Tessellations
Recognise and use combinations of transformations to create tessellations and other geometric patterns.
Read this first
Shapes tessellate when they fit with no gaps and no overlaps.
Squares fit together perfectly. There are no gaps.
Words you need
- Tessellate
- Fit together with no gaps.
- Transformation
- A slide, flip or turn.
- Pattern
- A design that repeats.
Worked example
e.g. Why do squares tessellate but circles do not?
- Look at the corners of a square. Each is 90 degrees.
- Four corners meet at a point. 4 x 90 = 360.
- A full turn is 360, so they fit exactly.
- Circles have no corners. Gaps are always left.
The angles that meet at a point must add to 360.
Practice
The pictures fade as you go. By the last few you are on your own.
1Do squares tessellate?with a picture
AnswerYes. Four corners make 360.
2Do rectangles tessellate?with a picture
AnswerYes. Their corners are also 90 degrees.
3Do equilateral triangles tessellate?with a hint
Need a hint?
Each angle is 60. How many make 360?
AnswerYes. Six meet at a point.
4Do regular pentagons tessellate?with a hint
Need a hint?
Each angle is 108. Does that divide into 360?
AnswerNo. 108 does not go into 360 exactly.
5Which transformation slides a tile along a row?on your own
AnswerA translation.
6How many hexagon corners meet at a point?on your own
AnswerThree. Each is 120 degrees.
7Why do bees build hexagons?on your own
AnswerHexagons tessellate with no wasted space.
Think about it
1
What test tells you if a shape will tessellate?
One good answerCheck whether its angle divides exactly into 360.
2
Which transformations are used to make a tessellation?
One good answerSlides, flips and turns.
Common mistakes
Thinking every shape tessellates.
Regular pentagons and circles do not.
Leaving small gaps and calling it a tessellation.
No gaps at all are allowed.