August 13

2025

Visual Patterns

An opportunity for art and math!

Xavier

goldenx@ghaps.org

​

John

goldenj@gvsu.edu

johngolden.bsky.social

mathhombre.blogspot.com

These slides:

gvsu.edu/s/3hP

Supplies:

• Paper
• Colored pencils, crayons, or markers

Nice to have:

• Colored paper
• Scissors
• Glue or tape

Online: polypad.amplify.com

Maker kit

These slides:

gvsu.edu/s/3hP

AL, Logical!

AL, Logical! Is a fantasy graphic novel coming soon from Natural Math. Al moves to a new neighborhood, a new school, and finds a very mysterious house that leads to some big problems and adventures.

These slides:

gvsu.edu/s/3hP

Passcode Required

One time Al sees this at the front door.

What would you punch in?

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gvsu.edu/s/3hP

More Information

11 is different…

What to try next?

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gvsu.edu/s/3hP

Even More

1, 1, 3, 5, 11…

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gvsu.edu/s/3hP

Patterns

Fawn Nguyen popularized Visual Patterns for math class. Not just numbers, but pictures. That adds a lot of information! Al encounters one at school…

What comes next? Can you describe it? Can you draw it?

Fawn likes to ask: how many shapes in step 43?

What do you notice? What do you wonder?

These slides:

gvsu.edu/s/3hP

How to add interest?

Art is problem-solving!

What can we do to make a visual pattern more interesting? What do we mean when we say interesting? What does an interesting piece of art look like?

Using art vocabulary (elements of art and the principles of design).

• Shape - organic, geometric… named, nameless…
• Color - temperature and value
• Contrast - Extreme differences (black and white, red and green; round shapes vs. angular shapes)
• Variety - subtler differences; (gray and a slightly lighter gray; light blue and blue)
• Movement - where are the shapes leading the eye?

​

Henri

Matisse

These slides:

gvsu.edu/s/3hP

Examples

Examples

Examples

Examples

Fold and Cut

Folding a paper in half three or four times will get you 8 or 16 copies of a shape. (Why is that?)

This depends on the size piece you want and what students can cut safely.

For more copies or different colors, trace one of your first shapes onto another folded piece of paper. Cut away from the edges and you’ll get separate pieces.

What will happen if you leave part of an edge as a part of your shape?

Here’s an example of 3 folds and 8 copies. You can trace one of your shapes on another folded sheet for even more of them.

Some Younger Examples

These slides:

gvsu.edu/s/3hP

Some Younger Examples

These slides:

gvsu.edu/s/3hP

Challenge

Have reasons & make a plan!

Mathematically Interesting

• Next step makes sense, but takes thinking!
• Newness - have you seen it before?
• What details matter?

Be mindful & make choices!

Artistically Interesting

• Next step makes sense, but takes thinking!
• Shape & color
• Contrast & movement
• Originality

These slides:

gvsu.edu/s/3hP

Work time

Share shapes…

Share sequences…

Share patterns…

• Ben Orlin

These slides:

gvsu.edu/s/3hP

More? More!

Fawn’s website: visualpatterns.org

• Analyze a pattern you like
• How can you add more math interest?

Integer sequences: oeis.org

• Look up your pattern…
• Pick a sequence, design a visual pattern for it!

Artistically develop your pattern:

• Henri Matisse
• Gustave Klimt
• Stuart Davis
• Annie Albers

These slides:

gvsu.edu/s/3hP

AL, Logical!

More about the book: bit.ly/ALLOGICAL

Sign up for notifications from Natural Math: naturalmath.com

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Math Maker Neighborhood

August 20, 2025 -Adventures with Modular Arithmetic from ‘Modultown’�Presenters: Sasha Fradkin (Main Line Classical Academy, USA), Allison Bishop (The City University of New York, USA)

August 27, 2025 - Tech Tools that Help Me Love Geometric Constructions�Presenter: Sue VanHattum (Contra Costa Community College, USA)

September 10, 2025 - Dragon Nests and Daffodils: Paper Models of Hyperbolic Surfaces�Presenter: Dr. Maria Droujkova (Natural Math Alliance, USA)

These slides:

gvsu.edu/s/3hP