Tuesday, April 7, 2015

Tessellations! RES

When my fourth graders came to class, I had on display M.C. Escher's mind-blowing print MetamorphosisIt is woodcut where each tessellated image gradually shifts into the next. Tessellations are shapes that can repeat infinitely over a plane without overlaps, gaps, or spaces in between.
Metamorphosis I, 1937, Woodcut

  Then I told my fourth graders that we were going on a field trip around our own school. There was some groaning. Admittedly, it's not much of a hook, right? What does one have to do with the other?

We got out in to the same hallways that they have walked down thousands of times, and I asked them to find things in our school that tessellate.
The wall.  (Of our hallway)
Ever had a field trip where you students are excited to see the hallway wall? Try it. Because, suddenly, mine were. Psyched, in fact, with hands flying up to tell me more things they were noticing.

"The walls!"
"The floor tiles!
"The ceiling panels!"
"The carpet squares!"
"The bricks!"
Have children ever been excited to see this before?
We came back to the classroom and brainstormed more.  
Soccer balls. Honeycomb. Fish scales. Paving stones.
Now the real question began- Why are tessellations useful?
Here are some of the fourth grade answers:

"Because you don't want air to come in through the wall, so it can't have gaps."
"Because if a soccer ball had space the air would come out."
"If the floor had gaps in it we could trip or fall through."
"The rain could come in the ceiling."

Tessellations have been used by architects for millennia (cue Alhambria here), both for structural and decorative reasons.

The tessellated tile mosaics of Alhambira in Spain are amazing. Parts of the building date back to 889B.C.
Back to M.C. Escher, whose artwork was inspired by Alhambria's decorative patterning.  Students set out to learn how to create tessellating shapes by beginning with squares, although it is relatively easy to begin with any four-sided parallelogram. Here is a simple how-to for making the most basic type, and creates a piece that is flat on two edges and more dynamic on the other two.

Grade four tessellating piece traced onto a grid
Most students chose to go above and beyond and create pieces that tessellated on all four sides without straight, flat edges.  Fourth graders then chose to either trace onto the page directly, or orient it to a grid to help with placement.

Afterward, students began to add color. Most students have chosen to add color in a pattern, but some are designing creatures:
Superhero Fish
Or adding color more at random:

A school of fish!
 The artist of the work above told me that "a real school of fish would just never be in a perfect pattern, so I colored it the way they would really look when swimming, just colors everywhere."

Grade four artists are very proud of using math skills and accuracy to create these.  
Such a happy marriage of measurement, geometry, and precision in an artwork!

Not surprisingly, tessellations are often used as fabric patterns.  

Via basbleu.com
Wouldn't these make terrific prints on fabric for scarves?!  New project brewing in my mind!

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