Geo-City Builders: Exploring Volume with 3D Designs
Created byAaron Oetting
1 views0 downloads

Geo-City Builders: Exploring Volume with 3D Designs

Grade 9Math1 days
Geo-City Builders is a project-based learning experience for 9th-grade students in which they explore and apply geometric concepts by designing a city using various 3D shapes. Through activities like calculating volumes and modifying formulas, students learn to maximize space and functionality in urban planning. The project emphasizes real-world applications of volume and geometry, fostering critical thinking and problem-solving skills as students engage with city simulation games and collaborate on their designs.
3D ShapesVolume CalculationUrban PlanningGeometryCity DesignProblem SolvingCollaboration
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 design a city using various 3D shapes that not only maximizes space but also effectively utilizes volume for functional and sustainable urban living?

Essential Questions

Supporting questions that break down major concepts.
  • How does the calculation of volume apply to real-world structures and designs, such as buildings in a city?
  • What are the mathematical relationships between different 3D shapes and their volumes?
  • How can understanding volume aid in efficient city planning and architecture?
  • What are the challenges and considerations when designing structures with varying volumes in a confined space?
  • In what ways does volume influence the functionality and design of urban areas?

Standards & Learning Goals

Learning Goals

By the end of this project, students will be able to:
  • Understand and calculate the volume of various 3D shapes including cubes, cylinders, cones, and spheres.
  • Apply volume calculation formulas to design real-world structures in the context of city planning.
  • Analyze the relationship between the dimensions of a structure and its volume.
  • Develop problem-solving skills by designing a city layout that maximizes space and functionality.
  • Enhance critical thinking by addressing challenges related to volume in urban planning.

Common Core Standards

HSG-GMD.3
Primary
Apply geometric methods to solve design problems.Reason: The project involves designing a city using geometric shapes and requires the application of geometric knowledge to solve urban planning problems.
HSG-MG.1
Primary
Use geometric shapes, their measures, and their properties to describe objects.Reason: Students will use 3D geometric shapes to describe and calculate volumes of structures in their city design.
HSG-GMD.1
Supporting
Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.Reason: The standard aligns with the project's focus on understanding and applying volume formulas for different geometric shapes.
HSA-CED.4
Supporting
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.Reason: Students might need to rearrange volume formulas based on given parameters to solve problems.

Entry Events

Events that will be used to introduce the project to students

Interactive City Simulation Game

Engage students with a city simulation game where they must build and manage a city using 3D shapes. They must calculate volumes for efficient resource management, blending math, strategy, and simulation to captivate students.
📚

Portfolio Activities

Portfolio Activities

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

Shape Selection Strategists

Students will begin by selecting various 3D geometric shapes to design the foundational elements of their city. Through brainstorming and collaboration, they will decide which shapes fit best with their urban plan and understand their basic properties.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Research the characteristics and properties of different 3D shapes like cubes, cylinders, cones, and spheres.
2. Discuss as a group how each shape might be used in urban design (e.g., a cylinder as a water tower).
3. Sketch a draft of the city indicating where each 3D shape will be positioned.

Final Product

What students will submit as the final product of the activityA drafted city plan with designated shapes for each structure, annotated with basic shape properties.

Alignment

How this activity aligns with the learning objectives & standardsAligns with HSG-MG.1 by using geometric shapes to describe city objects.
Activity 2

Volume Calculating Champions

In this activity, students will calculate the volume of each chosen 3D shape as per their initial city design. Accurate calculations will help them understand the space each structure occupies and allow them to make informed design adjustments.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Review volume formulas for cubes, cylinders, cones, and spheres.
2. Apply the formulas to calculate the volume of each structure in your city plan using specific dimensions.
3. Record each calculated volume next to the respective structure in your draft.

Final Product

What students will submit as the final product of the activityAn annotated city plan with calculated volumes included for each structure.

Alignment

How this activity aligns with the learning objectives & standardsAligns with HSG-GMD.1 by applying volume formulas to different geometric shapes.
Activity 3

Design Dynamics: Volume in Action

Students will apply their volume knowledge to analyze and refine their city design by examining how space and functionality are impacted by their calculated structures. They'll iterate on their designs as needed to enhance efficiency.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Evaluate the initial city design for efficiency and possible improvements in volume utilization.
2. Discuss potential design modifications to maximize space without losing functionality.
3. Redesign city plan, if necessary, for better space management or to add more functional elements.

Final Product

What students will submit as the final product of the activityA revised city design that effectively utilizes space and volumes based on student insights.

Alignment

How this activity aligns with the learning objectives & standardsAligns with HSG-GMD.3 by applying geometric methods to refine urban planning design problems.
Activity 4

Formula Flex Masters

This activity challenges students to rearrange volume formulas based on design changes or constraints. They'll deepen their understanding of geometry by exploring manipulations of volume calculations.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Identify scenarios where standard volume calculations must be adjusted (e.g., changing dimensions).
2. Learn techniques to rearrange volume formulas to fit design requirements.
3. Practice rearranging formulas using different city design scenarios.

Final Product

What students will submit as the final product of the activityA set of modified volume formulas tailored to specific design constraints in their city project.

Alignment

How this activity aligns with the learning objectives & standardsAligns with HSA-CED.4 by rearranging formulas to highlight and solve for different quantities of interest.
🏆

Rubric & Reflection

Portfolio Rubric

Grading criteria for assessing the overall project portfolio

Volume Variations: Building Geo-Cities Rubric

Category 1

Understanding of 3D Shapes

Evaluates students' ability to research, identify, and apply properties of different 3D geometric shapes in their city designs.
Criterion 1

Shape Knowledge

Assess student understanding of the characteristics and properties of 3D shapes used in their city design.

Exemplary
4 Points

Demonstrates exceptional understanding of 3D shapes, accurately integrates their properties in innovative city designs.

Proficient
3 Points

Shows thorough understanding of 3D shapes, correctly applies their properties in city designs.

Developing
2 Points

Displays basic understanding of 3D shapes and some knowledge of their properties.

Beginning
1 Points

Shows limited understanding of 3D shapes and struggles with identifying their properties.

Criterion 2

Selection and Application

Examines the ability to select appropriate 3D shapes for functional urban design.

Exemplary
4 Points

Selects and applies shapes with advanced insight, enhancing urban design functionality.

Proficient
3 Points

Selects suitable shapes, effectively contributing to functional urban design.

Developing
2 Points

Selects shapes with some relevance to urban design function.

Beginning
1 Points

Selects shapes with minimal consideration for design function.

Category 2

Volume Calculation

Assesses the ability to accurately calculate and apply volume formulas for city structures.
Criterion 1

Volume Accuracy

Evaluate the precision of volume calculations for 3D structures in the city plan.

Exemplary
4 Points

Executes volume calculations with exceptional precision, ensuring accurate representation of space.

Proficient
3 Points

Performs accurate volume calculations with occasional minor errors.

Developing
2 Points

Calculates volumes with notable errors impacting design accuracy.

Beginning
1 Points

Struggles with accurate volume calculations, leading to significant errors.

Criterion 2

Application of Formulas

Evaluates the student’s ability to apply and modify formulas based on design constraints.

Exemplary
4 Points

Applies and modifies formulas with full adaptation to complex design constraints.

Proficient
3 Points

Applies formulas effectively, adapting to basic design constraints.

Developing
2 Points

Applies formulas with limited consideration of design constraints.

Beginning
1 Points

Struggles to modify and apply formulas, largely overlooking design constraints.

Category 3

Design and Problem-Solving

Measures the ability to analyze, iterate, and improve urban designs based on volume considerations.
Criterion 1

Design Innovation

Assesses creativity and effectiveness in urban design solutions.

Exemplary
4 Points

Presents highly innovative design solutions enhancing functionality and spatial efficiency.

Proficient
3 Points

Proposes effective design solutions that improve urban function and space use.

Developing
2 Points

Offers basic design solutions with limited enhancement to functionality.

Beginning
1 Points

Contributes simplistic design solutions with minimal functional improvement.

Reflection Prompts

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

Reflect on how your understanding of volume and its practical application in city planning has evolved through this project. How did this knowledge influence your design decisions?

Text
Required
Question 2

On a scale of 1 to 5, how confident do you feel in applying volume formulas to real-world design problems after completing this project?

Scale
Required
Question 3

What challenges did you encounter when attempting to redesign your city plan to maximize space and functionality? How did you address these challenges?

Text
Optional
Question 4

Which geometric shape did you find most interesting to work with in your city design, and why?

Multiple choice
Optional
Options
Cube
Cylinder
Cone
Sphere
Question 5

Reflect on the collaborative aspect of this project. How did working with others enhance your understanding of geometric concepts and their real-world applications?

Text
Required