1. Tessellations!!!!! A tessellation is a way to tile a floor (that goes on forever) with shapes so that there is no overlapping and no gaps

3. Tile floors and puzzles are all tessellations, but these are not the only examples…… They are all around us

4. Where have you seen tessellations in your life?

5. REGULAR TESSELLATIONS: RULE #1: The tessellation must tile a floor (that goes on forever) with no overlapping or gaps. RULE #2: The tiles must be regular polygons - and all the same. RULE #3: Each vertex must look the same.

6. What's a vertex? where all the "corners" meet!

7. . A fact: all polygons with more than six sides will overlap! So, the only regular polygons that tessellate are triangles, squares and hexagons!

8. SEMI-REGULAR TESSELLATIONS: These tessellations are made by using two or more different regular polygons. The rules are still the same. Every vertex must have the exact same configuration.

10. The artist MC Escher made art based on tessellations.

21. Interactive tessellation sites GO PLAY! http://nlvm.usu.edu/en/nav/frames_asid_163_g_3_t_3.html http://shodor.org/interactivate/activities/Tessellate/

23. Shape 1 Cut a shape form one side of a tile, tape it on the opposite side directly across from the cut out.

24. Shape 1 Cut the shape in half, then tape them opposite each other. This is your tessellating shape!

25. Shape 2 Cut a square tile in half in the desired shape and tape one side to the other.

26. Shape 2 Cut the newly made shape in half again in the desired way. Take the top two pieces and move them below the bottom two pieces. Align and tape with the corners matching. This is your tessellating shape!

27. Use your imagination!

28. Make Your Own Tessellation Shape 1. Start with a square. Cut a shape form one side of a tile, tape it on the opposite side directly across from the cut out. Cut the shape in half, then tape them opposite each other. This is your tessellating shape! Shape 2 Cut a square tile in half in the desired shape and tape one side to the other. Cut the newly made shape in half again in the desired way. Take the top two pieces and move them below the bottom two pieces. Align and tape with the corners matching. This is your tessellating shape!

29. HAVE FUN! Us