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Tessellations

Objective :. Tessellations. To understand and construct tessellations using polygons. Level 5 and 6. Starter Activity. 360 n. What’s the size of an exterior angle of a regular:. What’s the size of an interior angle of a regular:. 180 – 90 = 90 o. 360 4. = 90 o. 360 5.

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Tessellations

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  1. Objective: Tessellations • To understand and construct tessellations using polygons • Level 5 and 6

  2. Starter Activity 360 n • What’s the size of an exterior angle of a regular: • What’s the size of an interior angle of a regular: 180 – 90 = 90o 360 4 = 90o 360 5 180 – 72 = 108o = 72o 360 6 180 – 60 = 100o = 60o a) square? b) pentagon? c) hexagon? a) square? b) pentagon? c) hexagon?

  3. Recap External angle Size of 1 external angle 360 n = Internal angle Size of 1 internal angle 180 – external angle =

  4. What shapes are used to make up the honeycomb? Can these shapes be arranged so that there are no gaps between them?

  5. What does this have to do with tessellations? So the bees honeycomb… is a regular tessellation of hexagons A regular tessellation is a repeating pattern of a regular polygon, which fits together exactly, leaving NO GAPS.

  6. Which regular polygons tessellate?

  7. Equilateral Triangles: Do tessellate 

  8. Which regular polygons tessellate?

  9. Squares: Do tessellate 

  10. Which regular polygons tessellate?

  11. Regular Pentagons: Don’t tessellate

  12. Which regular polygons tessellate?

  13. Regular Hexagons: Do tessellate 

  14. Which regular polygons tessellate?

  15. Regular Octagons: Don’ttessellate: This is called a semi-regulartessellation since more than one regular polygon is used.

  16. Which regular polygons tessellate?

  17. 360 3 = 120o 360 60 Yes = 6 180 – 120 = 60o 360 4 = 90o 360 90 180 – 90 = 90o = 4 Yes 360 5 360 108 = 72o 180 – 72 = 108o = 3.33 No 360 6 360 120 = 60o = 3 180 – 60 = 120o Yes 360 8 360 135 = 45o 180 – 45 = 135o = 2.67 No 360 10 360 144 = 36o 180 – 36 = 144o = 2.5 No

  18. There are only 3 regular tessellations. Can you see why? 60o 60o 90o 120o 60o 90o 90o 60o 120o 60o 108o 108o 135o 135o 108o Consider the sum of the interior angles about the indicated point. 60o 120o 90o 3 x 120o = 360o 6 x 60o = 360o 4 x 90o = 360o 36o 90o 2 x 135o = 270o 3 x 108o = 324o

  19. Non Regular Tessellations A non-regular tessellation is a repeating pattern of a non-regular polygon, which fits together exactly, leaving NO GAPS. All triangles and all quadrilaterals tessellate.

  20. Drawing tessellations Show that each of these shapes tessellate by drawing at least 8 more around each one b) ex. a) d) e) c) f) g)

  21. Drawing tessellations Show that the triangle tessellates. Draw at least 8 more on the grid

  22. Drawing tessellations Show that each of these shapes tessellate by drawing at least 8 more around each one b) ex. a) d) e) c) f) g)

  23. Drawing tessellations Show that the triangle tessellates. Draw at least 8 more on the grid

  24. Drawing tessellations Show that each of these shapes tessellate by drawing at least 8 more around each one b) ex. a) d) e) c) f) g)

  25. Drawing tessellations Show that the triangle tessellates. Draw at least 8 more on the grid

  26. Drawing tessellations Show that each of these shapes tessellate by drawing at least 8 more around each one b) ex. a) d) e) c) f) g)

  27. Drawing tessellations Show that the triangle tessellates. Draw at least 8 more on the grid

  28. Drawing tessellations Show that each of these shapes tessellate by drawing at least 8 more around each one b) ex. a) d) e) c) f) g)

  29. Drawing tessellations Show that the triangle tessellates. Draw at least 8 more on the grid

  30. Drawing tessellations Show that each of these shapes tessellate by drawing at least 8 more around each one b) ex. a) d) e) c) f) g)

  31. Drawing tessellations Show that the trapezium tessellates. Draw at least 8 more on the grid

  32. Drawing tessellations Show that each of these shapes tessellate by drawing at least 8 more around each one b) ex. a) d) e) c) f) g)

  33. Drawing Tessellations Show that the kite tessellates. Draw at least 8 more on the grid

  34. Drawing tessellations Show that each of these shapes tessellate by drawing at least 8 more around each one b) ex. a) d) e) c) f) g)

  35. Drawing tessellations Show that the hexagon tessellates. Draw at least 6 more on the grid

  36. Drawing tessellations Show that each of these shapes tessellate by drawing at least 8 more around each one b) ex. a) d) e) c) f) g)

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