# Tessellation

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Tessellation

Defining TessellationA tessellation can be defined as the covering of a surface with a repeating unit consisting of oneor more shapes in such a way that:• there are no spaces between, and no overlapping of, the shapes thus employed, and• the covering process has the potential to continue indefinitely (for a surface of infinitedimensions).Tessellation within the Primary School CurriculumPrimary school tessellation activities fall into two categories:• The mathematics of tessellation• Application of knowledge about tessellationThe ‘application of tessellation’ aspect is often seen in schools and features in mostpublished mathematics schemes. However, the ‘mathematics of tessellation’ aspect is oftenoverlooked. This results in poor progression with children often repeating the pattern-colouringactivities they have undertaken in previous years of their schooling. Moreover, such childrenhave little idea of why some combinations of shapes tessellate while others do not.The ‘mathematics of tessellation’ aspect should focus on providing children with theknowledge and skills to explain why tessellation is or is not possible for particular units ofshape. It is this which is the basis of good practice for teaching tessellation.That said, it is very worthwhile to show children real-life examples of the application oftessellation. Brick walls, paving, wall and floor tilings, woodblock floors, carpets, wallpapers,wrapping papers, textiles and works of art are often useful resources for whole-class or groupdiscussions about tessellation as a concept and about its application in everyday life. Typicalactivities when using these might be to identify the repeating unit of shape used to create thetessellation, to explain why the tessellation works, to consider other ways of tessellating thegiven surface or to develop mental visualisation skills (e.g. as part of a mental/oral starter orplenary within the daily mathematics lesson). Using resources of this kind demonstrate tochildren the value and purpose of understanding the mathematics of tessellation and thusprovide an incentive and reason to learn about it.Useful Vocabulary for TessellationIn common with other aspects of Shape and Space work, children will need to become familiarwith the following mathematical vocabularyPlane: two-dimensional or, colloquially, ‘flat’.Regular shape: a shape in which all the sides are the same length AND all the angles arethe same size.Irregular shape: a shape in which not all the sides are the same length AND/OR not all theangles are the same size.Polygon: a two-dimensional, closed shape in which all the sides are straight lines.Interior angles: the angles inside the boundary of a shape (see illustration below).Exterior angles: the angles through which one would turn at the corners of a shape ifwalking around the boundary of the shape (see illustration below).The sum of the exterior angles of any polygon is 360° or one whole turn.Re-entrant angle: an interior angle of more than 180°.Congruent shapes:shapes which are identical in terms of type of shape, lengths of sidesand sizes of angles. Their position in space and their orientation may beThe Mathematics of Tessellation 3 © 2000 Andrew Harris

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