All pupils understand and construct tessellations using polygons L.O. All pupils understand and construct tessellations using polygons
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
Recap External angle Size of 1 external angle 360 = n Internal angle Size of 1 internal angle = 180 – external angle
What shapes are used to make up the honeycomb? Can these shapes be arranged so that there are no gaps between them?
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
Which regular polygons tessellate?
Equilateral Triangles: Do tessellate
Which regular polygons tessellate?
Squares: Do tessellate
Which regular polygons tessellate?
Regular Pentagons: Don’t tessellate
Which regular polygons tessellate?
Regular Hexagons: Do tessellate
Which regular polygons tessellate?
Regular Octagons: Don’t tessellate: This is called a semi-regular tessellation since more than one regular polygon is used.
Which regular polygons tessellate?
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
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
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.
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)
Show that the triangle tessellates. Draw at least 8 more on the grid Drawing tessellations
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)
Show that the triangle tessellates. Draw at least 8 more on the grid Drawing tessellations
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)
Drawing tessellations Show that the triangle tessellates. Draw at least 8 more on the grid
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)
Drawing tessellations Show that the triangle tessellates. Draw at least 8 more on the grid
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)
Drawing tessellations Show that the triangle tessellates. Draw at least 8 more on the grid
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)
Drawing tessellations Show that the trapezium tessellates. Draw at least 8 more on the grid
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)
Drawing Tessellations Show that the kite tessellates. Draw at least 8 more on the grid
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)
Drawing tessellations Show that the hexagon tessellates. Draw at least 6 more on the grid
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)