Geometry in Action: Real-World Career Explorations
Inquiry Framework
Question Framework
Driving Question
The overarching question that guides the entire project.In various occupations, how can we ethically apply geometric principles and mathematical models through collaboration to enhance design, accuracy, and problem-solving?Essential Questions
Supporting questions that break down major concepts.- How do geometric principles inform design and construction in various occupations?
- In what ways can mathematical models enhance accuracy and efficiency in real-world projects?
- How does understanding spatial relationships improve problem-solving in professional settings?
- What are the ethical considerations in using geometric principles in design and construction?
- How can collaboration and diverse perspectives enhance the application of geometry in occupational roles?
Standards & Learning Goals
Learning Goals
By the end of this project, students will be able to:- Apply geometric principles to real-world scenarios.
- Collaborate effectively to solve complex design problems.
- Understand the ethical considerations in applying geometric principles in various occupations.
- Use mathematical models to enhance accuracy and efficiency in projects.
- Improve problem-solving skills through spatial reasoning and geometric understanding.
- Understand geometric principles inform design and construction in various occupations.
- Understand ways mathematical models enhance accuracy and efficiency in real-world projects.
- Understand spatial relationships improve problem-solving in professional settings.
- Understand ethical considerations in using geometric principles in design and construction.
- Understand collaboration and diverse perspectives enhance the application of geometry in occupational roles
Entry Events
Events that will be used to introduce the project to studentsThe Case of the Compromised Construction
Students receive a cryptic message detailing structural weaknesses in a local building (school, community center). They must use geometric principles to analyze blueprints, identify vulnerabilities, and propose solutions to reinforce the structure, simulating roles like structural engineers or architects.Geometric Cityscapes: Redesigning Our Town
The class is divided into 'urban planning' teams tasked with redesigning a section of the town to be more sustainable and efficient. Each team uses geometry to optimize space, design green areas, and plan infrastructure, presenting their designs to a panel of 'city officials'.The Geometry Escape Room Challenge
Students participate in a 'geometric escape room' challenge where they solve puzzles based on geometric theorems and spatial reasoning to 'unlock' clues about a fictional mystery related to architecture or design. This fosters collaboration and problem-solving skills in a high-stakes scenario.Geometric Habitats: Designing for Space Colonization
The class simulates a 'space colonization' mission where they must design a self-sustaining habitat on another planet using geometric principles to maximize space, resource utilization, and structural stability. This activity links geometry to broader science and engineering concepts.Sculpting the Future: A Geometric Art Installation
A local artist needs help creating a large-scale geometric sculpture for a public space. Students, acting as design consultants, must use their knowledge of geometric solids and transformations to create a proposal that balances aesthetics with structural integrity and cost-effectiveness.Portfolio Activities
Portfolio Activities
These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.Geometry in Action: Occupation Exploration
Students will select an occupation that heavily relies on geometric principles (e.g., architect, structural engineer, urban planner, surveyor, or even a set designer). They will then research the fundamental geometric concepts and tools used in that profession. This involves identifying specific geometric shapes, theorems, and principles that are crucial for the role. They will write a detailed report explaining these concepts and how they are applied in the chosen occupation.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA comprehensive report (3-5 pages) detailing the geometric principles used in the selected occupation, including diagrams and examples. The report should also include a reflection on why these principles are important for accuracy and efficiency in the field.Alignment
How this activity aligns with the learning objectives & standardsHSG-CO.A.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. HSG-MG.A.1: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).Geometric Solutions: Project Proposal
Building upon Activity 1, students will now focus on a specific project or problem commonly faced in their chosen occupation. They will use geometric theorems and principles to develop a solution. This could involve designing a structure, optimizing space, or creating a model that solves a practical problem. Students must document their process, explaining the geometric reasoning behind each step.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA detailed project proposal that includes a problem statement, proposed geometric solution, step-by-step explanation of the geometric reasoning, diagrams, and a discussion of potential challenges and limitations.Alignment
How this activity aligns with the learning objectives & standardsHSG-CO.C.10: Prove geometric theorems. HSG-MG.A.3: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).Geometric Modeling: Bringing Ideas to Life
Students will create a 3D model (physical or digital) of their proposed solution from Activity 2. This involves applying geometric concepts to accurately represent the design. They will calculate measurements such as area, volume, and angles to ensure the model is precise and to scale. The model should reflect an understanding of spatial relationships and geometric properties. They also must calculate material needs and costs of the project.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA 3D model of the proposed solution, accompanied by a report detailing the geometric measurements, calculations, and considerations involved in creating the model. Include a cost analysis of the materials used.Alignment
How this activity aligns with the learning objectives & standardsHSG-SRT.C.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. HSG-MG.A.2: Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).Geometric Showcase: Presentation and Defense
Students will prepare a presentation to showcase their project, including the initial research, problem statement, proposed solution, 3D model, and geometric reasoning. The presentation should be tailored to a specific audience (e.g., potential clients, city planners, or industry experts). They will practice presenting their work clearly and persuasively, highlighting the value of their geometric approach.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA professional presentation (PowerPoint, Prezi, etc.) that effectively communicates the project's purpose, process, and outcomes. The presentation should include visual aids, clear explanations, and a persuasive argument for the proposed solution.Alignment
How this activity aligns with the learning objectives & standardsMP.4: Model with mathematics. HSG-MG.A.3: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).Geometric Critique: Peer Review and Reflection
Students will participate in a peer review session where they present their projects to their classmates and receive feedback. They will also review and critique the projects of others, focusing on the validity of the geometric reasoning, the effectiveness of the solutions, and the clarity of the presentations. This activity promotes critical thinking, communication, and collaboration skills.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA written reflection on the peer review process, including feedback received on their own project and constructive criticism provided to others. This reflection should demonstrate an understanding of geometric principles and their application.Alignment
How this activity aligns with the learning objectives & standardsMP.3: Construct viable arguments and critique the reasoning of others. HSG-CO.C.10: Prove geometric theorems.Rubric & Reflection
Portfolio Rubric
Grading criteria for assessing the overall project portfolioGeometry in Action: PBL Assessment Rubric
Occupation Exploration
Focuses on the research, understanding, and explanation of geometric principles applied in a chosen occupation.Geometric Understanding
Depth of research into geometric principles used in the selected occupation.
Exemplary
4 PointsDemonstrates a sophisticated understanding of geometric principles and their application in the chosen occupation, going beyond basic concepts.
Proficient
3 PointsDemonstrates a thorough understanding of geometric principles and their application in the chosen occupation.
Developing
2 PointsShows an emerging understanding of geometric principles and their application in the chosen occupation, with some inaccuracies or omissions.
Beginning
1 PointsShows only an initial understanding of geometric principles and struggles to apply them to the chosen occupation.
Clarity and Accuracy
Clarity and accuracy of the report, including diagrams and examples.
Exemplary
4 PointsReport is exceptionally clear, well-organized, and free of errors, with insightful diagrams and relevant examples that enhance understanding.
Proficient
3 PointsReport is clear, well-organized, and mostly free of errors, with helpful diagrams and relevant examples.
Developing
2 PointsReport is somewhat unclear or disorganized, with some errors and diagrams or examples that are not always helpful or relevant.
Beginning
1 PointsReport is unclear, disorganized, and contains numerous errors, with missing or irrelevant diagrams and examples.
Reflection Quality
Quality of reflection on the importance of geometric principles for accuracy and efficiency in the chosen occupation.
Exemplary
4 PointsProvides a thoughtful and insightful reflection on the significance of geometric principles, demonstrating a deep understanding of their impact on accuracy and efficiency.
Proficient
3 PointsProvides a clear and relevant reflection on the importance of geometric principles for accuracy and efficiency.
Developing
2 PointsProvides a limited or superficial reflection on the importance of geometric principles.
Beginning
1 PointsFails to provide a meaningful reflection on the importance of geometric principles.
Project Proposal
Assesses the ability to apply geometric knowledge to solve problems within the context of the chosen occupation.Problem Identification
The identification of a specific project or problem relevant to the selected occupation.
Exemplary
4 PointsIdentifies a highly relevant and complex problem that demonstrates a deep understanding of the chosen occupation.
Proficient
3 PointsIdentifies a relevant and clear problem commonly faced in the chosen occupation.
Developing
2 PointsIdentifies a problem that is somewhat relevant or unclear.
Beginning
1 PointsFails to identify a relevant problem or the problem is poorly defined.
Solution Development
The development of a geometric solution, including the application of relevant theorems and principles.
Exemplary
4 PointsDevelops an innovative and effective geometric solution that demonstrates a sophisticated application of relevant theorems and principles.
Proficient
3 PointsDevelops a sound geometric solution using relevant theorems and principles.
Developing
2 PointsAttempts to develop a geometric solution, but the application of theorems and principles is inconsistent or inaccurate.
Beginning
1 PointsFails to develop a geometric solution or demonstrates a lack of understanding of relevant theorems and principles.
Reasoning and Limitations
Clarity of the explanation of the geometric reasoning and discussion of potential challenges and limitations.
Exemplary
4 PointsProvides an exceptionally clear and thorough explanation of the geometric reasoning, with a comprehensive discussion of potential challenges and limitations.
Proficient
3 PointsProvides a clear explanation of the geometric reasoning and discusses potential challenges and limitations.
Developing
2 PointsProvides a somewhat unclear or incomplete explanation of the geometric reasoning, with a limited discussion of potential challenges and limitations.
Beginning
1 PointsFails to provide a clear explanation of the geometric reasoning or discuss potential challenges and limitations.
Geometric Modeling
Focuses on the practical application of geometric principles in creating a 3D model and assessing its feasibility.Model Accuracy
Accuracy and precision of the 3D model, including geometric measurements and calculations.
Exemplary
4 PointsModel is exceptionally accurate and precise, demonstrating a deep understanding of geometric measurements and calculations.
Proficient
3 PointsModel is accurate and precise, with correct geometric measurements and calculations.
Developing
2 PointsModel contains some inaccuracies or imprecision in geometric measurements and calculations.
Beginning
1 PointsModel is inaccurate and imprecise, with significant errors in geometric measurements and calculations.
Report Quality
Thoroughness and clarity of the report detailing geometric measurements, calculations, and considerations.
Exemplary
4 PointsReport is exceptionally thorough and clear, providing a comprehensive overview of the geometric measurements, calculations, and considerations.
Proficient
3 PointsReport is thorough and clear, detailing the geometric measurements, calculations, and considerations.
Developing
2 PointsReport is somewhat incomplete or unclear, with some omissions in the geometric measurements, calculations, or considerations.
Beginning
1 PointsReport is incomplete and unclear, lacking essential details about the geometric measurements, calculations, and considerations.
Cost Analysis
Accuracy and relevance of the cost analysis of materials used.
Exemplary
4 PointsProvides a highly accurate and insightful cost analysis, demonstrating a deep understanding of material costs and implications.
Proficient
3 PointsProvides an accurate and relevant cost analysis of the materials used.
Developing
2 PointsProvides a somewhat inaccurate or incomplete cost analysis.
Beginning
1 PointsFails to provide an accurate or relevant cost analysis.
Geometric Showcase
Evaluates the ability to effectively communicate and defend the project to a specific audience.Presentation Clarity
Clarity and persuasiveness of the presentation, tailored to a specific audience.
Exemplary
4 PointsPresentation is exceptionally clear, persuasive, and perfectly tailored to the intended audience, demonstrating a deep understanding of their needs and interests.
Proficient
3 PointsPresentation is clear, persuasive, and appropriately tailored to the intended audience.
Developing
2 PointsPresentation is somewhat unclear or unpersuasive, with limited tailoring to the intended audience.
Beginning
1 PointsPresentation is unclear, unpersuasive, and not tailored to the intended audience.
Visual Communication
Effectiveness of visual aids and explanations in communicating the project's purpose, process, and outcomes.
Exemplary
4 PointsVisual aids and explanations are exceptionally effective in communicating the project's purpose, process, and outcomes, enhancing audience understanding and engagement.
Proficient
3 PointsVisual aids and explanations are effective in communicating the project's purpose, process, and outcomes.
Developing
2 PointsVisual aids and explanations are somewhat ineffective or unclear in communicating the project's purpose, process, or outcomes.
Beginning
1 PointsVisual aids and explanations are ineffective and fail to communicate the project's purpose, process, or outcomes.
Argument Strength
Strength of the argument for the proposed solution, highlighting the value of the geometric approach.
Exemplary
4 PointsPresents a compelling and insightful argument for the proposed solution, clearly demonstrating the value of the geometric approach.
Proficient
3 PointsPresents a clear and persuasive argument for the proposed solution, highlighting the value of the geometric approach.
Developing
2 PointsPresents a weak or unconvincing argument for the proposed solution, with limited emphasis on the value of the geometric approach.
Beginning
1 PointsFails to present a clear argument for the proposed solution or highlight the value of the geometric approach.
Geometric Critique
Assesses the ability to critically evaluate the work of peers and reflect on the learning process.Feedback Quality
Quality of feedback provided to peers, focusing on geometric reasoning and effectiveness.
Exemplary
4 PointsProvides insightful and constructive feedback to peers, demonstrating a deep understanding of geometric reasoning and effectiveness.
Proficient
3 PointsProvides constructive feedback to peers, focusing on geometric reasoning and effectiveness.
Developing
2 PointsProvides superficial or unhelpful feedback to peers.
Beginning
1 PointsFails to provide meaningful feedback to peers.
Understanding of Principles
Demonstrated understanding of geometric principles and their application in the projects of others.
Exemplary
4 PointsDemonstrates a sophisticated understanding of geometric principles and their application in the projects of others, identifying subtle nuances and potential improvements.
Proficient
3 PointsDemonstrates a clear understanding of geometric principles and their application in the projects of others.
Developing
2 PointsShows a limited understanding of geometric principles and their application in the projects of others.
Beginning
1 PointsDemonstrates a lack of understanding of geometric principles and their application in the projects of others.
Reflection Depth
Depth of reflection on the peer review process, including feedback received and criticism provided.
Exemplary
4 PointsProvides a deep and insightful reflection on the peer review process, demonstrating a strong awareness of both personal strengths and areas for improvement.
Proficient
3 PointsProvides a thoughtful reflection on the peer review process.
Developing
2 PointsProvides a superficial or incomplete reflection on the peer review process.
Beginning
1 PointsFails to provide a meaningful reflection on the peer review process.