1. What is a Tessellation? A tessellation is a pattern of repeating figures that fit together with NO overlapping or empty spaces. Tessellations are formed using geometric transformations.

2. Examples of Tessellations

6. How to Make a Tessellation 1. Start by drawing & cutting out a polygon (a 2” x 2” square works well) from a file folder, cereal box, or poster board. 2. From this polygon, make a template that will tessellate by performing at least one of the following transformations (described in the upcoming slides of this PowerPoint): – Translation – Glide Reflection (translation with reflection) – Rotation – Mid-point Rotation 3. Trace the template many times onto an 8.5” x 11” sheet of copy paper by rotating the template until your tessellation is complete with no overlapping or empty spaces. 4. Color neatly with vibrant colors. Do not leave any white space.

7. Translation Tessellation (EASY) For simple translation tessellations, your starting polygon should have opposite sides that are parallel and congruent. Squares, hexagons, and parallelograms work best.

8. 1. Draw a design on one side of the square and slide it to opposite side. Tape the cutout pieces to opposite sides. Slide (translation) the pattern when tracing. Start with a square 2. 3.4. Draw another design on the adjacent side of the square and slide it to opposite side. Translation Tessellation (HARD) You can create more complex designs starting with square tessellations and making changes on both pairs of sides.

9. Glide Reflection Tessellation For glide reflection tessellations, your polygons should have opposite sides that are parallel and congruent. Squares, hexagons, and parallelograms work best. *You can make this one more difficult by cutting out two pieces from different sides and doing a glide reflection for both.

10. Rotation Tessellation For rotation tessellations, the adjacent sides of the polygon must be congruent. Squares, equilateral triangles, regular hexagons, and rhombi work best. *You can make this one more difficult by cutting out two pieces from different sides and doing a rotation tessellation for both.

11. Midpoint Rotation Tessellations Triangles, squares, and quadrilaterals work best for this type. *You can make this one more difficult by cutting out two pieces from different sides and doing a mid-point rotation for both.

12. Example: Rotational Tessellation

14. Depending how you decide to color your tessellation, a very simple design can have a very creative result.

15. Watch this video to see an example of how to create your own tessellation: http://www.youtube.com/watch? v=Lc4LGZwlcvs&list=WL5358F76C6 A0EA557&index=7&feature=plpp_ video http://www.youtube.com/watch? v=Lc4LGZwlcvs&list=WL5358F76C6 A0EA557&index=7&feature=plpp_ video