1. All pupils understand and construct tessellations using polygons
L.O.
All pupils understand and construct tessellations using polygons

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:
a) square?
b) pentagon?
c) hexagon?
a) square?
b) pentagon?
c) hexagon?
180 – 90 = 90o
360 4
= 90o
360 5
= 72o
180 – 72 = 108o
360 6
180 – 60 = 100o
= 60o

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?
A regular tessellation is a repeating pattern of a regular polygon, which fits together exactly, leaving NO GAPS.
So the bees honeycomb… is a regular tessellation of hexagons

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’t tessellate:
This is called a semi-regular tessellation since more than one regular polygon is used.

16. Which regular polygons tessellate?

17. Regular Polygon
Size of each exterior angle
Size of each interior angle
Does this polygon tessellate?
Equilateral Triangle
Square
Regular Pentagon
Regular Hexagon
Regular Octagon
Regular Decagon
360 3
= 120o
360 60
= 6
Yes
180 – 120 = 60o
360 4
= 90o
360 90
180 – 90 = 90o
= 4
Yes
360 5
= 72o
360
108
180 – 72 = 108o
= 3.33 No
360 6
360
120
= 60o
180 – 60 = 120o
= 3
Yes
360 8
360
135
= 45o
180 – 45 = 135o
= 2.67 No
360 10
360
144
= 36o
180 – 36 = 144o
= 2.5 No

18. Consider the sum of the interior angles about the indicated point.
There are only 3 regular tessellations. Can you see why?
60o
60o
120o
90o
90o
Consider the sum of the interior angles about the indicated point.
120o
6 x 60o = 360o
4 x 90o = 360o
3 x 120o = 360o
108o
135o
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
ex. a) b) c) d) e) f) g)

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

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

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

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