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# Tessellations

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by

## Michelle Borderick

on 29 August 2014

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#### Transcript of Tessellations

Tessellations
What is a tessellation?
A tessellation is
a pattern of shapes that fit perfectly together!

A Tessellation (or Tiling) is when we cover a surface with a pattern of flat shapes so that there are no overlaps or gaps.
http://pbskids.org/cyberchase/math-games/cant-wait-tessellate/

EXAMPLES OF TESSELLATIONS
Investigate
You should have discovered that there are 3 regular tessellations.
Tessellations
Make a
tessellation
with the blocks
What is a
tessellation?
Six equilateral triangles at each point

Four squares are each point

Three regular hexagons at each point
Ref: Booker Teaching Primary Mathematics
The focus is on:
pattern and angle

8 Semi Regular Tessellations
Regular tessellations
T
I
M
E

F
O
R

A
N

A
C
T
I
V
I
T
Y
In small groups match the numbers with the semi regular tessellations.

Have a go at creating one of the tessellations.

DISCUSS:
How do you think this would work in your class?
How could you go beyond creating 'busy work' in to more mathematical concepts and understandings? i.e.angles, pattern, translations and different types of tessellations.
INVESTIGATIONS
AND
PROBLEM SOLVING IDEAS
What kind of
pattern
will this be?
Regular polygons
which tessellate and why?
Regular polygons which do not tessellate and why?
What's regular
Four triangles and a hexagon at each point.
Three triangles and two squares at each point.

Square and two octagons at each point.
Triangle and two dodecagons at each point.
Square, hexagon and dodecagon at each point.
Triangle, hexagon, triangle, hexagon at each point.
Triangle, square, hexagon and square at each point
Two triangles, square, triangle and square at each point.
http://illuminations.nctm.org/Lesson.aspx?id=3112
http://www.mathsisfun.com/geometry/tessellation.html

Look for tessellations in the school environment.
Which regular and irregular shapes tessellate by themselves?
Try to find a way to make a tessellation with two (or more) regular shapes. Which other combinations of shapes tessellate?
Try Illuminations – tessellation creator
http://illuminations.nctm.org/Activity.aspx?id=3533

I made a picture using 16 shapes which tessellate, what might my design look like?
Design brick paving for a driveway, tiling for a room. Show different possible designs for your client.

http://gwydir.demon.co.uk/jo/tess/index.htm
Create different online tessellations to print and colour
Provides information and examples about tessellations
INVESTIGATION
The principal has asked you to design the floor in the art room. The design should combine math and art. You have been asked to submit a design which is a tessellations. You will be given paper which you will transform into your own shape, using a vertical or horizontal translation, or both. You may translate, rotate or reflect (flip, turn, slide) your shape to form your tessellation design for the new floor. You may include designs or details and colour on your tessellation design.
Students to write a persuasive text as to why their tessellation should be chosen. Include a description of the design, which geometric shapes were selected and how it was transformed to create a new shape which tessellates. Describe how the tessellation combines math and art to create a beautiful design for the art room.
Differentiation
Calculate the area to be covered. Assign shapes and colours a monetary value.How cost effective is your design?
M.C. Escher
Prior Knowledge
* Vocabulary of polygons
*Understanding of transformations (translate, rotate, reflect)
*Recognise and understand types of symmetry
* Interior angles

Consider shapes and ‘gaps’ that tessellate.
Investigate, will all triangles and quadrilaterals tessellate with themselves? Create the different types on geoboards or paper and test.