Transformative Geometry: Creating Community Mandalas

9th Grade

Project
4 weeks

Transformative Geometry: Creating Community Mandalas

Lee Wenzel

Purpose

The project aims to engage students in exploring the intersection of mathematics and art through the creation of mandalas using geometrical transformations. By collaborating with local tattoo artists, students will gain insights into real-world applications of geometry, fostering a deeper understanding and appreciation of mathematical concepts. The project encourages students to personalize their artwork by integrating their interests, ultimately connecting mathematical learning to community themes and events.

Learning goals

The learning goals for this project include developing a deep understanding of geometric transformations such as rotation, reflection, and dilation, and applying these concepts creatively to design mandala art. Students will enhance their skills in using mathematical tools like protractors, compasses, and rulers to construct precise geometric shapes. They will also cultivate the ability to connect mathematical concepts with personal interests and community themes, fostering a sense of relevance and engagement. Through reflective journaling and peer critique, students will improve their ability to articulate their learning process and incorporate feedback into their work.

Standards

Common Core - CCSS.MATH.CONTENT.HSG.CO.A.5: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using graph paper, tracing paper, or geometry software.
Common Core - CCSS.MATH.CONTENT.HSG.CO.B.6: Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure.
Common Core - CCSS.MATH.CONTENT.HSG.CO.A.2: Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs.

Products

Throughout this project, students will create a series of mandala sketches, progressively incorporating more complex geometrical transformations. By the end, each student will produce a final mandala artwork that integrates their personal interests and community themes, accompanied by a video explanation of their creative process and mathematical concepts used. These projects will be displayed in a community art exhibition and featured in an interactive 'Geometry in Motion' art walk, offering an opportunity for public engagement and feedback.

Launch

Begin with a dynamic 'Geometric Scavenger Hunt' around the school or local community, where students work in teams to identify and photograph examples of geometric transformations in everyday objects. This activity will spark curiosity and provide real-world context, setting the stage for their creative exploration in designing mandalas. Encourage students to share their findings and discuss how these transformations can be translated into artistic expressions, linking their observations to personal interests and community themes.

Exhibition

Organize a vibrant 'Geometry in Motion' art walk in a local park where students exhibit their mandala creations along a designated path. Each display includes QR codes that link to student-made videos explaining the mathematical transformations and personal themes within their art. Invite community members, including local tattoo artists, to engage with students and provide feedback, fostering a dialogue between mathematics, art, and community culture.

Week 1	Day 1	Day 2	Day 3	Day 4
Activities	Launch the project with a 'Geometric Scavenger Hunt' around the school or local community. Students work in small groups to identify and photograph examples of geometric transformations in everyday objects, such as reflections in windows, rotations in door handles, and dilations in shadows.	Introduce geometric transformations through a hands-on workshop using manipulatives and geometry software. Students practice identifying and creating basic transformations (rotation, reflection, and dilation) on graph paper and digital platforms.	Facilitate a brainstorming session where students discuss how they might incorporate personal interests and community themes into their mandala designs. Encourage them to sketch initial ideas and note down connections between their interests and geometric shapes.	Begin individual portfolio creation: students start a digital or physical portfolio to document their learning journey, which will include photos from the scavenger hunt, sketches, and reflections.
Deliverables	1. A collection of photographs from the Geometric Scavenger Hunt, annotated with identified transformations. 2. Initial mandala sketches that incorporate at least one geometric transformation. 3. A digital or physical portfolio containing the week's work, including scavenger hunt findings and preliminary mandala sketches.
Preparation	1. Prepare a list of potential scavenger hunt locations and examples of geometric transformations for each location. 2. Gather materials for the hands-on workshop, including graph paper, protractors, compasses, rulers, and access to geometry software. 3. Set up a digital platform or provide materials for students to create their portfolios, ensuring all students have access to necessary technology. 4. Coordinate with local community members or tattoo artists to introduce the project to students and provide insights into the real-world application of geometric art.

Week 2	Day 1	Day 2	Day 3	Day 4
Activities	Conduct a workshop on advanced geometric transformations, focusing on the integration of multiple transformations to create complex designs. Use examples from mandala art to demonstrate how rotation, reflection, and dilation can interact.	Facilitate a collaborative session where students explore different cultural mandala designs and identify the geometric transformations used. Encourage them to discuss these designs in relation to their personal themes.	Guide students in creating a detailed draft of their mandala design, incorporating at least two transformations. Have students use mathematical tools like protractors, compasses, and rulers to ensure precision.	Organize peer review sessions where students present their draft mandalas to small groups, receive feedback, and discuss potential improvements and how they plan to incorporate suggestions.
Deliverables	1. A detailed draft of the student's mandala design, showcasing the use of at least two geometric transformations. 2. Peer review feedback forms filled out by students, documenting the suggestions and reflections from their group discussions.
Preparation	1. Prepare a presentation on advanced geometric transformations and their application in mandala art, including examples from various cultures. 2. Gather resources and examples of cultural mandala designs for students to analyze during the collaborative session. 3. Ensure availability of mathematical tools such as protractors, compasses, rulers, and graph paper for the design drafting activity. 4. Set up a structured format for peer review sessions, including guidelines and feedback forms.

Week 3	Day 1	Day 2	Day 3	Day 4
Activities	Organize a studio visit or virtual meeting with local tattoo artists specializing in mandalas and sacred geometry. Students will engage in a Q&A session to learn about professional techniques and applications of geometric transformations in art.	Facilitate a workshop where students experiment with digital tools to enhance their mandala designs. Introduce software that allows for precise application of transformations and layering of complex patterns.	Guide students through refining their mandala drafts based on feedback received in peer review sessions and insights gained from the tattoo artists. Encourage the incorporation of personal themes more deeply into their designs.	Conduct a reflective journaling session where students document their learning progress, challenges faced, and how they are integrating community themes into their artwork.
Deliverables	1. Refined mandala designs incorporating feedback and professional insights, with at least three geometric transformations clearly applied. 2. A digital or enhanced version of their mandala design using graphic software. 3. Reflective journal entries summarizing learning experiences and connections to personal interests and community themes.
Preparation	1. Coordinate with local tattoo artists to arrange a studio visit or virtual meeting, ensuring alignment with the project's learning goals. 2. Provide access to digital design software or tools and prepare a tutorial session on how to use these tools for mandala creation. 3. Review student feedback from Week 2 to tailor support and resources needed for refining mandala designs. 4. Prepare prompts and guidelines for the reflective journaling session to encourage thoughtful and meaningful student reflections.

Week 4	Day 1	Day 2	Day 3	Day 4	Day 5
Activities	Organize a final peer review session where students present their near-complete mandala designs. Peers will provide constructive feedback focusing on the integration of geometric transformations and personal themes.	Facilitate a session for students to finalize their mandala designs, incorporating final adjustments based on peer feedback and ensuring all transformations and themes are clearly represented.	Guide students in preparing video explanations of their creative process, highlighting the mathematical transformations used and their connection to personal and community themes. Assist students in uploading these videos to a platform accessible via QR codes.	Host a reflective journaling session where students write about their overall learning journey, the challenges they overcame, and the skills they developed throughout the project.	Prepare for and conduct the 'Geometry in Motion' art walk exhibition in a local park. Students will set up their mandala displays and engage with community members, explaining their designs and the mathematical concepts applied.
Deliverables	1. Final mandala artwork, demonstrating the integration of geometric transformations and personal/community themes. 2. Video explanation of the mandala art piece, linked via a QR code for the exhibition. 3. Final reflective journal entry summarizing the student's learning journey and the application of geometric transformations.
Preparation	1. Prepare guidelines and a rubric for the final peer review session to ensure focused and constructive feedback. 2. Ensure access to technology and platforms for students to create and upload their video explanations. 3. Coordinate logistics and permissions for the 'Geometry in Motion' art walk, including setup arrangements with the local park and community invitations. 4. Prepare exhibition materials, such as display boards and QR code labels, and ensure all students have the necessary resources to present their work effectively. 5. Plan and set up a system for collecting community feedback during the art walk, which students can reflect upon in their journals.