If there is one item in my 4 year-old class that thrills every single one of my students, it is my set of pattern blocks.  My class loves to create patterns and pictures with shapes, creating art and objects using squares, hexagons, triangles and quadrilaterals.  This activity always manages to lead the child to discover the properties of shapes in regards to angles and sides: how different shapes can “interlock”, which shapes work best for creating patterns, and which shapes do not work at all.

Tessellations are, simply put, a “tiled” pattern.  They are a design created by interlocking, non-overlapping, repetitive shapes that leave no “holes” or gaps between them.  Much like floor tile, tessellations can go on forever, repeating the same pattern over and over.  Tessellations do not have to be regular polygons (such as triangles and squares); they can be created with non-traditional shapes and figures as well.  Dutch artist M.C. Escher is one of the most famous names associated with tessellations.  Check out a terrific collection of his work at Platonic Realms’ site, complete with a short biography and a variety of his sketches and drawings.

While playing with shapes and their relationships with each other can create amazing art and designs, children are also exploring mathematical concepts closely tied with geometry and spatial relationships.  Incorporating toys and tools such as Fractallations and Puzzellations, children are able to experience the joy of creating a unique design or picture while still learning and internalizing key mathematical concepts.  For a more direct look at tessellations, products such as tessellation activity books can provide opportunities for children to explore the use of design and color to enhance a tessellation design.