week 3	Day 1	Day 2	Day 3	Day 4	Day 5
Activities	Activity 1: Advanced Trigonometric Concepts - Dive deeper into trigonometric concepts, focusing on inverse trigonometric functions and their applications in solving construction-related problems. Conduct exercises that involve determining unknown angles and lengths.	Activity 2: Construction Techniques Seminar - Host a seminar on construction techniques, emphasizing the role of trigonometry in ensuring structural integrity and design efficiency. Invite an expert to discuss real-world challenges and solutions.	Activity 3: Prototype Testing and Evaluation - Allow students to test their prototypes for structural soundness and accuracy. Facilitate a discussion on the outcomes and potential improvements based on the test results.	Activity 4: Iterative Design Workshop - Guide students through an iterative design process where they refine their blueprints and prototypes based on feedback and testing. Encourage experimentation and creative problem-solving.	Activity 5: Reflection and Documentation - Have students reflect on their prototype testing and design iteration experiences. Encourage them to document their process, challenges faced, and solutions implemented.
Deliverables	1. Deliverable 1: Reflection Journal Entry - Students will submit a reflection on their prototype testing experiences and the iterative design process. 2. Deliverable 2: Revised Blueprint - Students will submit updated blueprints that incorporate changes and improvements based on prototype testing and feedback.
Preparation	1. Teacher Preparation Task 1: Prepare advanced trigonometry exercises and resources for the class. 2. Teacher Preparation Task 2: Coordinate with a construction expert for the seminar and prepare discussion points. 3. Teacher Preparation Task 3: Set up a testing area with necessary tools and materials for prototype evaluation. 4. Teacher Preparation Task 4: Develop guidelines for the iterative design workshop to support student creativity and problem-solving. 5. Teacher Preparation Task 5: Create reflection journal prompts to guide students in documenting their experiences and insights.

Week 4	Day 1	Day 2	Day 3	Day 4	Day 5
Activities	Activity 1: Final Construction and Detailing - Students will finalize their model structures, focusing on any detailed work required to enhance both the functionality and aesthetic appeal of their designs. Encourage students to ensure that their models reflect accurate trigonometric calculations.	Activity 2: Presentation Preparation - Guide students in preparing their presentations for the 'Trigonometry in Construction Expo.' Discuss effective communication strategies and how to highlight the mathematical concepts applied in their projects.	Activity 3: Rehearsal and Feedback - Allow students to rehearse their presentations in front of peers. Facilitate a feedback session where classmates provide constructive criticism and suggestions for improvement.	Activity 4: Exhibition Setup - Assist students in setting up their booths for the 'Trigonometry in Construction Expo.' Ensure that each group has the necessary materials and space to effectively display their projects and presentations.	Activity 5: Trigonometry in Construction Expo - Host the exhibition event where students present their projects to classmates, teachers, and invited guests. Encourage active participation, questioning, and interaction between students and attendees.
Deliverables	1. Deliverable 1: Final Model Structure - Completed and detailed model structures ready for display at the expo. 2. Deliverable 2: Presentation Slides and Materials - Students will submit their presentation slides and any supplementary materials used during their presentation. 3. Deliverable 3: Expo Reflection Journal Entry - Students will submit a reflection on their experience presenting at the expo, including feedback received and lessons learned.
Preparation	1. Teacher Preparation Task 1: Organize the logistics for the 'Trigonometry in Construction Expo,' including venue setup, scheduling, and invitations to local construction professionals. 2. Teacher Preparation Task 2: Provide guidance and resources for students to prepare their presentations, including templates and tips for effective communication. 3. Teacher Preparation Task 3: Coordinate with students to ensure all necessary materials and equipment are available for the exhibition setup. 4. Teacher Preparation Task 4: Develop a rubric or criteria for evaluating student presentations and projects during the expo. 5. Teacher Preparation Task 5: Create reflection journal prompts to guide students in documenting their expo experience and learning outcomes.