Shape Up City: A Volume-Based Design Project
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Shape Up City: A Volume-Based Design Project

Grade 9Math3 days
In "Shape Up City," students act as city managers to design a sustainable "dream city" using geometric shapes and volume principles. They address real-world urban planning challenges, balancing aesthetics, resource management, and environmental impact. Students calculate volumes of structures, research environmental impacts, and create a 3D model of their city, culminating in a presentation of their design solutions.
Volume CalculationUrban PlanningGeometric ShapesSustainable DesignCity DesignEnvironmental Impact3D Modeling
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Inquiry Framework

Question Framework

Driving Question

The overarching question that guides the entire project.How can we, as city managers, design a sustainable and functional "dream city" that balances aesthetics, resource management, and environmental impact, using geometric shapes and the principles of volume to address real-world urban planning challenges?

Essential Questions

Supporting questions that break down major concepts.
  • How can we use geometric shapes to design functional structures and spaces?
  • How does the volume of different shapes impact the overall design and resource management of a city?
  • In what ways can mathematical principles guide sustainable urban planning and development?
  • How do city planners balance aesthetics, functionality, and environmental impact in urban design?
  • What are the real-world applications of calculating volume in urban planning and architecture?

Standards & Learning Goals

Learning Goals

By the end of this project, students will be able to:
  • Apply the concept of volume to design various structures in a city.
  • Use geometric shapes effectively to create functional urban spaces.
  • Balance aesthetics, functionality, and environmental impact in urban design.
  • Understand real-world applications of volume calculation in urban planning and architecture.
  • Demonstrate problem-solving skills in addressing urban planning challenges.

Entry Events

Events that will be used to introduce the project to students

The Urban Planning Challenge

The current city layout is causing major problems, from traffic jams to unequal access to resources. Students are given real data on population density, resource distribution and traffic flow. They must redesign the city using their understanding of volume and spatial arrangement to create a more efficient and equitable urban environment.
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Portfolio Activities

Portfolio Activities

These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.
Activity 1

Sustainable City Planner

Students will now calculate the volume of the structures they designed in the previous activity, considering factors like building materials and energy efficiency. They will explore how different shapes and sizes impact resource consumption and environmental sustainability.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Choose specific dimensions for each building design from the previous activity.
2. Calculate the volume of each building using the appropriate formula.
3. Research the environmental impact of different building materials and energy sources.
4. Analyze the environmental impact and resource consumption of each building design based on its volume, materials, and energy usage.
5. Write a report summarizing the volume calculations, environmental impact analysis, and suggestions for improving sustainability.

Final Product

What students will submit as the final product of the activityA report detailing the volume calculations for each building design, along with an analysis of its environmental impact and resource consumption. The report should include suggestions for optimizing the design to improve sustainability.

Alignment

How this activity aligns with the learning objectives & standardsLearning Goal: Balance aesthetics, functionality, and environmental impact in urban design.
Activity 2

Urban Planning Researcher

Students will research real-world examples of urban planning projects that utilize volume calculations to optimize space, resource management, and environmental sustainability. They will present their findings and discuss the challenges and successes of these projects.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Research and select 2-3 real-world urban planning projects that utilize volume calculations.
2. Gather information about the project's goals, challenges, solutions, and outcomes.
3. Prepare a presentation showcasing the key aspects of each project.
4. Present the findings to the class and participate in a discussion about the real-world applications of volume calculations in urban planning.

Final Product

What students will submit as the final product of the activityA presentation (e.g., slideshow, poster, or short video) showcasing real-world examples of urban planning projects that utilize volume calculations. The presentation should include a description of the project, the challenges faced, the solutions implemented, and the outcomes achieved.

Alignment

How this activity aligns with the learning objectives & standardsLearning Goal: Understand real-world applications of volume calculation in urban planning and architecture.
Activity 3

Dream City Architect

Students will integrate all the knowledge and skills they have acquired throughout the project to design their dream city, addressing specific urban planning challenges such as traffic congestion, resource allocation, and environmental sustainability. They will create a 3D model of their city and present their design to the class.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Review all the previous activities and gather the designs, calculations, and research findings.
2. Develop a comprehensive plan for their dream city, addressing specific urban planning challenges.
3. Create a 3D model of the city using materials like cardboard, paper, or digital modeling software.
4. Prepare a presentation explaining the design choices, volume calculations, and solutions to urban planning challenges.
5. Present the dream city design to the class and answer questions.

Final Product

What students will submit as the final product of the activityA 3D model of their dream city, accompanied by a presentation explaining the design choices, volume calculations, and solutions to urban planning challenges.

Alignment

How this activity aligns with the learning objectives & standardsLearning Goal: Demonstrate problem-solving skills in addressing urban planning challenges.
Activity 4

3D Shape Explorer

Students will begin by exploring different 3D shapes and their corresponding volume formulas. This activity will lay the groundwork for designing structures in their dream city.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Research and select six different 3D shapes (e.g., cube, sphere, cylinder, pyramid, cone, rectangular prism).
2. For each shape, find and write down the formula for calculating its volume.
3. Draw a clear diagram of each shape and label its dimensions (e.g., radius, height, length, width).
4. Create a reference sheet compiling all the shapes, formulas, and diagrams.

Final Product

What students will submit as the final product of the activityA reference sheet containing labeled diagrams of at least six different 3D shapes with their volume formulas.

Alignment

How this activity aligns with the learning objectives & standardsLearning Goal: Apply the concept of volume to design various structures in a city.
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Rubric & Reflection

Portfolio Rubric

Grading criteria for assessing the overall project portfolio

Dream City Rubric

Category 1

Sustainable City Design

Assesses the accuracy of volume calculations, the effective application of geometric shapes, the analysis of environmental impact, and the overall quality of the final report.
Criterion 1

Volume Calculation Accuracy

Accuracy of volume calculations for different shapes

Exemplary
4 Points

All volume calculations are accurate and precise, demonstrating a deep understanding of geometric formulas and their application.

Proficient
3 Points

Most volume calculations are accurate, with only minor errors that do not significantly impact the overall results.

Developing
2 Points

Some volume calculations are accurate, but there are noticeable errors that affect the overall results.

Beginning
1 Points

Volume calculations are largely inaccurate, indicating a lack of understanding of geometric formulas and their application.

Criterion 2

Geometric Shape Application

Application of geometric shapes in the city design

Exemplary
4 Points

City design showcases innovative and effective use of various geometric shapes, enhancing both functionality and aesthetics.

Proficient
3 Points

City design effectively uses geometric shapes to create functional urban spaces.

Developing
2 Points

City design incorporates some geometric shapes, but their use could be more effective and intentional.

Beginning
1 Points

City design shows limited use of geometric shapes, and their application is not effective.

Criterion 3

Environmental Impact Analysis

Consideration of environmental impact and sustainability

Exemplary
4 Points

Report thoroughly analyzes the environmental impact of the city design and provides innovative and practical suggestions for improving sustainability.

Proficient
3 Points

Report adequately addresses the environmental impact of the city design and offers reasonable suggestions for improving sustainability.

Developing
2 Points

Report touches on the environmental impact of the city design but lacks depth and specific suggestions for improvement.

Beginning
1 Points

Report fails to adequately address the environmental impact of the city design or provide meaningful suggestions for sustainability.

Criterion 4

Report Quality

Quality and clarity of the final report

Exemplary
4 Points

Report is exceptionally well-written, organized, and presented, demonstrating a high level of attention to detail and clarity.

Proficient
3 Points

Report is well-written, organized, and presented, with clear explanations and supporting evidence.

Developing
2 Points

Report is adequately written but may lack organization or clarity in some areas.

Beginning
1 Points

Report is poorly written, disorganized, and lacks clarity, making it difficult to understand the findings and suggestions.

Category 2

Real-World Urban Planning

Evaluates the relevance of chosen projects, the depth of research, the quality of presentation, and the level of engagement in class discussions.
Criterion 1

Project Relevance

Selection of relevant urban planning projects

Exemplary
4 Points

Projects selected are highly relevant and provide insightful examples of volume calculations in urban planning.

Proficient
3 Points

Projects selected are relevant and demonstrate the application of volume calculations in urban planning.

Developing
2 Points

Projects selected are somewhat relevant, but the connection to volume calculations in urban planning is not always clear.

Beginning
1 Points

Projects selected are not relevant to urban planning or do not demonstrate the application of volume calculations.

Criterion 2

Research Depth

Depth of research and information gathering

Exemplary
4 Points

Research is thorough and comprehensive, providing detailed information about the projects' goals, challenges, solutions, and outcomes.

Proficient
3 Points

Research is adequate and provides sufficient information about the projects' goals, challenges, solutions, and outcomes.

Developing
2 Points

Research is limited and lacks detail in describing the projects' goals, challenges, solutions, or outcomes.

Beginning
1 Points

Research is minimal and provides insufficient information about the projects.

Criterion 3

Presentation Quality

Clarity and organization of the presentation

Exemplary
4 Points

Presentation is exceptionally clear, well-organized, and engaging, effectively showcasing the key aspects of each project.

Proficient
3 Points

Presentation is clear, well-organized, and effectively showcases the key aspects of each project.

Developing
2 Points

Presentation is adequately organized but may lack clarity or engagement in some areas.

Beginning
1 Points

Presentation is poorly organized, lacks clarity, and fails to effectively showcase the key aspects of each project.

Criterion 4

Discussion Participation

Participation in class discussion

Exemplary
4 Points

Student actively participates in class discussion, providing insightful comments and thoughtful questions that enhance the learning experience for all.

Proficient
3 Points

Student participates in class discussion, providing relevant comments and questions.

Developing
2 Points

Student participates in class discussion but may not always provide relevant comments or questions.

Beginning
1 Points

Student rarely participates in class discussion or provides irrelevant comments.

Category 3

Dream City Design

Focuses on the integration of knowledge, problem-solving skills, the quality of the 3D model, and the effectiveness of the presentation in addressing urban planning challenges.
Criterion 1

Knowledge Integration

Integration of knowledge and skills from previous activities

Exemplary
4 Points

City design seamlessly integrates knowledge and skills from all previous activities, resulting in a cohesive and well-thought-out plan.

Proficient
3 Points

City design effectively integrates knowledge and skills from most previous activities, resulting in a functional and reasonable plan.

Developing
2 Points

City design integrates some knowledge and skills from previous activities, but the connections could be stronger.

Beginning
1 Points

City design shows limited integration of knowledge and skills from previous activities.

Criterion 2

Problem-Solving

Effectiveness in addressing urban planning challenges

Exemplary
4 Points

City design effectively addresses a wide range of urban planning challenges with innovative and practical solutions.

Proficient
3 Points

City design addresses several urban planning challenges with reasonable solutions.

Developing
2 Points

City design addresses some urban planning challenges, but the solutions may not be fully effective or practical.

Beginning
1 Points

City design fails to adequately address urban planning challenges or provide meaningful solutions.

Criterion 3

Model Quality

Quality and creativity of the 3D model

Exemplary
4 Points

3D model is exceptionally detailed, creative, and well-constructed, showcasing a high level of craftsmanship and attention to detail.

Proficient
3 Points

3D model is well-constructed and effectively represents the city design.

Developing
2 Points

3D model is adequately constructed but may lack detail or creativity.

Beginning
1 Points

3D model is poorly constructed and fails to adequately represent the city design.

Criterion 4

Presentation Skills

Clarity and persuasiveness of the presentation

Exemplary
4 Points

Presentation is exceptionally clear, persuasive, and engaging, effectively conveying the design choices and solutions to urban planning challenges.

Proficient
3 Points

Presentation is clear, persuasive, and effectively conveys the design choices and solutions to urban planning challenges.

Developing
2 Points

Presentation is adequately clear but may lack persuasiveness or engagement in some areas.

Beginning
1 Points

Presentation is unclear, lacks persuasiveness, and fails to effectively convey the design choices or solutions.

Category 4

Geometric Foundations

Assesses students' ability to accurately identify shapes, select appropriate formulas, create clear diagrams, and compile a comprehensive reference sheet.
Criterion 1

Shape Identification

Accuracy of shape identification and formula selection

Exemplary
4 Points

Accurately identifies all six shapes and selects the correct volume formula for each, demonstrating a strong understanding of geometric concepts.

Proficient
3 Points

Accurately identifies most shapes and selects the correct volume formulas with only minor errors.

Developing
2 Points

Identifies some shapes correctly but makes several errors in shape identification or formula selection.

Beginning
1 Points

Struggles to identify shapes and selects incorrect volume formulas, demonstrating a limited understanding of geometric concepts.

Criterion 2

Diagram Quality

Clarity and completeness of diagrams

Exemplary
4 Points

Draws clear, detailed diagrams of each shape with all dimensions accurately labeled, enhancing understanding and clarity.

Proficient
3 Points

Draws clear diagrams of each shape with most dimensions accurately labeled.

Developing
2 Points

Draws diagrams of each shape, but some may lack clarity or accurate labeling of dimensions.

Beginning
1 Points

Draws incomplete or unclear diagrams with inaccurate or missing labels, hindering understanding.

Criterion 3

Reference Sheet

Organization and accuracy of the reference sheet

Exemplary
4 Points

Creates a well-organized, visually appealing reference sheet that accurately compiles all shapes, formulas, and diagrams, making it easy to use and understand.

Proficient
3 Points

Creates a reference sheet that accurately compiles all shapes, formulas, and diagrams in a clear and organized manner.

Developing
2 Points

Creates a reference sheet that includes most shapes, formulas, and diagrams but may lack organization or accuracy in some areas.

Beginning
1 Points

Creates a poorly organized reference sheet with missing or inaccurate information, making it difficult to use.

Reflection Prompts

End-of-project reflection questions to get students to think about their learning
Question 1

Reflecting on your 'Dream City' project, what was the most significant challenge you faced while balancing aesthetics, functionality, and environmental impact, and how did you overcome it?

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Question 2

In what ways did your understanding of volume calculations evolve throughout the project, and how did this impact your approach to designing sustainable urban spaces?

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Question 3

If you could revisit one aspect of your 'Dream City' design, what would it be and why?

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Question 4

How effectively do you believe your 'Dream City' addresses real-world urban planning challenges, such as traffic congestion or resource allocation, and what alternative solutions might you consider in the future?

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