"Triangle Tales: Solving Congruence Mysteries!"

10th Grade Project 1 week

"Triangle Tales: Solving Congruence Mysteries!"

Debra Seidell

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Purpose

The purpose of this project is to engage 10th-grade students in exploring the principles of triangle congruence through hands-on activities and real-world applications. Students will investigate and apply the Side-Angle-Side (SAS) and Side-Side-Side (SSS) postulates to prove triangles are congruent, fostering a deeper understanding of geometric concepts. By working collaboratively on creative projects, students will connect mathematical theory to practical scenarios, culminating in a reflective exhibition that demonstrates their learning and problem-solving skills.

Learning goals

Students will develop a deep understanding of triangle congruence through the application of the Side-Angle-Side (SAS) and Side-Side-Side (SSS) postulates. They will enhance their problem-solving skills by exploring real-world scenarios where proving congruence is essential, such as in architecture and engineering. By engaging in a creative project, students will illustrate solutions to these scenarios, fostering collaboration and critical thinking. The project will culminate in a reflection and exhibition, allowing students to articulate their learning journey and demonstrate mastery of the concepts.

Standards

Common Core - CCSS.MATH.CONTENT.HSG.CO.B.8: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) are established using transformations.
Common Core - CCSS.MATH.CONTENT.HSG.SRT.B.5: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Common Core - CCSS.MATH.PRACTICE.MP3: Construct viable arguments and critique the reasoning of others.

Products

Students will collaboratively create a scaled model of a real-world structure, such as a bridge or a building, demonstrating the application of triangle congruence principles using SAS and SSS. Throughout the week, they will document their process in a digital portfolio, including sketches, calculations, and reflections on their learning journey. At the end of the project, students will present their models and portfolios in an exhibition, explaining how their understanding of triangle congruence helped solve structural design challenges.

Launch

Begin the project by engaging students in a real-world scenario where triangle congruence is crucial, such as designing a bridge or creating a blueprint for a small structure. Present a short video or case study highlighting how engineers and architects use triangle congruence in their work. Then, challenge students to brainstorm how they might apply these concepts to solve a practical problem, setting the stage for their project work. This launch will spark curiosity and provide context for the hands-on activities to follow.

Exhibition

At the end of the project, students will host a "Geometry in Action" showcase where they present their creative projects that solve real-world problems using triangle congruence. Each student will display their work, explaining how they applied SAS and SSS to demonstrate congruence and solve a practical issue. The exhibition will include interactive stations where visitors can engage with models and diagrams, allowing students to articulate their understanding and answer questions. Parents, peers, and community members will be invited to attend, providing an authentic audience for students to share their learning journey and insights.

Plan

Week 1	Day 1	Day 2	Day 3	Day 4	Day 5
Activities	Project Launch - Engage students with a real-world scenario video demonstrating the importance of triangle congruence in architecture and engineering, followed by a brainstorming session on potential applications (20 min) Introduction to Triangle Congruence - Explore the Side-Angle-Side (SAS) and Side-Side-Side (SSS) postulates through interactive demonstrations using geometric tools (20 min) Reflection - Students write a short entry in their digital portfolio reflecting on what they learned about congruence and its applications (10 min)	Hands-On Activity: Building Congruent Triangles - Students work in pairs to construct triangles using SAS and SSS postulates with physical materials, documenting their process and outcomes (25 min) Collaborative Exploration - In small groups, students analyze how triangle congruence can solve structural design challenges, sharing ideas and examples with peers (15 min) Reflection - Update digital portfolios with insights gained from the collaborative exploration, focusing on the application of triangle congruence in real-world scenarios (10 min)	Guided Practice: Solving Congruence Problems - Students tackle congruence problems using SAS and SSS, supported by teacher guidance and peer discussion (30 min) Skill Assessment - Conduct a short quiz to assess mastery of SAS and SSS postulates in proving triangle congruence (15 min) Reflection - Students reflect on their performance in the quiz, identifying areas of improvement and strategies for mastering the concepts (5 min)	Project Development: Model Construction - Begin creating a scaled model of a structure, applying triangle congruence principles. Students document their progress and problem-solving approaches (35 min) Peer Feedback - Students share their models in progress with peers for constructive feedback and suggestions for improvement (10 min) Reflection - Reflect on the feedback received and plan next steps for refining their model, including how congruence will be utilized (5 min)	Final Model Completion - Students finalize their scaled models, ensuring accurate application of SAS and SSS postulates, and prepare for exhibition (40 min) Exhibition Preparation - Plan and rehearse presentations for the 'Geometry in Action' showcase, focusing on explaining their models and the practical applications of triangle congruence (5 min) Reflection - Write a comprehensive reflection on the learning journey throughout the week, summarizing key insights and achievements (5 min)
Deliverables	1. Day 1: Students will submit a brainstormed list of real-world scenarios where triangle congruence can be applied, along with initial ideas for their project. 2. Day 2: Each student will create a preliminary sketch of their chosen structure, highlighting areas where triangle congruence will be applied. 3. Day 3: Students will complete and submit a digital portfolio entry detailing their calculations and proof of congruence using SAS and SSS postulates for their model. 4. Day 4: Teams will present a draft model of their structure to peers for feedback, including explanations of triangle congruence application. 5. Day 5: Finalize and present the scaled model and digital portfolio at the "Geometry in Action" showcase, featuring reflections on their learning journey and problem-solving process.
Preparation	1. Prepare a short video or case study on the use of triangle congruence in engineering and architecture to launch the project. 2. Gather materials for model construction such as rulers, protractors, paper, cardboard, glue, and scissors. 3. Set up digital platforms for students to create and share their portfolios, such as Google Classroom or Padlet. 4. Organize interactive stations for the exhibition, including tables, display boards, and markers. 5. Invite parents, peers, and community members to the "Geometry in Action" showcase to provide an authentic audience for students.