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 the child 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. The
child will find that he or she 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 the child does not, after a time the teacher can show him
or her 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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