Mathematical Art: Teaching Students to Create Art Using Math Principals

Mathematical art is a fascinating intersection of two seemingly disparate fields. At first glance, math and art may appear to have little in common, but in reality, they share many underlying principles. Mathematical art uses mathematical concepts to create aesthetically pleasing and thought-provoking pieces.

Mathematical art can take many forms, from intricate geometric designs to fractal patterns. It provides a unique opportunity to explore the beauty and complexity of mathematical concepts in a visually engaging way. Mathematical art has practical applications, such as architecture, where geometric patterns create visually stunning structures.

Mathematical art is a valuable tool for both mathematicians and artists. It allows for the exploration of complex mathematical concepts in a creative and accessible way while also providing a new form of artistic expression.

Lesson Plan Title: Mathematical Art

Grade Level: Middle School (but could be adapted for all grade levels)

Duration: 2-3 Class Periods (50 minutes each)

Objective: Students will learn about mathematical principles and create their own artwork using these principles.

Materials:

• Rulers
• Compasses
• Protractors
• Graph paper
• Colored pencils or markers
• Examples of mathematical art found through a Google search or Pixabay.com
• Chromebooks for research

Introduction (10 minutes):

1. Introduce the lesson by showing students examples of mathematical art.
2. Discuss the mathematical principles used in each piece of art.
3. Explain to students that they will learn about these principles and use them to create their artwork.

Instruction (30 minutes):

1. Review the principles of geometry and symmetry.
2. Demonstrate how to create basic shapes using a ruler and compass.
3. Show how to create symmetry by folding a shape in half and drawing lines to create identical sections.
4. Discuss the concept of tessellation. (Patterns made up of repeated shapes that fit together without gaps or overlaps. They can be created using various mathematical techniques, such as symmetry groups and transformational geometry.) and show examples.
5. Demonstrate how to create a tessellation using a basic shape or a piece of art found at Pixabay.com by typing tessellations in the search bar at Pixabay.com.

Modeling Activity (50 minutes):

1. Display a simple tessellation for all students to see.
2. Model how to create the tessellation by stacking diamonds.
3. Teach students how to shade the diamonds to add dimension.
4. For example, something simple like this: ​
5. Make sure students can recreate the simple artwork before going on to the next research step—self-imagination and creation.

Day Two-Independent Activity (40 minutes): 

1. Provide students with graph paper, rulers, compasses, and protractors.
2. Instruct students to create a piece of mathematical art using the principles taught the day before.
3. Encourage students to visit Pixabay.com to find an example of what they would like to create.
4. Encourage students to experiment with color and shading to enhance their artwork to make it their own.
5. Circulate the room and assist students as needed.

Closure (10 minutes):

1. Ask students to share their artwork with the class.
2. Discuss the mathematical principles used in each piece of art.
3. Reflect on the experience of creating mathematical art and how math can be used creatively.

Extend:

1. Have students write a short paragraph explaining the mathematical principles used in the artwork and why they find it interesting.

Assessment:

1. Students will be assessed based on their ability to use mathematical principles to create a piece of artwork.
2. The artwork will be assessed for creativity, use of color and shading, and incorporation of mathematical principles.
3. The written paragraph will be assessed for accuracy and depth of understanding of the mathematical principles used in the chosen artwork.

Additional Potential Assignments:

1. Students can create a larger, more complex piece of mathematical art.
2. They can explore other mathematical principles, such as fractals or spirals, and incorporate them into their artwork.
3. Students can work in groups to create a collaborative piece of mathematical art.
4. Students can create additional mathematical art as a homework assignment or take home project.

Differentiation:

1. Students can work in pairs or small groups to support each other in creating their artwork.
2. Students who struggle with math can be provided with templates or simplified instructions to follow.
3. Advanced students can be challenged to incorporate multiple mathematical principles into their artwork or create a more complex piece.

Safety Considerations:

1. Ensure that students handle the rulers, compasses, and protractors with care to avoid injury.
2. Provide clear instructions for the use of the materials to prevent accidents or misuse of items.

Written by Deborah Andrus
Education World Contributor
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