Tesselations
To tessellate
 to cover an area without leaving gaps and without overlapping.
MATERIAL:
 Examples
of each of the straight sided geometrical plane figures
 cut out in
thin plastic in at least two colors. All figures have
 at least
one side in common. Triangles, squares, rectangles,
 parallelograms,
rhombuses, trapezia, trapezoids, pentagons,
 hexagons,
octagons, and dodecagons. Each shape is kept in a
 separate
box with a drawing of the shape and the name on the lid.


PURPOSE:
 1) Mathematical
understanding of symmetry
 2) Understanding
of geometry, e.g. any side of the square will fit
 any side
of the other squares; the equilateral triangles will
 tessellate,
but every other triangle must be rotated 180 degrees
 3) Understanding
of art, appreciation of the beauty of geometrical
 design, developing
an ability to create designs
 4) Intelligent
observation of the environment

 Man makes
use of tessellations in tiling walls, floors, pavements, etc., in making
patchwork quilts, in inlay designs on boxes and furniture, and many in other
ways.
 The teacher
should show the child examples of geometrical designs from other
 countries
and from other epochs, e.g. designs of early man. Have books available which
show designs such as in the Islamic buildings. The mosques of Turkey, the
Alhambra
 of Spain,
and the Taj Mahal in India are some of the most beautiful buildings in the
 world and
show a very rich use of geometrical design. The child should appreciate
the Islamic contribution to our culture and the contributions of people
around the world.

 Patchwork
was used in Eurpose, but developed to its highest form and use in America.
Books showing beautiful designs for quilts can be put in the book corner,
as well as other books on design.

 Many paintings
show geometrical design in floors, clothes, backgrounds, borders, artifacts,
etc. Books of great paintings should be in the book corner and the teacher
should show the children a few examples and leave them to find others.
PRESENTATION:
 Take a box
of shapes that will tessellate, e.g. squares, to the child's table. Show
him how to make a symmetrical pattern with some of them. Let the child take
any box of shapes and try to tessellate and make patterns with them. If
the child wishes to transfer the pattern to paper, he can draw around the
shapes and color the resulting design.


EXERCISE:
 The child
takes any shape and finds if it will tessellate. He finds that he can tessellate
with triangles, squares, hexagons, etc., but that pentagons, octagons, etc.,
leave gaps. A child usually begins to use two or more shapes to tessellate
without being shown. When using the octagon, the space left is a square.
A child often fetches the box of squares and tessellates with octagons and
squares. If he does not, after a time the teacher can show him how to do
so.
 Octagon with
gaps

 Octagon with
squares

 Decagon with
triangles




 Decagon with
squares and triangles (border design)
 All triangles



 SHAPES USED
FOR TESSELATING







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