1. Tessellations This is a Roman inlaid marble tiling pattern For more see http://www2.spsu.edu/math/tile/historical/roman/http://www2.spsu.edu/math/tile/historical/roman/

2. Roman Mosaic

3. Do all shapes tessellate? Triangles? Quadrilaterals? Pentagons? Hexagons? Heptagons? Octagons?

5. 11

6. Triangles always tessellate

8. Quadrilaterals always tessellate.

10. There are only three regular tessellations: Jump to transformations

11. Activity for the computer: Start a new PowerPoint Presentation. Save it in your network folder. Make the following slides: Slide 1 is the title slide “Tessellations” by Your name. The following slides should all show tessellations in two colours. Before you start click Draw  Grid  Snap objects to other objects. Use Autoshapes to select your shape (hold down shift to get the regular shape) Slide 2 is a tessellation of equilateral triangles Slide 3 is a tessellation of squares Slide 4 is a tessellation of hexagons Slide 5 is a tessellation of Octagons and Squares Are there any other pairs of regular shapes that tessellate?

12. Eight semi-regular tessellations 3,3,3,4,43,3,3,4,4 3,6,3,63,6,3,6 3,3,4,3,43,3,4,3,4 3,3,3,3,63,3,3,3,6 4,8,84,8,8 3,4,6,43,4,6,4 3,12,123,12,12 4,6,124,6,12

13. Semi-regular Tessellations

16. None edge to edge patterns

17. Combining shapes

19. Modifying by translation

20. Start with a two by three rectangle in your exercise book.

21. Cut a section out from the left and add it to the right.

22. Start with a two by three rectangle in your exercise book. Cut a section out from the left and add it to the right. Show, using at least six copies of your shape how it tessellates.