Wonder Wednesday 149: Tessellations
Tesse-what?
I said the same thing when my 12 year old (7th grade) nephew began showing me a new technique he'd learned in art class. He was very excited about it, so I was even more curious to discover what it was all about.
Once I learned from him, I began to wonder why, even after graduating art school, has I never heard (or remembered?) this term? Perhaps because it is math and so I avoided it or blocked it out :D!
Whatever the reason, I am glad he taught me - because not only is this way of making patterns historically significant, it is also really fun! This is just one more reminder of how many things we can learn from children if we take the time to listen!
Tessellations are a type of mathematical repeat patterns - perhaps most familiar in the tile work and geometric designs of ancient Islamic architecture and art. A modern example is the work of Dutch Op Artist, M.C. Escher - aka the “father of modern tessellations.”
Basically, a tessellation is a repeat pattern that meets at one or more vertex. There are various types of tessellations ranging from simple - like a checkerboard pattern to mind-bendingly complex. In this Wonder Wednesday project we'll explore making tessellations somewhere in between these two!
What's the history?
It's estimated that humans have been creating tessellations since about 4000 BCE in southern Mesopotamia. The ancient Sumerians would create repeating geometric clay tile patterns as decoration on their homes and temples.
Since this time nearly every human civilization has created tessellations of some sort. Tessellations have had a strong influence on the science, math, art, and architecture worlds (and all the places they intersect) across the global since years 5 & 6 BCE and continue to allure humans with the facts and fascinations they reveal about our world. And - since 2016, World Tessellations Day has been celebrated on June 17, and is described as "a vibrant celebration of the beauty and intricacies of tessellations."
Montessori Great Lesson Extension
The word “tessellation” comes from the Latin: tessera - a small, tile-like stone. Tessera was used to make tessellata - mosaics and tilings which decorated ancient Roman buildings.
This project would make a great extension for the Montessori Great Lessons 3-5, particularly 3 and/or 5 as it incorporates human history, culture, and math. I would do the drawing geometrically first (you could even use the geometric insets to trace). This would be a repeat periodic tessellation.
Then you can experiment with more organic explorations, like I offer below in this Wonder Wednesday project. Although it isn't a standard polygon, I would call this project a regular tessellation as it only uses a repeat single shape, but I'm no mathematician so double check! There are even tessellations that incorporate fractals - so you can see how this project can grow with the students through their history and math curricula!
I recommend the geometric ones for lower elementary, (or at least the younger ages of lower elementary), and the more organic and complex for upper elementary and secondary.
Wonder Wednesday 149: Tessellations
Materials
Paper - 2 pieces of any kind. I use regular drawing paper. I only use 2 colors for clarity. Any color you like is fine.
Pencil
Tape
Scissors
Optional: Eraser, Pen for outlining, Markers, Paint
Preparation
Draw a 3 inch x 3 inch square on one of the pieces of paper.
This is the size I use for this project, but you can make the square any size you like as long as it is a square.
Procedure
Once your square is drawn - Inside the square, on 2 sides only, draw lines that meet in the corners in some way.
Meeting in the corners (vertexes) is key for the pattern to work.
Next, cut out the square on the outer lines
Then, cut along the inner lines.
Now, slide these pieces exactly across the square.
Match up the straight edges and the corners exactly.
Tape the pieces in place.
Now you have a new shape.
Flip your shape over so the tape is on the back.
Ponder - what does it look like to you? Turn it around in various directions and see what comes to mind.
Geometric forms will likely be non-representational, but in these organic forms, our eyes & minds often discover the shape looks like something from our world.
(I thought mine looked like a stingray.)
Using a pencil, trace this new shape onto the center of the other piece of paper.
Now, once traced, slide the shape over to one side - matching up the left side of the shape with the right side of the tracing.
Make sure the corners/vertexes meet and align.
Trace again - without tracing over the line that is matched up.
Continue shifting your shape to match one side of the shape & vertexes with one side of a previous tracing.
Now you are making a repeat pattern!
Fill the page with the pattern.
Once your Tessellation pattern is complete, you can:
outline with a thicker pen (I used an 08)...
...add details
(I took design influence from a type of spotted ray)
...add color.
This amazing one was created by my nephew.
He thought his shape looked like an axolotl.
He researched the actual colors of the various types of this animal and added a repeat color and texture pattern to his shape repeat pattern!
And there you have it! Tessellations! Start making them today!
They are great for relaxation, as well as for lessons - or even a rainy day recess project.
I guarantee once your students start making them they won't want to stop!
Seeds to Sprout:
Drawing More Patterns!
Keep diving into pattern making with this Wonder Wednesday 59: Patters from Patterns, live video replay! We make patterns inspired by patterns we find in nature!
Finding Forms
Sort of the opposite of making a pattern, in this Wonder Wednesday 140: Paint with the Wind, we let the wind do the drawing (perfect for March winds!) and then we look to discover what forms we see and draw from there
Tracking Patterns
Nature is full of patterns if we take the time to notice. In this Wonder Wednesday 135: Wheel of the Year project, we document nature observations on the prominent nature spots on the calendar. & there is no need to start on the calendar year because nature's time is one big circle - start at the Spring equinox (Thursday, March 20, 2025) or any time you like!
This project includes a pdf printable.