9th Grade
Project
4 weeks
Triangle Time: Congruence Carnival!
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.B.5
Self Directed Learning
+ 2 more
1-pager
Purpose
This project aims to deepen students' understanding of triangle congruence and its practical applications in real-world contexts such as design and construction. By engaging with hands-on activities, collaborating with community partners, and showcasing their work, students will develop critical thinking and problem-solving skills while exploring the significance of geometric principles. The project encourages self-directed learning and reflection, fostering a sense of belonging and academic growth through interactive and experiential learning opportunities.
Learning goals
Students will develop a deep understanding of triangle congruence criteria (ASA, SAS, SSS) and apply these principles to solve real-world design and construction challenges. They will enhance their critical thinking and problem-solving skills by analyzing architectural blueprints and creating scaled models. Through peer teaching and technology integration, students will actively engage in hands-on activities that foster self-directed learning and academic mindset, culminating in a Geometry Showcase Night where they demonstrate their mastery and reflect on their socio-emotional growth.
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.B.5 - Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Competencies
- Self Directed Learning - Students use teacher and peer feedback and self-reflection to monitor and direct their own learning while building self knowledge both in and out of the classroom.
- Academic Mindset - Students establish a sense of place, identity, and belonging to increase self-efficacy while engaging in critical reflection and action.
- Critical Thinking & Problem Solving - Students consider a variety of innovative approaches to address and understand complex questions that are authentic and important to their communities.
Products
Throughout the project, students will create scaled models of buildings or structures, applying triangle congruence criteria to ensure accuracy and stability. They will also develop digital portfolios that include their reflections, designs, and analyses of congruent triangles in real-world contexts. By the end of the project, students will present their models and portfolios at the 'Geometry Showcase Night,' demonstrating their understanding and practical application of triangle congruence to peers, teachers, and community partners.
Launch
Begin the project with an interactive workshop led by a local architect who introduces students to real-world applications of triangle congruence in building design. Students will engage in a hands-on activity where they analyze blueprints and identify congruent triangles within architectural structures. This initial experience will spark curiosity and set the stage for exploring how geometry principles are applied in professional settings.
Exhibition
Organize a 'Geometry Showcase Night' where students present their digital portfolios and scaled models, highlighting their application of triangle congruence criteria in design projects. Invite local architects and engineers to offer feedback and discuss the practical implications of geometric principles in their work. Encourage students to engage in dialogue with professionals, fostering a deeper understanding of real-world applications and inspiring potential career paths.
Plan
| Week 1 | Day 1 | Day 2 | Day 3 | Day 4 |
|---|---|---|---|---|
| Activities |
Introduction to Triangle Congruence - Begin with an interactive workshop led by a local architect to explore real-world applications of triangle congruence, analyzing blueprints to identify congruent triangles in architectural structures (30 min)
Hands-on Activity: Blueprint Analysis - Students work in pairs to identify congruent triangles in provided blueprints, discussing the significance of triangle congruence in design and construction (30 min)
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Exploring Angles of Triangles - Engage in a hands-on activity using protractors to measure angles and sides of physical objects to understand triangle properties (30 min)
Peer Teaching: Triangle Congruence Basics - Students present their findings on angles and triangle properties to peers, fostering understanding through creative demonstrations (30 min)
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Congruent Polygons and Triangle Congruence - Use geometry software to simulate triangle congruence scenarios, experimenting with configurations and observing outcomes (40 min)
Reflective Discussion: Understanding Congruence - Facilitate a discussion on how congruent polygons relate to triangle congruence, encouraging self-reflection and peer feedback (20 min)
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Proving Triangle Congruence by SAS - Conduct a session on SAS congruence criteria with hands-on activities using rulers and protractors to prove congruence in triangles (30 min)
Critique and Revision: Peer Feedback Session - Facilitate a peer feedback session where students present their SAS proofs and receive constructive feedback for improvement (30 min)
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| Deliverables |
1. Create a reflection journal entry summarizing insights gained from the workshop with the architect.
2. Develop a group presentation on one of the triangle congruence criteria (ASA, SAS, SSS) and demonstrate understanding through a creative or interactive format. 3. Compile measurements and observations from the hands-on activity into a report, including visual representations of congruent triangles. 4. Submit a brief report showcasing the digital simulations created using geometry software and explain the scenarios explored. |
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| Preparation |
1. Coordinate with a local architect to schedule and plan the interactive workshop, ensuring relevant examples and blueprints are available.
2. Prepare materials for peer teaching sessions, including guidelines and resources for each group's presentation. 3. Gather necessary tools for the hands-on measurement activity, such as protractors, rulers, and various objects for analysis. 4. Ensure access to geometry software and provide instructions for students to use it effectively during the technology integration session. |
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| Week 2 | Day 5 | Day 6 | Day 7 | Day 8 |
|---|---|---|---|---|
| Activities |
Analyzing Congruent Triangles in Architecture - Students will examine blueprints provided by local architecture firms to identify congruent triangles, applying their understanding of triangle congruence criteria (ASA, SAS, SSS) (30 min)
Peer Teaching Session on Triangle Congruence - Small groups will create and present interactive demonstrations explaining ASA, SAS, and SSS criteria to their peers, encouraging collaborative learning (30 min)
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Hands-On Measurement Activity - Using protractors and rulers, students will measure angles and sides of classroom objects to verify congruence, reinforcing the practical application of geometric principles (30 min)
Digital Simulation of Congruence - Students will use geometry software to simulate triangle congruence scenarios, experimenting with different configurations to observe outcomes (30 min)
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Critique and Revision Workshop - Facilitate reflective discussions where students assess their project progress, incorporating peer and mentor feedback to improve their scaled models and digital portfolios (30 min)
Portfolio Development - Students will update their digital portfolios with reflections and analyses of congruent triangles, preparing for the 'Geometry Showcase Night' (30 min)
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Real-World Problem Solving - Students will work in teams to design a small-scale architectural structure using congruent triangles, considering real-world constraints and design principles (30 min)
Feedback Loop Implementation - Students submit their structure designs for review on a digital platform, receiving feedback from teachers and community partners to refine their projects (30 min)
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| Deliverables |
1. A group presentation demonstrating understanding of triangle congruence criteria (SAS, ASA, SSS) using physical models or digital tools.
2. Annotated blueprints showcasing identified congruent triangles, submitted digitally for feedback. |
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| Preparation |
1. Gather materials such as paper, scissors, protractors, and rulers for creating physical models of triangles.
2. Set up digital devices and software for students to create interactive presentations. 3. Coordinate with local architecture firms to obtain sample blueprints for student analysis. 4. Prepare a digital platform for students to submit their annotated blueprints and receive feedback. |
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| Week 3 | Day 9 | Day 10 | Day 11 | Day 12 |
|---|---|---|---|---|
| Activities |
Real-World Application of Triangle Congruence - Students collaborate with local architects via a virtual meeting to discuss the application of triangle congruence in current architectural projects, fostering connections between classroom learning and real-world usage (30 min)
Peer Teaching: Equilateral and Isosceles Triangles - Students work in small groups to create and present interactive lessons on the properties and significance of equilateral and isosceles triangles, enhancing understanding through peer instruction (30 min)
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Hands-On Activity: Proving Congruence by SSS - Engage students in measuring and constructing triangles to prove congruence through the SSS criterion, using tools to reinforce precision and understanding (30 min)
Feedback and Reflection Session - Conduct a session where students present their SSS proofs to peers and receive constructive feedback, integrating self-reflection to assess their learning progress (30 min)
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Technology Integration: Simulating ASA and AAS Congruence - Students use geometry software to explore and simulate scenarios of triangle congruence by ASA and AAS, allowing experimentation with different configurations (30 min)
Critique and Revision: Digital Portfolio Update - Facilitate a workshop for students to incorporate peer feedback into their digital portfolios, focusing on their understanding and application of ASA and AAS congruence (30 min)
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Collaborative Design Challenge - Students team up to design a simple structure using congruent triangles, applying their understanding of triangle congruence in a practical design task (30 min)
Community Partner Feedback Loop - Students submit their designs to a digital platform for feedback from community partners, allowing for iterative refinement and enhancing real-world relevance (30 min)
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| Deliverables |
1. Completed physical models of triangles meeting SAS, SSS, and ASA criteria.
2. Updated digital portfolios with documented reflections and peer feedback. 3. Analysis of architectural blueprints identifying congruent triangles and their roles in design. |
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| Preparation |
1. Gather materials for triangle construction: straws, connectors, protractors, rulers.
2. Set up a digital platform for peer feedback and portfolio updates. 3. Coordinate with a local architecture firm to obtain sample blueprints for student analysis. |
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| Week 4 | Day 13 | Day 14 | Day 15 | Day 16 |
|---|---|---|---|---|
| Activities |
Finalize Scaled Models - Students complete their scaled architectural models incorporating congruent triangles, ensuring accuracy and stability in their design (30 min)
Digital Portfolio Enhancement - Students refine their digital portfolios by adding final reflections and analyses, preparing for the Geometry Showcase Night (30 min)
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Peer Review and Feedback Session - Students present their models and digital portfolios to peers for constructive feedback, focusing on triangle congruence applications (30 min)
Iterative Design Improvement - Based on peer feedback, students make revisions to their models and portfolios to enhance their projects (30 min)
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Rehearsal for Geometry Showcase Night - Students practice presenting their projects, emphasizing the use of triangle congruence in their designs (30 min)
Community Partner Q&A Preparation - Students prepare questions for local architects and engineers, focusing on the practical applications of triangle congruence in their work (30 min)
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Geometry Showcase Night Setup - Students set up their models and digital portfolios for display, preparing to present to the community (30 min)
Geometry Showcase Night - Students present their projects to peers, teachers, and community partners, demonstrating their understanding and receiving feedback from professionals (30 min)
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| Deliverables |
1. Finalized scaled model incorporating triangle congruence criteria
2. Completed digital portfolio with reflections and analyses 3. Presentation for Geometry Showcase Night |
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| Preparation |
1. Gather materials for model adjustments (e.g., rulers, protractors, construction paper)
2. Set up a digital platform for students to finalize and submit their portfolios 3. Coordinate with community partners to confirm attendance at the Geometry Showcase Night 4. Organize the venue for the showcase event, ensuring space for model displays and audience engagement |
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