Circular City: Sustainable Design with Geometry
Inquiry Framework
Question Framework
Driving Question
The overarching question that guides the entire project.How can understanding the geometry of circles—such as arcs, sectors, tangents, chords, secants, segments, and inscribed angles—help us investigate buildings around the world and ensure that our designs are both sustainable and beautiful?Essential Questions
Supporting questions that break down major concepts.- How can we identify and describe the key parts of a circle to begin planning for our model, and where can we find these elements in our chosen building?
- How can we use arcs and sectors to design functional and amazing features? Give examples from your building and calculate sector areas and arc lengths.
- How are tangents and chords used in our building to create symmetrical and balanced design? Do your calculations
- How can all circle geometry concepts help us create a well-designed, accurately measured building that serves its real purpose?
- How can we use our geometry knowledge to finalize and present a sustainable and beautiful building design?
Standards & Learning Goals
Learning Goals
By the end of this project, students will be able to:- Understand and apply circle geometry concepts.
- Use math to solve real-world design problems.
- Collaborate and communicate effectively.
- Connect math to sustainability
Common Core Standards
Entry Events
Events that will be used to introduce the project to studentsPop-Up Circular Space
Challenge students to design a temporary, pop-up circular space for a community event (farmers market, concert). They must consider geometry for space optimization, sustainable materials for construction/deconstruction, and how the design promotes circularity (e.g., waste reduction, resource reuse), presenting their design via a scaled model or digital rendering.Portfolio Activities
Portfolio Activities
These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.Circle Geometry Blueprint
Students will identify and describe key parts of a circle and find these elements in existing buildings. They'll create a blueprint showing circles.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 blueprint of a circular space design with labeled geometric elements.Alignment
How this activity aligns with the learning objectives & standardsAligns with CCSS.Math.Content.HSG-C.A.1 (Understand and apply circle geometry concepts)Arc and Sector Design Challenge
Students design functional features using arcs/sectors, calculate areas/lengths, and apply them to their building model.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 model incorporating arc and sector designs with accurate area and length calculations.Alignment
How this activity aligns with the learning objectives & standardsAligns with CCSS.Math.Content.HSG-C.A.1 (Understand and apply circle geometry concepts) and CCSS.Math.Content.HSG-MG.A.3 (Apply geometric methods to solve design problems)Symmetry and Balance Analysis
Students will analyze how tangents and chords are used to create symmetry and balance in building design and in their model.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 design analysis explaining the use of tangents/chords for symmetry, with supporting calculations.Alignment
How this activity aligns with the learning objectives & standardsAligns with CCSS.Math.Content.HSG-C.A.1 (Understand and apply circle geometry concepts) and CCSS.Math.Content.HSG-MG.A.3 (Apply geometric methods to solve design problems)Sustainability Integration Report
Students will write a report detailing how their geometric design contributes to sustainability and waste reduction.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 sustainability report detailing the design's environmental impact and circularity aspects.Alignment
How this activity aligns with the learning objectives & standardsAligns with CCSS.Math.Content.HSG-MG.A.3 (Apply geometric methods to solve design problems) and CCSS.Math.Content.MP.4 (Model with mathematics)Final Design Presentation
Students will present their sustainable building design, explaining geometric concepts, calculations, and sustainability features.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 presentation of the sustainable building design, including geometric concepts, calculations, and sustainability features.Alignment
How this activity aligns with the learning objectives & standardsAligns with CCSS.Math.Content.HSG-C.A.1 (Understand and apply circle geometry concepts), CCSS.Math.Content.HSG-MG.A.3 (Apply geometric methods to solve design problems), and CCSS.Math.Content.MP.4 (Model with mathematics)Rubric & Reflection
Portfolio Rubric
Grading criteria for assessing the overall project portfolioSustainable Circular Space Design Rubric
Geometric Accuracy and Application
Evaluates the accuracy of geometric calculations and the effective application of circle geometry concepts (arcs, sectors, tangents, chords) in the design.Accuracy of Calculations
Assesses the precision and correctness of geometric calculations related to arcs, sectors, tangents, and chords.
Exemplary
4 PointsAll geometric calculations are accurate and precisely applied. Demonstrates a deep understanding of geometric principles.
Proficient
3 PointsMost geometric calculations are accurate with minor errors. Shows a good understanding of geometric principles.
Developing
2 PointsSome geometric calculations are accurate, but there are noticeable errors. Demonstrates a basic understanding of geometric principles.
Beginning
1 PointsGeometric calculations are largely inaccurate or missing. Shows a limited understanding of geometric principles.
Application of Geometric Concepts
Evaluates how effectively circle geometry concepts are applied to the design of the circular space.
Exemplary
4 PointsGeometric concepts are innovatively and effectively applied to enhance the design and functionality of the circular space.
Proficient
3 PointsGeometric concepts are appropriately applied to the design of the circular space, demonstrating a clear understanding of their use.
Developing
2 PointsGeometric concepts are inconsistently applied, with some areas showing a lack of understanding of their practical use.
Beginning
1 PointsGeometric concepts are poorly applied or missing, indicating a limited understanding of their relevance to the design.
Sustainability Integration
Assesses the integration of sustainability principles and practices in the design, including material choices, waste reduction, and circularity.Sustainable Material Choices
Evaluates the selection and justification of sustainable materials used in the design.
Exemplary
4 PointsMaterial choices are exceptionally sustainable, thoroughly justified with detailed environmental impact analysis, and innovatively integrated into the design.
Proficient
3 PointsMaterial choices are sustainable and well-justified, considering environmental impact and resource efficiency.
Developing
2 PointsSome material choices are sustainable, but the justification is limited or unclear.
Beginning
1 PointsMaterial choices are not sustainable, with little to no consideration of environmental impact.
Waste Reduction and Circularity
Evaluates the design's approach to waste reduction, resource reuse, and the implementation of circularity principles.
Exemplary
4 PointsThe design demonstrates innovative strategies for waste reduction and resource reuse, fully embracing circularity principles throughout the entire lifecycle of the space.
Proficient
3 PointsThe design effectively incorporates strategies for waste reduction and resource reuse, aligning with circularity principles.
Developing
2 PointsThe design includes some elements of waste reduction and resource reuse, but the connection to circularity principles is not fully developed.
Beginning
1 PointsThe design lacks consideration of waste reduction, resource reuse, and circularity principles.
Design Communication and Presentation
Assesses the clarity, organization, and effectiveness of the design presentation, including visual aids and explanations of geometric and sustainability features.Clarity and Organization
Evaluates the clarity and logical organization of the design presentation.
Exemplary
4 PointsThe presentation is exceptionally clear, logically organized, and engaging, effectively conveying the design concept and rationale.
Proficient
3 PointsThe presentation is clear, well-organized, and easy to follow, effectively communicating the key aspects of the design.
Developing
2 PointsThe presentation is somewhat disorganized and lacks clarity in certain areas, making it difficult to fully understand the design.
Beginning
1 PointsThe presentation is disorganized, unclear, and difficult to follow, failing to effectively communicate the design concept.
Visual Aids and Explanations
Assesses the quality and effectiveness of visual aids (blueprints, models, diagrams) and explanations of geometric calculations and sustainability features.
Exemplary
4 PointsVisual aids are outstanding, clearly illustrating geometric concepts and sustainability features. Explanations are thorough, insightful, and demonstrate a deep understanding of the design.
Proficient
3 PointsVisual aids are effective in illustrating geometric concepts and sustainability features. Explanations are clear, concise, and accurate.
Developing
2 PointsVisual aids are present but may lack clarity or relevance. Explanations are basic and may contain some inaccuracies.
Beginning
1 PointsVisual aids are missing or ineffective. Explanations are unclear, incomplete, or inaccurate.