Tessellations

Tes­sel­la­tions are all around us! A tile floor is a good exam­ple. Encour­age your stu­dents to find other tes­sel­lat­ing pat­terns in the world around them. Then make your own tes­sel­la­tions inspired by artist M.C. Escher. (Don’t be afraid to try these… they are much eas­ier than they look!)

First, some help­ful vocab­u­lary:
M.C. Escher — a Dutch artist (1898–1972) who is best known for his math­e­mat­i­cally inspired draw­ings and prints which dis­played great real­ism, while at the same time show­ing impos­si­ble per­spec­tive, eye trick­ery and meta­mor­pho­sis.
Tes­sel­la­tion
— a pat­tern made with poly­gons that com­pletely fills a space with no gaps, spaces or over­laps.
Poly­gon - a shape with three or more sides

Direc­tions:
1. Cut a lined index card to 3“x3”.
2. Next, cut a shape from one side of your 3“x3’ card, and slide it to the oppo­site side of the card, with­out flip­ping it over or turn­ing it. (The lines on your index card will show you if you’ve flipped or turned it!)
3. Now, tape the shape so that it is
exactly across from the spot you cut it from. If you include a cor­ner in your cut, it makes it eas­ier to line the shape up on the oppo­site side. (For older stu­dents, you can make this project more chal­leng­ing by hav­ing them repeat this step on an adja­cent side of their card, as in the sam­ple project above.)
4. Turn your newly cre­ated shape (we’ll call this your “tile”) in dif­fer­ent direc­tions and use your imag­i­na­tion to see if it “looks like” any­thing. Lightly sketch your idea onto your tile.… be cre­ative!
5. Place your tile on the cen­ter of a 9“x12” paper and care­fully trace around it. (I use 12“x18” paper when I do this with 6th graders.)
6. Now, pick up your tile and place it next to your traced design, as if it were a piece fit­ting into a jig­saw puz­zle. There shouldn’t be any gaps or over­lap­ping. Then, trace around your tile again.
7. Repeat this step until your whole paper is cov­ered and there are no gaps or spaces.

8. Trace over your pen­cil lines with a
Sharpie and add details to each shape to help oth­ers rec­og­nize what you “saw” in it. (Remem­ber that what­ever details you add to one shape, will need to be added to EVERY shape! Keep your details sim­ple.)
9. Finally, color your design with mark­ers, col­ored pen­cils or crayons.


Below is an exam­ple of a more basic tes­sel­la­tion done with first graders, where the shape was cut from one side of the card only. We treated this as an abstract design and didn’t add any details, but just col­ored it in an alter­nat­ing pattern.

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One Response to Tessellations

  1. Emily & Co. October 21, 2009 at 11:16 am #

    I just found your blog. My 6 year old daugh­ter wants to be artist when she grows up — now I have tons of ideas of projects I can do with her so she can pur­sue that dream!THANKS!

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