Tessellation Nation: Art in Perfect Pattern!

Design for Mastery Kit

NEW

All grades Project 2 weeks

Tessellation Nation: Art in Perfect Pattern!

Shelley N

M100 Quantitative Reasoning - 100.b

M152 Reasoning and Proof through Congruence - 152.d

M152 Reasoning and Proof through Congruence - 152.e

M152 Reasoning and Proof through Congruence - 152.f

Self Directed Learning

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Purpose

This project invites students to explore the intersection of mathematics and art through the creation of a kaleidoscope-inspired collaborative tessellation. Students from diverse grade levels will engage in hands-on activities, applying mathematical principles of congruence and rigid motions to design cohesive tessellated patterns. The project emphasizes self-directed learning, academic mindset, and critical thinking, encouraging students to reflect on their identities and contributions to a community art piece. Through this creative process, students will deepen their understanding of mathematical concepts while cultivating a sense of belonging and shared achievement.

Learning goals

Students will develop quantitative reasoning skills by applying mathematical concepts to design tessellating art pieces, ensuring consistency and cohesion through congruence and rigid motions. They will enhance their understanding of triangle congruence criteria (ASA, SAS, SSS) to create seamless tessellations. Additionally, students will engage in self-directed learning by reflecting on their processes and using feedback to refine their designs, fostering a sense of identity and belonging through collaborative art creation. Critical thinking and problem-solving will be emphasized as students explore innovative approaches to address real-world questions about math and art integration within their community project. Incorporating kaleidoscope elements, students will also investigate the symmetry and geometric patterns found in kaleidoscopes, enriching their exploration of tessellations and congruence.

Standards

M100 Quantitative Reasoning - 100.b - Reason with units in problems, formulas, and data displays to solve problems.
M152 Reasoning and Proof through Congruence - 152.d - Given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
M152 Reasoning and Proof through Congruence - 152.e - Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
M152 Reasoning and Proof through Congruence - 152.f - Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

Competencies

Self Directed Learning - Students use teacher and peer feedback and self-reflection to monitor and direct their own learning while building self knowledge both in and out of the classroom.
Academic Mindset - Students establish a sense of place, identity, and belonging to increase self-efficacy while engaging in critical reflection and action.
Critical Thinking & Problem Solving - Students consider a variety of innovative approaches to address and understand complex questions that are authentic and important to their communities.

Products

Throughout the project, students will collaboratively create a large-scale tessellated mural that incorporates individual tessellation designs contributed by each student. Each design will demonstrate an understanding of congruence through rigid motions, ensuring seamless integration into the overall mural. Additionally, students will document their learning journey and reflections in a digital portfolio, showcasing their process, feedback, and insights gained from the project. Incorporating kaleidoscope elements, students will explore symmetry and pattern repetition, adding depth and complexity to their designs. At the conclusion, the mural will be displayed in a communal area of the school, fostering a sense of place and identity while celebrating the collective effort and creativity of the students.

Launch

Kick off the project with Kaleidoscope Tessellation Day, where students explore tessellations through interactive kaleidoscope demonstrations and hands-on activities. Begin with a gallery walk showcasing tessellated patterns in nature, art, and kaleidoscopes, highlighting their mathematical beauty. Students will then create their own kaleidoscope-inspired tessellations using geometric shapes and colored paper, fostering an understanding of congruence and rigid motions. This launch will cultivate a sense of community and shared artistic expression, setting the stage for deeper learning and collaboration.

Exhibition

The exhibition will feature a kaleidoscope of tessellated designs created by students across all grade levels, forming a vibrant mural that highlights the beauty of math in art. Each section of the mural will demonstrate the application of congruence through rigid motions, with students presenting their work and sharing insights on the mathematical principles used. The event will include interactive stations where visitors can explore tessellation concepts and engage in hands-on activities, fostering community interaction and appreciation for the project's collaborative nature.

Plan

Week 1	Day 1	Day 2	Day 3	Day 4
Activities	Kaleidoscope Exploration - Begin with a gallery walk showcasing tessellated patterns in nature, art, and kaleidoscopes, introducing students to the mathematical beauty of tessellations (15 min) Tessellation Basics - Engage students in an interactive demonstration using kaleidoscopes to explore symmetry, pattern repetition, and congruence through rigid motions (30 min)	Design Your Tessellation - Students will use geometric shapes and colored paper to create their own small-scale kaleidoscope-inspired tessellations, focusing on understanding congruence and rigid motions (45 min)	Peer Feedback Session - Students present their tessellation designs to peers for feedback, fostering self-directed learning and critical reflection (20 min) Design Revision - Using peer feedback, students refine their tessellations to ensure cohesion and congruence, enhancing their critical thinking and problem-solving skills (25 min)	Community Connection - Discuss how tessellations can build a sense of community through collaborative art, connecting the project to the essential question (15 min) Collaborative Mural Planning - Begin planning the layout for the large-scale mural, discussing how individual designs will integrate into the collective project, emphasizing academic mindset and community engagement (30 min)
Deliverables	1. Individual tessellation designs created by each student, demonstrating understanding of congruence and rigid motions. 2. Documentation in a digital portfolio of students' learning process, reflections, and feedback received from peers and teachers.
Preparation	1. Prepare a gallery of tessellated patterns in nature, art, and kaleidoscopes for the gallery walk. 2. Gather materials: geometric shape cut-outs, colored paper, scissors, and glue for hands-on activities. 3. Create demonstration tools for illustrating rigid motions and triangle congruence criteria. 4. Set up a digital platform for students to document their reflections and feedback.

Week 2	Day 5	Day 6	Day 7	Day 8
Activities	Mural Layout Execution - Students work in teams to arrange their individual tessellations according to the collaborative mural plan, focusing on congruence and cohesion across the design (25 min) Feedback and Adjustment - Conduct a peer and teacher feedback session to identify any areas of misalignment or lack of congruence, then make necessary adjustments to ensure seamless integration (20 min)	Mural Assembly - Begin attaching the tessellation pieces to the mural base, ensuring that patterns align and congruence is maintained throughout the design (30 min) Reflective Journaling - Students individually reflect on their learning journey, discussing how mathematical concepts were applied and how the experience has influenced their academic mindset (15 min)	Final Touches - Complete the mural assembly by adding final touches and ensuring all pieces are secure and congruent, preparing the artwork for display (20 min) Community Presentation Prep - Students practice presenting their mural and the mathematical principles behind it, preparing for the exhibition and community engagement (25 min)	Exhibition Setup - Arrange the mural in its exhibition space, ensuring it is prominently displayed for community viewing and appreciation (20 min) Exhibition and Reflection Workshop - Host the mural exhibition with interactive stations, facilitating a reflection workshop where students discuss the role of math in art and the impact of the project on their understanding of community (25 min)
Deliverables	1. Individual tessellation design finalized and documented in digital portfolio 2. Collaborative tessellated mural completed and prepared for exhibition 3. Reflection entries recorded in digital portfolio
Preparation	1. Ensure that large sheets of backing paper for the mural are available 2. Provide geometric tools such as protractors and rulers for checking congruence 3. Set up digital devices for students to update their digital portfolios 4. Organize the exhibition space for the mural display 5. Prepare reflection prompts and materials for the workshop