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Exploring Geometry through Architecture

A High school STEM lesson

Jasmine Coleman

09/15/2024

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Notes for teachers

Lesson Context:

Designed for middle school math classes; adaptable for clubs, camps, or STEM events.
Ideal for 2-3 class periods; can be adjusted based on available time and depth of exploration.

Differentiation Strategies:

Provide templates or simple model examples for students needing extra guidance.
Challenge advanced students with complex shapes and detailed calculations (surface area, volume).

Assessment Overview:

Formative: Class discussions, peer reviews, and blueprint drafts.
Summative: Final project presentation with architectural model and geometric explanations.

List of Materials

For the Engage and Explore Activities:

Printed or digital images of famous architectural structures.
Rulers, protractors, and compasses.
Pre-cut geometric shapes (e.g., triangles, squares, circles) made from cardstock, paper, or plastic.
Handouts with basic geometric terms and properties for reference.

For the Elaborate Activity (Architectural Model Project):

Cardboard sheets or foam board (for the base of the models).
Construction paper, cardstock, or thin cardboard (for creating geometric shapes).
Scissors, X-Acto knives, and cutting mats.
Glue, tape, or hot glue guns (with supervision).
Rulers, protractors, and compasses (continued from earlier activities).
Markers, pencils, and erasers.
Optional: Craft sticks, straws, string, and other materials for added structural elements.

For the Explain and Evaluate Activities:

Whiteboard or chart paper for group discussions and brainstorming.
Computers or tablets with access to architectural design software or websites for additional research (optional).
Blueprints or graph paper for drafting model designs.
Reflection worksheets for the final assessment.

Technology Needed:

Projector/Screen: To show videos or images during the Engage phase.
Microscopes/Tablets: For any digital exploration of geometric shapes or architectural software.

This lesson is designed for a High/middle school math class but can be adapted for use in an after-school club, summer camp, or STEM-focused event. It provides a hands-on approach to learning geometry by connecting mathematical concepts with real-world architectural design.

The lesson is structured to be completed over 2-3 class periods, depending on the depth of exploration and time available for the hands-on project. The "Engage" and "Explore" sections can be completed in one class, while the "Explain," "Elaborate," and "Evaluate" sections can span 1-2 additional classes.

Differentiation:

For students who need additional support, consider providing templates or examples of simple geometric models to guide their design process.
For advanced students, challenge them to calculate the surface area and volume of their entire architectural model or to incorporate more complex geometric shapes.

Assessment: The lesson includes both formative and summative assessments. Formative assessments include class discussions, peer reviews, and the blueprint draft. The final project presentation serves as the summative assessment, with students demonstrating their understanding of geometric concepts through their models and explanations.

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Standards

HS-ETS1-2: Design a solution to a complex real-world problem by breaking it down into smaller, manageable problems that can be solved through engineering.
HS-ETS1-3: Evaluate a solution to a real-world problem based on prioritized criteria and trade-offs that account for a range of constraints (e.g., cost, safety, reliability).
HS-PS3-4: Investigate the relationship between energy and forces in architectural structures, which is relevant when students learn about load-bearing structures and forces acting on buildings.

G.G-MG.A.1 Use geometric shapes, their measures, and their properties to describe objects utilizing real-world context.
G.G-MG.A.2 Apply concepts of density based on area and volume in modeling situations utilizing real-world context.
G.G-MG.A.3 Apply geometric methods to solve design problems utilizing real-world context.

Standards

Crosscutting Concepts such as "scale, proportion, and quantity" are essential when students apply geometric principles to architectural models. This connects to measuring dimensions, calculating areas, and scaling up designs.

Systems and System Models: Building architectural models provides an opportunity for students to engage with systems thinking by designing models based on real-world architectural systems.

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Objective(s):

Students will identify and classify basic geometric shapes and their properties.
Students will analyze famous architectural structures to recognize geometric principles.
Students will apply their understanding of geometry to design and construct an architectural model.
Students will calculate the area and volume of geometric shapes used in their architectural design.
Students will develop collaboration and presentation skills through group work and project presentations.

Objective(s): In this lesson, students will be introduced to the fundamentals of geometry through an engaging, real-world application—architecture. The first goal is to help them recognize basic geometric shapes and understand their properties. We'll be using famous architectural structures as case studies to explore how geometry is applied in real life.

Next, students will have the opportunity to apply this knowledge by designing and building their own architectural models, incorporating geometric principles they’ve learned. While doing this, they'll also be calculating the area and volume of the shapes used in their designs, enhancing their mathematical skills.

Additionally, this project promotes collaboration, as students will work in groups, and it will develop their communication skills as they present their models to the class. This hands-on approach is meant to show how math is not only theoretical but also creative and practical in the world around them

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Introduction: Engage

Opening Question: "Have you ever noticed the shapes used in buildings?"

Famous Structures Examples:

Eiffel Tower
Sydney Opera House
The Parthenon

�"What shapes do you see in these buildings?"�"How do these shapes help the design and strength of the structures?"

Goal:�Connect geometry to real-world architecture to spark curiosity.

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Explore Objective: Allow students to investigate geometric shapes and their properties through hands-on activities.

Activity:

Shape Investigation Stations: Set up stations with various geometric shapes (e.g., triangles, rectangles, circles) made from different materials (e.g., paper, straws, sticks). Have students rotate through the stations, exploring the properties of each shape by constructing 2D and 3D figures.
Geometry Tools Practice: Provide rulers, protractors, and compasses for students to measure angles, calculate areas, and draw perfect shapes.

Guiding Questions:

How do different shapes compare in terms of stability and strength?
Which shapes are easiest to construct, and why?

Here is a brief script to explore this topic further:

In this part of the lesson, we're going to move from observing geometric shapes in buildings to actually investigating and manipulating these shapes ourselves. The objective is to let students explore the properties of geometric shapes through hands-on activities, helping them deepen their understanding of the role these shapes play in architecture.

We’ll be setting up shape investigation stations around the room. Each station will focus on different geometric shapes—triangles, rectangles, circles, and more. At some stations, students will use materials like paper, straws, and sticks to build both 2D and 3D versions of these shapes. This will allow them to see firsthand how these shapes behave structurally. For example, triangles tend to be more stable, while rectangles might bend more easily depending on how they're constructed.

As they rotate through the stations, I’ll provide them with geometry tools like rulers, protractors, and compasses. These tools will help them measure angles, calculate areas, and practice drawing shapes with precision. The goal here is to reinforce their understanding of the mathematical properties of each shape, which will help them in the design phase later on.

I’ll encourage them to think critically about what they observe by asking guiding questions at each station:

‘How do different shapes compare in terms of stability and strength?’ This question will push them to consider why triangles are often used in structures for support, while other shapes may serve more decorative or spatial functions.
‘Which shapes are easiest to construct, and why?’ Here, students will reflect on the challenges they faced when building the shapes, which will deepen their understanding of practical constraints in architectural design.

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Explain Objective: Provide formal instruction on geometric shapes and their application in architecture.

Activity:

Interactive Lesson on Geometry in Architecture: Deliver a lesson that explains the properties of geometric shapes, such as the stability of triangles in structures or the aesthetic appeal of circles and arches. Use examples from the video shown earlier to illustrate how these shapes are applied in real-world architecture.
Class Discussion: Discuss how architects use geometry to solve design challenges and create aesthetically pleasing and structurally sound buildings.

Guiding Questions:

Why are certain shapes, like triangles, commonly used in construction?
How do geometric principles help architects create both beautiful and functional structures?

Now that the students have had a chance to explore geometric shapes hands-on, it’s time to solidify their understanding with some formal instruction. The objective here is to connect what they’ve learned so far to real-world architectural design and show them how geometry plays a crucial role in creating structures that are both functional and visually appealing.

We’ll start with an interactive lesson on geometry in architecture. I’ll explain the properties of geometric shapes, focusing on why certain shapes, like triangles, are so important in construction. For example, triangles are one of the most stable shapes because their sides reinforce one another, which is why they are used in trusses and bridges. I’ll also talk about how circles and arches are used in architecture not just for aesthetic reasons but because they can distribute weight evenly, which is why we see them in domes and arches in buildings.

To make this more engaging, I’ll refer back to the video examples we watched during the 'Engage' phase. I’ll ask students to think about where they saw triangles or arches in those famous structures, like in the Eiffel Tower’s triangle-based support system or the Sydney Opera House’s curved shapes. This will help students connect theory to practice and see that geometry isn’t just about drawing shapes—it’s about solving real-world problems.

After the lesson, we’ll move into a class discussion to explore how architects use geometry to address design challenges. I’ll pose the following guiding questions to prompt critical thinking:

‘Why are certain shapes, like triangles, commonly used in construction?’ This will encourage students to think about stability and strength in building designs.
‘How do geometric principles help architects create both beautiful and functional structures?’ This will push them to think about the balance between form and function in architecture, and how mathematics can lead to visually pleasing designs that are also practical and safe.

Now would be a good time for a formative assessment on the geometry shapes and their properties.

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Elaborate Objective: Allow students to apply their knowledge of geometry to a creative and practical task.

Activity:

Architectural Model Project: Divide students into small groups and challenge them to design and build a model of a structure using geometric shapes. Provide materials such as cardboard, paper, glue, and sticks. Encourage students to incorporate different shapes in their design and consider how the shapes contribute to the structure's stability and appearance.
Blueprint and Calculation: Have each group create a blueprint of their structure, labeling the shapes used and calculating the area and volume of different sections.

Guiding Questions:

How did you decide which shapes to use in your design?
What challenges did you encounter when building your model, and how did you overcome them?

In the Elaborate phase, students will get to apply the geometry concepts they've learned by diving into a creative, hands-on task—the Architectural Model Project. The objective here is for them to use their understanding of geometric shapes to design and build a structure that’s both stable and visually appealing.

I’ll divide the class into small groups, so they can collaborate on their designs. Each group will be challenged to create a model of a structure using various geometric shapes. I’ll provide materials such as cardboard, paper, glue, and sticks for them to work with, and they’ll be encouraged to use triangles, rectangles, circles, arches, and other shapes in their designs. I’ll emphasize that they need to think about how these shapes contribute to both the stability of their structure and its appearance—just like architects do in the real world.

To add a layer of complexity and make the project more practical, each group will also be responsible for creating a blueprint of their structure. This blueprint should label the geometric shapes they used, and they’ll need to calculate the area and volume of different sections of their model. This reinforces their math skills and ensures they’re not just building based on intuition but also applying the principles we’ve discussed.

I’ll circulate among the groups as they work, asking guiding questions to stimulate critical thinking and problem-solving:

‘How did you decide which shapes to use in your design?’ This will help them reflect on the choices they made in terms of stability and aesthetic appeal.
‘What challenges did you encounter when building your model, and how did you overcome them?’ This question encourages them to think about how they solved design problems, whether it was figuring out how to balance certain parts of the structure or adjusting the dimensions to make the model work.

It’s important to remind students that architects face similar challenges in real life, and solving these problems is part of the design process. I’ll encourage collaboration within the groups, as teamwork is a key aspect of successful architectural projects.

By the end of this activity, students will have a completed model that showcases their understanding of geometric shapes and their applications in architecture, as well as a blueprint that demonstrates their ability to calculate and plan based on geometry principles.

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Evaluate Objective: Assess students' understanding and application of geometric concepts in architecture.

Activity:

Group Presentations: Each group presents their architectural model to the class, explaining the geometric principles behind their design and how they ensured the structure’s stability.
Peer Review: Have students provide constructive feedback on each other’s models, focusing on the use of geometric shapes and the accuracy of their calculations.
Reflection Worksheet: Give students a worksheet where they reflect on what they learned about geometry and how it applies to architecture. Include questions that prompt them to consider the connection between the shapes they used and the overall design and stability of their model.

Assessment Criteria:

Accuracy in identifying and applying geometric shapes.
Creativity and practicality of the architectural model.
Quality of explanations during the presentation and reflections in the worksheet.

In the Evaluate phase, we will assess the students' understanding of the geometric concepts they've learned and how well they applied them in their architectural models. This part of the lesson allows students to demonstrate their learning and receive feedback, both from me and from their peers.

We'll begin with group presentations. Each group will present their architectural model to the class, explaining the geometric principles behind their design. They should highlight key features like:
Which geometric shapes they used.
How those shapes contributed to the stability of the structure.
Any challenges they faced while building and how they overcame them.�I will be looking for how well they can articulate the connection between geometry and architecture during these presentations.

After each presentation, we’ll engage in peer review. The class will provide constructive feedback on the models, focusing on the use of geometric shapes and whether the calculations for area and volume seem accurate. This peer review will help students develop critical thinking skills and encourage them to consider different design approaches.

Next, I’ll hand out a reflection worksheet to each student. The worksheet will include questions such as:
What did you learn about the importance of geometric shapes in building design?
How did the shapes you used contribute to your model’s design and stability?
What would you do differently if you had to redesign your structure? This reflection gives students a chance to process what they’ve learned and think critically about their own project.

Finally, I’ll assess their performance based on three key assessment criteria:

Accuracy in identifying and applying geometric shapes—Did they use the correct shapes, and did they understand why they used them?

Creativity and practicality of the model—Was the design original but also feasible from a structural standpoint?

Quality of their explanations—Were they able to clearly explain their design choices during the presentation and provide thoughtful responses on their reflection worksheet?

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5 E’s Lesson Timeframe

Engage (15-20 minutes)

Objective: Capture students' interest and assess prior knowledge.

Explore (30-40 minutes)

Objective: Allow students to investigate geometric shapes and their properties through hands-on activities.

Explain (25-30 minutes)

Objective: Provide formal instruction on geometric shapes and their application in architecture.

Elaborate (60-75 minutes)

Objective: Apply knowledge of geometry to a creative and practical task.

Evaluate (15-20 minutes)

Objective: Assess students' understanding and allow them to reflect on their work.

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Differentiation

Guided Practice
Modified Instructions
Visual Aids
Peer Support
Focused Reflection

Remediation

Extension/Enrichment

Advanced Projects
Research Component
Mathematical Calculations
Creative Design Challenges
Technology Integration

Remediation

Guided Practice:

Provide additional one-on-one or small group instruction on geometric concepts and their applications in architecture.
Use simplified examples and models to help students grasp basic concepts before moving on to more complex tasks.

Modified Instructions:

Offer step-by-step instructions and templates for the architectural model project to help students who need more structure.
Provide pre-cut geometric shapes and simplified materials for students who may struggle with crafting their own shapes from scratch.

Visual Aids:

Use visual aids such as diagrams, charts, and physical models to reinforce understanding of geometric shapes and their properties.
Display visual examples of architectural structures that use basic shapes to support comprehension.

Peer Support:

Pair students with stronger understanding with those who need more help during group work to facilitate peer learning.
Implement structured peer review sessions where students receive guided feedback from classmates.

Focused Reflection:

Provide a more structured reflection worksheet with guiding questions and prompts to help students articulate their understanding more clearly.
Offer additional time and support for students to complete their reflections.

Extension/Enrichment

Advanced Projects:

Challenge students to design and build more complex structures using a wider variety of geometric shapes and materials.
Encourage students to incorporate advanced geometric concepts, such as symmetry and fractals, into their models.

Research Component:

Assign a research task where students investigate the use of geometry in famous architectural landmarks or innovative modern designs.
Have students present their findings to the class, incorporating visual aids and additional geometric analysis.

Mathematical Calculations:

Introduce more advanced calculations, such as surface area and volume of complex shapes, and have students apply these calculations to their models.
Provide enrichment worksheets that involve solving real-world architectural problems using geometry.

Creative Design Challenges:

Create a challenge where students must redesign a famous building or structure with an emphasis on optimizing its geometric properties for improved stability or aesthetics.
Include criteria for judging creativity, functionality, and application of geometric principles.

Technology Integration:

Encourage students to use architectural design software or apps to create digital models of their structures, allowing them to explore geometric design in a digital environment.
Offer opportunities for students to collaborate on a virtual architecture project, incorporating feedback and revisions based on peer and teacher reviews.