Make a Tessellation!

M. C. Escher was a Dutch graphic designer who created mathematically inspired symmetrical shapes that joined together like a puzzle. This technique of fitting together multiple shapes without any gaps or overlapping is called tessellation. The edges of a tessellation look like the edges of a jigsaw puzzle, and fit together like one as well.

In this activity, your child will create her own shape to use as a repeating pattern to form a tessellation. Equilateral triangles, hexagons, rectangles and squares will all usually tessellate. But you can even make more complex shapes that tessellate.  But making a shape that tessellates isn't as easy as it may seem!  This activity is something she can do on her own to get those wheels turning and those creative juices flowing, as your child builds up her analytical and mathematical thinking skills.

What You Need:

• Pencil
• Tracing paper
• Construction Paper
• Hobby knife

What to Do:

1. Choose a shape (square, rectangle or hexagon).  Draw the shape of your choice making sure opposite sides are equal of equal length.
2. When your basic shape is done you can make alterations to the edge of the shape if need be. Draw a line inside the shape from one corner on one side to the other corner on the same side.  A new shape will be created as a section of the first shape.
3. Cut out the new shape that was made when drawing a line from one corner to the other.
4. Tape this new shape (that is a section of the old shape as a whole) on the opposite side of the old shape that was left when you cut the new section from it.
5. Use this shape as your “tile” and trace around it to create a template.  Cut the template out.
6. Test your shape to see if it still tessellates (fits together in a repeating pattern). Cut out more than one copy of your sample tile, being very careful to duplicate the shape as exactly as possible. Lay your duplicates down turning them as needed. Can you interlock the shapes from various sides? If so, you have a successful tessellation tile!
7. Make light parallel lines across the back of your sheet paper. They should be the width of your basic shapes (from external corner to external corner, in other words not the diagonal)
8. Trace your shape several times so that it fits together in a repeating pattern, filling up the entire page with your interlocking shape without any spaces in between.
9. You can use a utility knife to remove the in between shapes so that the remaining shapes form a pattern.
10. Glue a contrasting sheet of paper to the back of your cut out sheet to really make it pop! 
11. Enjoy the fruits of your labor!  You'll end up with an incredible visual arrangement

Did You Know?

Variation: At step 5, after you have your basic shape, make one copy. Make sure they interconnect. What do the shapes suggest? Can you see a profile along the edge? Can you imagine an animal inside the shape? If so, draw it in. Make copies and cut them out. Fit them together and color them as desired. The shapes should contrast either in color or in the drawn details so that when pieced together they flow from one image to another, separating out the different animal forms.

You can see a practical example of tessellations in pieced quilts. Each piece must fit together smoothly in order to create a flat sewn surface with no gaps or holes.  It's rather difficult!