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Tessellations – Year 9 Learning Object N: L3547 (The Learning Federation website)
Axis of Symmetry
Our Wikispace: http://tessellations-kjk.wikispaces.com/
Tessellation: An infinitely repeating pattern of shapes which completely covers a
plane without overlapping or gaps, while displaying various types of symmetry.
Types:
Regular tessellation:
A pattern made by repeating a regular polygon.
(only 3 polygons will form a regular tessellation – square, equilateral triangle, hexagon)
Semi-regular tessellation:
Is a tessellation made up of a
combination of two or more regular polygons.
Non-regular tessellation: (Abstract)
Tessellations that do not use regular polygons.
Transformational Geometry – Actions for moving shapes
Reflection (flip)
Rotation (turn)
Translation (slide)
Interior & Exterior Angles:
Polygon
No.
Interior Angles
Exterior Angles
of
(of a Regular Polygon) n = number of sides
n = number of sides
sides
Sum of Internal Angles = (n-2) × 180° / n
360*/n
Triangle (Trigon)
3
180 x 1 / 3 = 60
360 / 3 = 120
Square (Tetragon)
4
180 x 2 / 4 = 90
360 / 4 = 90
Pentagon
5
180 x 3 / 5 = 108
360 / 5 = 72
Hexagon
6
120
60
Heptagon
7
127.57
51.40
Octagon
8
135
45
Nonagon
9
140
40
Decagon
10
144
36
Can also be written as
‘3-gon’ / ‘8-gon’
Each interior angle =
http://www.mcescher.com/ An original Artist of tessellations… M.C. Escher
3 Digital Resources:
http://www.aleph0.clarku.edu/~djoyce/poincare/poincare.html (google Poincare)
http://www.paec.org/fdlrstech/escher.pdf
http://www.shodor.org/interactivate/activities/Tessellate/
Declarative Knowledge: Students will know...
Differentiate between the different types of Tessellations
Functions of transformational geometry - Flip (reflections), Slide (translation) & Turn (rotation)
Algebraic formula relating to internal angles of shapes.
How conservation of area and various types of symmetry can be applied to tessellations.
Procedural Knowledge: Students will be able to...
Separate geometric shapes into categories i.e. polygons (regular & non regular), triangles
Create a non-regular, tessellating polygon
Use rules relating to conservation of area
Create regular & semi-regular tessellations
Prove congruence of various polygons using triangle and angle properties.
Define axis of symmetry, and identify various types of symmetry within a pattern.
Make your own Non-regular tessellation: