Making Art With Math: MathArt Stickers

I teach computer science and engineering at Cincinnati Country Day School in Cincinnati, Ohio. For the first 17 years of my teaching career, I taught mathematics. I have always been intrigued by the intersection of art and math and enjoy creating projects that enable students to see the beauty in mathematics. This lesson was inspired by the graphs of trigonometric functions; while teaching these topics, I thought that it would be fun to make math wallpaper one day. I wrote the idea on a sticky note, and the note sat on my bulletin board for years until this past summer, when I finally turned it into a project that is smaller in scale: math art stickers.

Students begin by learning about artists who use math to create art. They brainstorm how they could create art, explore new math material (hopefully through the lens of an emerging math artist), then apply their learnings to create a math art sticker in 2D design software. Students can use makerspace equipment (such as a large format printer or printer-cutter machine) to create their sticker, or teachers can print the stickers for students.

The materials posted with this project are geared towards an Algebra II class or a pre-calculus class. However, teachers can easily adapt the activities to be relevant to the material in their class. This project can also be adapted to topics in geometry (shapes, tessellations, etc.).

This project is easily enhanced by collaborating with the art department at your school. One of the steps asks students to communicate and reflect on their learning by writing an artist statement that describes their work. Teachers could ask an art teacher to explain the purpose and provide examples of student-written artist statements, to assist students with writing artist statements, or to provide feedback on students' written work.

• Graphing software, such as Desmos (free), GeoGebra (free), or Mathematica (requires license).
• 2D design software, such as Cuttle (free, easy to use) or Inkscape (free, steeper learning curve).
• Color printer (inkjet or laser).
• Printable sticker paper, such as Avery 6465 removable label paper sheets.
• Optional: paper/vinyl cutter (such as Cricut), large-format printer, or printer-cutter machine.

Many students do not realize that there are people who use mathematics to create art. To begin this project, students will explore a variety of math artists and share what they notice and wonder about the works of art.

Provide several resources (online and/or print) for students to explore a variety of math art, such as:

Where Art Meets Math | Smithsonian Institution (si.edu)

For these artists, math is their muse (snexplores.org)

"Math Art: Truth, Beauty, and Equations" by Stephen Ornes (print book)

www.DominoArtwork.com

How Diarra Bousso Turned Her Love of Math Into a Formula-Driven Fashion Brand - Fashionista

Muslim rule and compass: the magic of Islamic geometric design | Alex Bellos | The Guardian

Why the history of maths is also the history of art | Mathematics | The Guardian

Math Is Beautiful (sciencefriday.com)

Creating The Never-Ending Bloom - Science Friday

Give students 10-15 minutes to explore the resources on their own or in small groups.

For an additional 10-15 minutes, ask students to share their observations with the class. Write "What Did You Notice? What Do You Wonder?" on the board and record their observations. Discuss their observations.

Ask students to brainstorm and share how they could use math to create art.

In this step, students will explore the mathematics concepts that they will be using to create math art. Teachers can easily modify this step to meet the content needs of their classroom. Two examples are provided below.

Example 1: Transformations of Functions in Algebra II

The attached file could be used in an Algebra II class to explore transformations of functions.

Teachers can alter this activity to include any functions, including polynomial, radical, rational, absolute value, exponential/logarithmic, or trigonometric.

Example 2: Polar Equations in Pre-Calculus

I created this exploration (published on the Tech-Based Teaching Blog in 2019) for use in Mathematica software. Students explore the behavior of basic polar equations, then look at patterns that are not typically included in textbooks. Teachers can alter this exploration for use in Desmos or GeoGebra.

At the end of any exploration, recap the patterns or learnings with the class to ensure student understanding.

To ensure students understand the material, ask them to practice applying what they learned. The attached file provides suggestions for the Algebra II example.

In this step, students demonstrate what they have learned -- and become math artists -- by creating their own math art sticker! Using Desmos, GeoGebra, or Mathematica, students will:

• create functions that have transformations (or apply the math concepts learned).
• graph the functions.
• use their graphs to create an artistic 2D design in 2D design software such as Cuttle (free, easy to use) or Inkscape (free, steeper learning curve).
• submit the design to you for printing as a sticker.

To publicly describe their work, students create an artist statement. This is a great opportunity to collaborate with your school's art department -- ask an art teacher to explain the purpose of an artist statement and provide examples.

An optional step is to ask students to complete reflection questions about the activity.

The first attached document explains the student process to create a sticker using Desmos and Cuttle.

The second attached document contains a suggested student reflection.

The BLUE sticker above was created in Inkscape. It contains several copies of a polar equation, some with a white outline and some filled with magenta color. The gold squiggle is a graph of the rectangular form of the polar equation.

The WHITE sticker above was also created in Inkscape. It contains various transformations of the square root function, tiled across the page.

To print student work, ask students to send you their PNG design files. Print each student’s design in color. Options for printing:

•  If you don’t have a machine that makes print-and-cut stickers: Arrange multiple designs in one document (i.e. Word or Google Docs). Print on removable label paper (such as Avery 6465) and cut out each student’s design by hand.
• If you have a machine that prints and cut stickers: use the process for your machine to create stickers for each student.
• Prefer wall art instead of stickers? Print larger wall hangings for each student on letter or large-format paper.

If possible, display student work in a classroom, hallway, or other public space. Optional activities:

• Ask students to stroll around the “art gallery” and view the work of their peers.
• Ask students to describe the transformations of parent functions in another student’s work.

Want to give an additional challenge to your students? Give them the option to design wallpaper tiles. With wallpaper tiles, the designs on each edge of one “tile” should meet the designs on edges of the adjacent tiles. This is more challenging than it seems! The WHITE sticker example will tile like wallpaper, but the BLUE sticker will not tile like wallpaper.

Suggested checklist for assessing student work:

•  At least three function transformation graphs are included in the wall hanging. (Teacher: Adjust this number as desired.)
• The artist statement looks professional, contains proper grammar, spelling, and capitalization and includes the required information. Mathematical explanations are written in a way that others can understand.
• Answers to reflection questions are thorough and complete.