Created byMaya Tobias

18 views0 downloads

Tessellation Art: Geometry in Patterns

Grade 10Math2 days

In this project, 10th-grade students explore the concept of tessellations by integrating mathematical principles, cultural influences, and symmetry into their designs. They begin with immersive entry events, participate in workshops to understand geometric shapes and symmetry, and research cultural uses of tessellations. Students then design their own tessellation patterns, incorporating mathematical accuracy and aesthetic appeal, to cover complex surfaces. The project culminates in a portfolio and presentations showcasing their creative and analytical skills.

TessellationsSymmetryGeometryCultural PerspectivesDesign InnovationMathematical PrinciplesReal-World Applications

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 and create a tessellation that effectively covers complex surfaces while incorporating mathematical principles, symmetry, and cultural perspectives?

Essential Questions

Supporting questions that break down major concepts.

What is a tessellation, and how can it be identified in both natural and human-made environments?
How do mathematical principles apply in creating a tessellation?
What geometric shapes can be used to create tessellations, and what are their properties?
How does the concept of symmetry influence the design and function of tessellations?
In what ways can tessellations be applied in the real world, both aesthetically and practically?
How do different cultural perspectives and historical contexts influence the art and application of tessellations?

Standards & Learning Goals

Learning Goals

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

Understand and explain the concept of tessellations and identify examples in natural and human-made environments.
Apply mathematical principles to design and create a tessellation that covers a complex surface.
Explore the properties of geometric shapes used in tessellations and their mathematical relationships.
Analyze the role of symmetry and proportionality in the design of tessellations.
Investigate the cultural significance and historical context of tessellations in various cultures.
Apply geometric concepts to create a tessellation model for a practical or aesthetic real-world application.

Common Core State Standards for Mathematics

G-GMD.1

Primary

Explain volume formulas and use them to solve problems.Reason: Understanding how geometric shapes and their measurements relate to tessellations, especially in covering complex surfaces, is directly aligned with explaining and utilizing volume formulas.

G-GMD.5

Primary

Apply geometric concepts in modeling situations.Reason: Tessellations as a modeling situation require the application of geometric concepts to solve aesthetic and practical covering problems, aligning directly with this standard.

Entry Events

Events that will be used to introduce the project to students

Mosaic of the Mystics

Students walk into a classroom transformed into a dazzling room filled with intricate tessellation patterns from various cultures. The history and cultural relevance of tessellations in art from different cultures, such as Islamic, Chinese, and M.C. Escher's works, spark curiosity about how these patterns are applied to complex surfaces.

Tessellation Treasure Hunt

The school grounds become a treasure map, where students seek naturally occurring tessellations in nature and architecture. This real-world adventure connects the geometric principles to their environment, prompting them to question the tessellations' purpose and functionality in the world around them.

📚

Portfolio Activities

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

Activity 1

Symmetry & Shapes Workshop

Students will dive into the mathematics of tessellations by exploring the geometric shapes that make up these patterns and understanding the role of symmetry.

Steps

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

1. Participate in hands-on sessions to explore different geometric shapes that form tessellations. Use manipulatives like pattern blocks to create simple tessellations first.

2. Analyze the role of symmetry in tessellations through guided activities that demonstrate reflection, rotation, and translation.

3. Document your findings and reflections on how each type of symmetry applies to tessellations in a portfolio entry.

Final Product

What students will submit as the final product of the activityA detailed portfolio entry documenting various geometric shapes, types of symmetry, and their application in tessellations.

Alignment

How this activity aligns with the learning objectives & standardsCovers G-GMD.1 by explaining the properties and measurements of geometric shapes involved in tessellations.

Activity 2

Culture & Tessellations Seminar

This activity focuses on the cultural and historical significance of tessellations, linking mathematical understanding with artistic expressions from different cultures.

Steps

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

1. Research different cultural uses of tessellations, focusing on three distinct cultures such as Islamic, Chinese, and Western (e.g., M.C. Escher).

2. Create a presentation that showcases the unique attributes and historical relevance of tessellations in these cultures.

3. Present your findings to the class, emphasizing the interplay between art, culture, and mathematics.

Final Product

What students will submit as the final product of the activityA multimedia presentation on the cultural and historical significance of tessellations, highlighting artistic expressions and mathematical principles.

Alignment

How this activity aligns with the learning objectives & standardsSupports understanding of G-GMD.5 by modeling the intersection of geometric concepts and cultural perspectives.

Activity 3

Design Your Tessellation

Students will apply their comprehensive understanding of tessellations to design their unique patterns that can cover complex surfaces, utilizing mathematical principles and creativity.

Steps

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

1. Sketch initial designs for tessellation patterns using geometric software or drawing tools.

2. Refine designs to ensure mathematical accuracy and aesthetic appeal, incorporating feedback from peers and educators.

3. Create a final model of the tessellation that effectively covers a designated complex surface.

Final Product

What students will submit as the final product of the activityA completed tessellation model that accurately and creatively covers a complex surface, ready for exhibition.

Alignment

How this activity aligns with the learning objectives & standardsThis activity integrates G-GMD.1 and G-GMD.5 by leveraging volume understanding and applying geometric concepts in a practical design scenario.

Activity 4

Tessellation Explorer

Students will embark on a journey to understand and identify tessellations in both human-made and natural environments. This activity builds foundational knowledge on what tessellations are and how they appear globally.

Steps

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

1. Explore provided resources on tessellations, including videos and articles explaining their features and importance.

2. Create a visual journal with sketched examples of tessellations found in the classroom exhibits and on a nature walk around the school.

3. Discuss findings in small groups, focusing on different types of tessellations observed and their characteristics.

Final Product

What students will submit as the final product of the activityA visual journal containing sketches and descriptions of various tessellations from the classroom exhibit and natural environment.

Alignment

How this activity aligns with the learning objectives & standardsAligns with G-GMD.5, as students apply geometric concepts to identify tessellations in different modeling situations.

🏆

Rubric & Reflection

Portfolio Rubric

Grading criteria for assessing the overall project portfolio

Tessellation Mastery Rubric

Category 1

Mathematical Understanding

Evaluates the depth of geometric knowledge and the ability to apply mathematical principles to create accurate tessellations.

Criterion 1

Geometric Concepts

Assesses understanding and application of geometric shapes and their properties in tessellations.

Exemplary

4 Points

Shows profound understanding of geometric concepts and applies shapes with complete accuracy in tessellations.

Proficient

3 Points

Demonstrates solid understanding of geometric concepts and applies shapes accurately in tessellations.

Developing

2 Points

Exhibits basic understanding of geometric concepts with some accuracy in shape application.

Beginning

1 Points

Shows minimal understanding and struggles with accurate shape application.

Criterion 2

Symmetry Application

Assesses the ability to utilize symmetry principles in tessellation designs.

Advanced

5 Points

Demonstrates exceptional mastery and innovation beyond standard expectations

Exemplary

4 Points

Skillfully incorporates all types of symmetry (reflection, rotation, translation) into tessellation designs.

Proficient

3 Points

Effectively incorporates most types of symmetry into tessellation designs.

Developing

2 Points

Incorporates some symmetry types, but with inconsistent application.

Beginning

1 Points

Struggles to incorporate symmetry into designs.

Category 2

Cultural and Historical Connections

Assesses the ability to connect cultural and historical contexts to tessellations.

Criterion 1

Cultural Analysis

Evaluates understanding of cultural influences on tessellation patterns.

Exemplary

4 Points

Presents deep analysis of how different cultures influence tessellation patterns with insightful examples.

Proficient

3 Points

Provides a clear analysis of cultural influences, supported by relevant examples.

Developing

2 Points

Describes some cultural influences but lacks depth and example support.

Beginning

1 Points

Provides minimal analysis of cultural influences, with little or no examples.

Criterion 2

Historical Context

Assesses the integration of historical context in understanding tessellations.

Exemplary

4 Points

Integrates comprehensive historical context showing how tessellations evolved in different periods.

Proficient

3 Points

Clearly connects historical context to tessellations with appropriate details.

Developing

2 Points

Attempts to connect tessellations to historical contexts with some relevant details.

Beginning

1 Points

Makes little connection between tessellations and historical contexts.

Category 3

Creative and Practical Application

Evaluates the creativity and practicality of student-designed tessellations.

Criterion 1

Design Innovation

Assesses creativity in the design of tessellations and their aesthetic quality.

Exemplary

4 Points

Exhibits outstanding creativity with engaging and unique tessellation designs.

Proficient

3 Points

Displays creative and attractive tessellation designs.

Developing

2 Points

Shows basic creativity with straightforward tessellation designs.

Beginning

1 Points

Produces conventional and uninspired tessellation designs.

Criterion 2

Functionality and Coverage

Evaluates the practical application of tessellations to complex surfaces.

Exemplary

4 Points

Designs tessellations that excellently cover complex surfaces, balancing both aesthetics and function.

Proficient

3 Points

Designs tessellations that adequately cover complex surfaces with some aesthetic elements.

Developing

2 Points

Attempts to cover surfaces with tessellations but with limited success in aesthetics or function.

Beginning

1 Points

Designs fail to effectively cover surfaces, missing functional or aesthetic considerations.

Reflection Prompts

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

Question 1

Reflect on your experience in the 'Symmetry & Shapes Workshop'. How did the exploration of geometric shapes and the role of symmetry deepen your understanding of tessellations? Please provide specific examples from your activities.

Text

Required

Question 2

On a scale from 1 to 5, how would you rate your understanding of cultural influences on tessellations after participating in the 'Culture & Tessellations Seminar'?

Scale

Required

Question 3

What challenges did you face while designing your tessellation, and how did you overcome them?

Text

Required

Question 4

In your opinion, which type of symmetry (reflection, rotation, or translation) played the most significant role in your tessellation design, and why?

Multiple choice

Required

Options

Reflection

Rotation

Translation

Question 5

Reflect on the 'Tessellation Explorer' activity. How has identifying tessellations in various environments changed your perspective on their real-world applications?

Text

Required