## 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