Created byMelanie Heberling

1 views0 downloads

Geometry City: Design Your Dream City

Grade 6Math5 days

★★★★★

4.0 (1 rating)

In this project, 6th-grade students take on the role of urban planners to design a sustainable and visually appealing city using geometric principles. They will use 2D and 3D shapes to create city structures, incorporate transformations and symmetry to enhance the city's design, and use coordinates to map the city layout. Students will apply their knowledge of lines, angles, shapes, transformations, and coordinates to create a functional and aesthetically pleasing urban environment.

GeometryUrban Planning2D Shapes3D ShapesTransformationsCoordinatesCity Design

Want to create your own PBL Recipe?Use our AI-powered tools to design engaging project-based learning experiences for your students.

📝

Inquiry Framework

Question Framework

Driving Question

The overarching question that guides the entire project.How can we, as urban planners, design a sustainable and visually appealing city using geometric principles to optimize functionality and enhance the lives of its citizens?

Essential Questions

Supporting questions that break down major concepts.

How can geometric shapes be used to design functional and aesthetically pleasing cities?
What geometric principles (angles, lines, symmetry) are essential for city planning and design?
How do different 2D and 3D shapes contribute to the overall structure and organization of a city?
How can transformations (translations, reflections, rotations) and symmetry be used to create visually appealing and balanced city layouts?
How can coordinates and the Cartesian plane be used to accurately map and plan the layout of a city?

Standards & Learning Goals

Learning Goals

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

Apply geometric principles to design a functional and aesthetically pleasing city.
Utilize 2D and 3D shapes to create city structures and layouts.
Incorporate transformations and symmetry to enhance city design.
Use coordinates and the Cartesian plane to map and plan the city layout.

Teacher Provided

9.1

Primary

Points, lines and angles. Know that a point indicates a place on a line. Measure and draw straight, vertical, horizontal, diagonal, perpendicular and parallel lines with given lengths. Define concepts: line segment, ray, straight line, parallel lines and perpendicular lines. Construct angles up to 360° and use a ruler and protractor. Identify, name and draw acute angles, right angles, obtuse angles, straight angles, reflex angles and revolutions. Use a protractor to measure and classify angles in terms of: < 90° (acute angles), Right angles, > 90° (obtuse angles), Straight angles, > 180° (reflex angles)Reason: Students will apply these concepts to design the city layout.

9.2

Primary

2D shapes. Describe, sort, name and compare different types of quadrilaterals in terms of the length of their sides, angles and symmetry. Describe, sort, name and compare the different triangles in terms of their sides and angles. Identify and describe the properties of isosceles, equilateral and scalene triangles as well as right-angled, obtuse-angled and acute-angled triangles. Make circle patterns with compasses. Identify and use the following terminology related to circles: Radius, Diameter, Chord, Arc, Sector, Semicircle, Segment. Determine whether a shape is convex or concave. Similar and congruent 2-D shapes according to shape and sizeReason: Students will use various 2D shapes in their city designs.

9.3

Secondary

3D figures. Describe, sort and compare prisms and pyramids with respect to: Faces, Edges, VerticesReason: Students will incorporate 3D figures into their city designs.

9.4

Secondary

Transformation. Identify translations, reflections and rotations of figures. Recognize and draw lines of symmetry on figures. Enlargement and reduction of figuresReason: Students can use transformations and symmetry to create balanced city layouts.

9.5

Primary

Position and movement. Describe the position of a point on a grid with coordinates. Plot points in the first quadrant of the Cartesian plane. Draw shapes with given vertices as coordinates on a Cartesian planeReason: Students will use coordinates to map and plan their city layout.

9.6

Primary

Construction. Construct geometric figures accurately using a compass, ruler and protractor, including: Angles, accurate to one degree, Circles, Parallel lines, Perpendicular linesReason: Students will construct geometric figures accurately in their city designs.

Entry Events

Events that will be used to introduce the project to students

'Geometry in Disguise' Photo Challenge

Students receive cryptic photos of cityscapes, challenged to identify hidden geometric shapes and angles within the images. This sparks curiosity about the prevalence of geometry in urban design and encourages them to look at their own surroundings with a mathematical eye.

📚

Portfolio Activities

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

Activity 1

Shape Surveyor's Starter Kit

Students will begin by identifying and classifying different types of lines and angles found in real-world cityscapes. This activity reinforces their understanding of fundamental geometric concepts.

Steps

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

1. Research and collect images of different cityscapes from magazines, books, or the internet.

2. Identify and label various types of lines (straight, vertical, horizontal, diagonal, parallel, perpendicular) in each image.

3. Measure and classify angles (acute, right, obtuse, straight, reflex) found in the cityscapes using a protractor.

4. Create a presentation showcasing the identified lines and angles, explaining their properties and classifications.

Final Product

What students will submit as the final product of the activityA visual presentation (e.g., poster, slideshow) showcasing labeled lines and angles in cityscapes with explanations.

Alignment

How this activity aligns with the learning objectives & standardsAligns with standard 9.1 (Points, lines, and angles).

Activity 2

2D Design Blueprint

Students will explore various 2D shapes and their properties, then apply this knowledge to create a blueprint for a city block, focusing on the functional use of each shape.

Steps

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

1. Review the properties of different quadrilaterals (squares, rectangles, parallelograms, trapezoids) and triangles (isosceles, equilateral, scalene, right-angled).

2. Design a city block blueprint using various 2D shapes to represent buildings, parks, and other urban elements.

3. Label each shape and explain its properties and how it contributes to the functionality and aesthetics of the city block.

4. Write a short paragraph justifying the choice of shapes and their arrangement in the blueprint.

Final Product

What students will submit as the final product of the activityA detailed blueprint of a city block using various 2D shapes, with labels and explanations of their properties and functions.

Alignment

How this activity aligns with the learning objectives & standardsAligns with standard 9.2 (2D shapes).

Activity 3

3D Cityscape Model

Students will extend their understanding of geometric shapes by creating 3D models of city buildings using prisms and pyramids, focusing on accurately representing faces, edges, and vertices.

Steps

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

1. Research and explore different types of prisms and pyramids (e.g., rectangular prism, triangular prism, square pyramid).

2. Choose specific buildings for your city (e.g., skyscraper, museum, house) and design 3D models using prisms and pyramids.

3. Construct the 3D models using materials like cardboard, paper, or modeling clay, ensuring accurate representation of faces, edges, and vertices.

4. Write a description of each building, identifying the types of prisms and pyramids used and explaining their structural properties.

Final Product

What students will submit as the final product of the activity3D models of city buildings constructed from prisms and pyramids, with descriptions of their geometric properties.

Alignment

How this activity aligns with the learning objectives & standardsAligns with standard 9.3 (3D figures).

Activity 4

Transformation Station

Students will explore geometric transformations by applying translations, reflections, and rotations to building designs, and incorporating lines of symmetry to create balanced and visually appealing urban layouts.

Steps

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

1. Design a simple building facade using geometric shapes.

2. Apply transformations (translations, reflections, rotations) to the building facade to create variations.

3. Identify and draw lines of symmetry on the original and transformed building designs.

4. Incorporate the transformed building designs into a city layout, explaining how the transformations enhance the visual appeal and balance of the city.

Final Product

What students will submit as the final product of the activityA city layout incorporating transformed building designs with identified lines of symmetry, and explanations of how transformations enhance visual appeal.

Alignment

How this activity aligns with the learning objectives & standardsAligns with standard 9.4 (Transformation).

Activity 5

Coordinate City Planner

Students will use coordinates and the Cartesian plane to plan and map the layout of their city, accurately plotting points and drawing shapes to represent buildings, roads, and other city features.

Steps

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

1. Create a Cartesian plane on graph paper or using digital tools.

2. Assign coordinates to the vertices of different buildings and landmarks in your city.

3. Plot the points and draw the shapes representing the buildings and landmarks on the Cartesian plane.

4. Write the coordinates of each building/landmark and explain how the Cartesian plane helps to accurately map the city layout.

Final Product

What students will submit as the final product of the activityA city map plotted on a Cartesian plane with labeled coordinates for buildings and landmarks, and an explanation of the mapping process.

Alignment

How this activity aligns with the learning objectives & standardsAligns with standard 9.5 (Position and movement).

Activity 6

Geometry City Construction Crew

Students will apply their knowledge of geometric construction to accurately create angles, circles, and parallel and perpendicular lines within their city designs, using tools like compasses, rulers, and protractors.

Steps

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

1. Plan the layout of a specific area in your city, including roads, buildings, and public spaces.

2. Use a compass, ruler, and protractor to construct accurate angles (to one degree), circles, parallel lines, and perpendicular lines within the planned layout.

3. Label all constructed geometric elements (angles, circles, lines) with their measurements and properties.

4. Write a detailed explanation of the construction process, justifying the use of specific geometric elements and their impact on the functionality and aesthetics of the city area.

Final Product

What students will submit as the final product of the activityA detailed city area plan with accurately constructed geometric elements (angles, circles, parallel lines, perpendicular lines), labeled measurements, and a construction process explanation.

Alignment

How this activity aligns with the learning objectives & standardsAligns with standard 9.6 (Construction).

🏆

Rubric & Reflection

Portfolio Rubric

Grading criteria for assessing the overall project portfolio

Geometry City Portfolio Rubric

Category 1

Geometric Knowledge and Application

Demonstrates understanding of geometric concepts (lines, angles, shapes, transformations) and their application in city design.

Criterion 1

Lines and Angles

Accurately identifies, classifies, and applies different types of lines and angles in the city design.

Exemplary

4 Points

Demonstrates a sophisticated understanding of lines and angles, accurately classifying and applying them creatively and effectively in the city design.

Proficient

3 Points

Demonstrates a thorough understanding of lines and angles, accurately classifying and applying them appropriately in the city design.

Developing

2 Points

Shows an emerging understanding of lines and angles, with some inconsistencies in classification and application in the city design.

Beginning

1 Points

Shows a limited understanding of lines and angles, struggling with classification and application in the city design.

Criterion 2

2D and 3D Shapes

Effectively utilizes 2D and 3D shapes to create city structures, demonstrating an understanding of their properties and relationships.

Exemplary

4 Points

Masterfully utilizes a wide variety of 2D and 3D shapes to create innovative and functional city structures, showcasing a deep understanding of their properties.

Proficient

3 Points

Effectively utilizes 2D and 3D shapes to create well-designed city structures, demonstrating a good understanding of their properties.

Developing

2 Points

Uses 2D and 3D shapes in the city design, but the application is inconsistent and understanding of properties is limited.

Beginning

1 Points

Struggles to utilize 2D and 3D shapes effectively in the city design, showing a minimal understanding of their properties.

Criterion 3

Transformations and Symmetry

Skillfully applies transformations (translations, reflections, rotations) and incorporates symmetry to create balanced and visually appealing city layouts.

Exemplary

4 Points

Expertly applies transformations and symmetry to create a visually stunning and harmonious city layout, demonstrating a sophisticated understanding of these concepts.

Proficient

3 Points

Skillfully applies transformations and incorporates symmetry to create a balanced and visually appealing city layout.

Developing

2 Points

Applies transformations and incorporates symmetry in the city layout, but the application is inconsistent and the impact on visual appeal is limited.

Beginning

1 Points

Struggles to apply transformations and incorporate symmetry in the city layout, showing a minimal understanding of these concepts.

Category 2

Construction and Mapping Skills

Demonstrates proficiency in geometric construction techniques and the use of coordinates and the Cartesian plane for city planning and mapping.

Criterion 1

Geometric Construction

Accurately constructs geometric figures (angles, circles, parallel/perpendicular lines) using tools like compasses, rulers, and protractors.

Exemplary

4 Points

Demonstrates masterful geometric construction skills, accurately creating complex figures with precision and attention to detail.

Proficient

3 Points

Accurately constructs geometric figures using appropriate tools and techniques.

Developing

2 Points

Shows emerging skills in geometric construction, with some inaccuracies in the construction of figures.

Beginning

1 Points

Struggles with geometric construction, showing limited proficiency in using tools and creating accurate figures.

Criterion 2

Coordinate Mapping

Effectively uses coordinates and the Cartesian plane to accurately map the city layout, demonstrating an understanding of spatial relationships.

Exemplary

4 Points

Expertly uses coordinates and the Cartesian plane to create a detailed and accurate map of the city layout, demonstrating a sophisticated understanding of spatial relationships and precise mapping skills.

Proficient

3 Points

Effectively uses coordinates and the Cartesian plane to accurately map the city layout.

Developing

2 Points

Uses coordinates and the Cartesian plane to map the city layout, but the accuracy and detail are limited.

Beginning

1 Points

Struggles to use coordinates and the Cartesian plane to map the city layout, showing a minimal understanding of spatial relationships.

Category 3

Design and Functionality

Creates a city design that is both aesthetically pleasing and functional, considering the needs of its citizens and the principles of urban planning.

Criterion 1

Aesthetic Appeal

Creates a visually appealing city layout that incorporates geometric principles to enhance its overall aesthetics.

Exemplary

4 Points

Creates a visually stunning and harmonious city layout that demonstrates exceptional creativity and a deep understanding of aesthetic principles.

Proficient

3 Points

Creates a visually appealing city layout that effectively incorporates geometric principles to enhance its aesthetics.

Developing

2 Points

Creates a city layout with some visual appeal, but the incorporation of geometric principles is limited.

Beginning

1 Points

Creates a city layout with limited visual appeal, showing minimal consideration of aesthetic principles.

Criterion 2

Functional Design

Designs a city that is functional and meets the needs of its citizens, considering factors like transportation, housing, and public spaces.

Exemplary

4 Points

Designs an exceptionally functional and sustainable city that comprehensively addresses the needs of its citizens and demonstrates a deep understanding of urban planning principles.

Proficient

3 Points

Designs a functional city that meets the needs of its citizens, considering factors like transportation, housing, and public spaces.

Developing

2 Points

Designs a city with some functional elements, but the consideration of citizen needs and urban planning principles is limited.

Beginning

1 Points

Designs a city with limited functional elements, showing minimal consideration of citizen needs and urban planning principles.

Reflection Prompts

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

Question 1

What was the most challenging aspect of designing a city using geometric principles, and how did you overcome it?

Text

Required

Question 2

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

Text

Required

Question 3

Which geometric principle (angles, lines, symmetry, coordinates) do you think is most important in urban planning, and why?

Text

Required

Question 4

To what extent do you think the geometric design of a city impacts the lives of its citizens?

Scale

Required

Question 5

If you could redesign one aspect of your city using different geometric principles, what would it be and why?

Text

Required