Created byBenton Fletcher

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Geometric City Planning

Grade 10Math20 days

In this project, students in grade 10 math will act as city planners, applying geometric transformations to design a functional and sustainable city layout. They will optimize space and resources using geometric principles, incorporating various shapes for different urban functions and utilizing technology for design and visualization. Students will explore geometric definitions, transformations, and coordinate representation to create a cohesive city plan, documented with a coordinate map and justifications for design choices.

Geometric TransformationsCity PlanningCoordinate GeometrySustainable DesignUrban PlanningGeometric Principles

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Inquiry Framework

Question Framework

Driving Question

The overarching question that guides the entire project.How can we design a functional and sustainable city layout that optimizes space and resources using geometric transformations and principles?

Essential Questions

Supporting questions that break down major concepts.

How can geometric transformations be used to optimize space?
What geometric shapes are most efficient for different urban functions?
How do transformations affect the properties of geometric figures?
How can coordinates be used to represent locations and transformations in the city plan?
How can technology be used to aid in the design and visualization of the city plan?

Standards & Learning Goals

Learning Goals

By the end of this project, students will be able to:

Apply geometric transformations (translations, rotations, reflections, dilations) to design city layouts.
Calculate and optimize area and perimeter of city blocks using geometric principles.
Use coordinates to represent locations and transformations in the city plan.
Incorporate various geometric shapes for different urban functions (residential, commercial, recreational).
Utilize technology for design and visualization of the city plan.

Common Core Standards

HSG-CO.A.1

Primary

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.Reason: The project involves understanding and applying geometric definitions in the city design.

HSG-CO.A.2

Primary

Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).Reason: The project requires students to apply geometric transformations to optimize space and resources.

Entry Events

Events that will be used to introduce the project to students

Urban Expansion Challenge

The local city council announces a rapid population increase and needs student teams to propose geometrically optimized expansion plans using only transformations. The team that designs the most efficient and aesthetically pleasing expansion, while adhering to a strict budget, wins.

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Portfolio Activities

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

Activity 1

Geometric Vocabulary Builder

Students will define key geometric terms and illustrate them, building a foundation for applying these concepts in city planning.

Steps

Here is some basic scaffolding to help students complete the activity.

1. Define 'point', 'line', 'angle', 'circle', 'perpendicular line', 'parallel line', and 'line segment'.

2. Draw an example of each term, labeling all parts.

3. Write a sentence explaining how each term will be relevant in city design.

Final Product

What students will submit as the final product of the activityA glossary of geometric terms with definitions, illustrations, and relevance statements.

Alignment

How this activity aligns with the learning objectives & standardsHSG-CO.A.1 (Know precise definitions of geometric terms)

Activity 2

Transformation Station

Students explore geometric transformations (translations, rotations, reflections, dilations) using geometry software and physical manipulatives to understand how these transformations affect geometric figures.

Steps

Here is some basic scaffolding to help students complete the activity.

1. Using geometry software (e.g., GeoGebra), perform translations, rotations, reflections, and dilations on basic shapes.

2. Record the coordinates of the original shape and the transformed shape.

3. Describe the transformation as a function, noting how the coordinates change.

4. Compare transformations that preserve distance and angle to those that do not.

Final Product

What students will submit as the final product of the activityA presentation or report detailing each transformation, its effect on coordinates, and whether it preserves distance and angle.

Alignment

How this activity aligns with the learning objectives & standardsHSG-CO.A.2 (Represent transformations and compare their properties)

Activity 3

City Planner

Students integrate individual city blocks into a cohesive city layout, using coordinates to map locations and transformations, ensuring efficient use of space and resources.

Steps

Here is some basic scaffolding to help students complete the activity.

1. Combine the individual city block designs into a larger city layout.

2. Use a coordinate system to map the locations of key features (e.g., residential areas, commercial zones, parks).

3. Apply geometric transformations to reposition or reorient city blocks to optimize space and resources.

4. Document all transformations with coordinates and function descriptions.

Final Product

What students will submit as the final product of the activityA comprehensive city plan, including a coordinate map, descriptions of transformations, and a rationale for the overall design in terms of efficiency and sustainability.

Alignment

How this activity aligns with the learning objectives & standardsHSG-CO.A.1 (Applying definitions to design) and HSG-CO.A.2 (Applying transformations to optimize space)

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Rubric & Reflection

Portfolio Rubric

Grading criteria for assessing the overall project portfolio

Geometric City Planning Portfolio Rubric

Category 1

Geometric Vocabulary

Understanding and accurate application of geometric definitions (point, line, angle, circle, perpendicular line, parallel line, line segment).

Criterion 1

Accuracy of Definitions

Correctness and completeness of geometric definitions.

Exemplary

4 Points

Provides precise and comprehensive definitions for all geometric terms, demonstrating a deep understanding of fundamental concepts.

Proficient

3 Points

Provides accurate definitions for most geometric terms, with only minor inaccuracies or omissions.

Developing

2 Points

Provides basic definitions for some geometric terms, but with significant inaccuracies, omissions, or misunderstandings.

Beginning

1 Points

Struggles to define geometric terms accurately, demonstrating limited understanding of fundamental concepts.

Criterion 2

Clarity of Illustrations

Quality and accuracy of visual representations of geometric terms.

Exemplary

4 Points

Creates clear, accurate, and detailed illustrations for all geometric terms, enhancing understanding and application.

Proficient

3 Points

Creates accurate illustrations for most geometric terms, with adequate clarity and detail.

Developing

2 Points

Creates illustrations for some geometric terms, but with limited accuracy, clarity, or detail.

Beginning

1 Points

Struggles to create accurate or clear illustrations for geometric terms, hindering understanding.

Criterion 3

Relevance to City Design

Explanation of how each geometric term is relevant to city planning and design.

Exemplary

4 Points

Provides insightful and comprehensive explanations of how each geometric term is directly relevant to practical applications in city design, showcasing a strong connection between theory and practice.

Proficient

3 Points

Provides clear explanations of how most geometric terms are relevant to city design, demonstrating a good understanding of their practical applications.

Developing

2 Points

Provides basic explanations of how some geometric terms are relevant to city design, but with limited detail or connection to practical applications.

Beginning

1 Points

Struggles to explain the relevance of geometric terms to city design, demonstrating a weak connection between theory and practice.

Category 2

Geometric Transformations

Application and understanding of geometric transformations (translations, rotations, reflections, dilations) and their properties.

Criterion 1

Accuracy of Transformations

Correctness and precision in performing geometric transformations using software or manipulatives.

Exemplary

4 Points

Performs all geometric transformations accurately and precisely, demonstrating a sophisticated understanding of their effects on geometric figures.

Proficient

3 Points

Performs most geometric transformations accurately, with only minor errors or inconsistencies.

Developing

2 Points

Performs some geometric transformations accurately, but with significant errors or inconsistencies.

Beginning

1 Points

Struggles to perform geometric transformations accurately, demonstrating limited understanding of their effects.

Criterion 2

Coordinate Representation

Accurate representation of transformations using coordinates and function descriptions.

Exemplary

4 Points

Accurately represents all transformations using coordinates and clear function descriptions, demonstrating a deep understanding of their mathematical representation.

Proficient

3 Points

Accurately represents most transformations using coordinates and function descriptions, with only minor errors or omissions.

Developing

2 Points

Represents some transformations using coordinates, but with significant errors, omissions, or unclear function descriptions.

Beginning

1 Points

Struggles to represent transformations using coordinates, demonstrating limited understanding of their mathematical representation.

Criterion 3

Property Comparison

Comparison of transformations that preserve distance and angle to those that do not.

Exemplary

4 Points

Provides a comprehensive and insightful comparison of transformations that preserve distance and angle to those that do not, explaining the underlying mathematical principles.

Proficient

3 Points

Provides a clear comparison of transformations that preserve distance and angle to those that do not, demonstrating a good understanding of their properties.

Developing

2 Points

Provides a basic comparison of transformations that preserve distance and angle to those that do not, but with limited detail or explanation.

Beginning

1 Points

Struggles to compare transformations that preserve distance and angle to those that do not, demonstrating a weak understanding of their properties.

Category 3

City Design and Optimization

Integration of geometric principles and transformations in the design of a functional and sustainable city layout.

Criterion 1

Cohesiveness of Design

Integration of individual city blocks into a cohesive and well-organized city layout.

Exemplary

4 Points

Creates a highly cohesive and well-organized city layout, demonstrating a sophisticated understanding of urban planning principles and geometric relationships.

Proficient

3 Points

Creates a cohesive and well-organized city layout, demonstrating a good understanding of urban planning principles.

Developing

2 Points

Creates a city layout with some degree of cohesiveness, but with noticeable organizational issues or inconsistencies.

Beginning

1 Points

Struggles to create a cohesive or well-organized city layout, demonstrating limited understanding of urban planning principles.

Criterion 2

Coordinate Mapping

Accurate and effective use of a coordinate system to map locations and transformations.

Exemplary

4 Points

Uses a coordinate system to accurately and effectively map the locations of all key features and transformations, providing a clear and comprehensive representation of the city plan.

Proficient

3 Points

Uses a coordinate system to accurately map the locations of most key features and transformations, with only minor errors or omissions.

Developing

2 Points

Uses a coordinate system to map the locations of some key features, but with significant errors, omissions, or inconsistencies.

Beginning

1 Points

Struggles to use a coordinate system to map the locations of key features, demonstrating limited understanding of coordinate geometry.

Criterion 3

Rationale and Sustainability

Justification of the city design in terms of efficiency, sustainability, and geometric principles.

Exemplary

4 Points

Provides a compelling and well-supported rationale for the city design, demonstrating a deep understanding of efficiency, sustainability, and the application of geometric principles.

Proficient

3 Points

Provides a clear rationale for the city design, demonstrating a good understanding of efficiency, sustainability, and the application of geometric principles.

Developing

2 Points

Provides a basic rationale for the city design, but with limited detail or connection to efficiency, sustainability, or geometric principles.

Beginning

1 Points

Struggles to provide a rationale for the city design, demonstrating a weak understanding of efficiency, sustainability, and geometric principles.

Reflection Prompts

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

Question 1

How did your understanding of geometric transformations evolve throughout this project?

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Question 2

To what extent were you able to optimize space and resources in your city design using geometric principles?

Scale

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Question 3

Which geometric shape did you find most effective for urban planning, and why?

Multiple choice

Required

Options

Squares

Rectangles

Circles

Triangles

Hexagons

Other

Question 4

How effectively did you use coordinates to represent locations and transformations in your city plan?

Scale

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Question 5

In what ways did technology aid in the design and visualization of your city plan?

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Question 6

What challenges did you encounter during the integration of individual city blocks into a cohesive city layout, and how did you address them?

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