# Tessellation

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Tessellation

the sum of the interior angles = (5 - 2) × 180° = 3 × 180° = 540°so one interior angle = 540° ÷ 5 = 108°.Note that these methods only work for regular polygons.Measuring the angles with a protractor is possible in all cases, regular or irregular.In summation, children will need to know or learn about the angle properties of all regularpolygons and of common irregular polygons in order to understand the mathematics oftessellation.Useful Resources for Teaching TessellationThe following may be found useful when teaching about tessellation:• a large number of various cardboard or plastic regular plane (i.e. flat/2D) shapes eachof which have sides of the same length;• gummed paper shapes which have sides of the same length;• tiling mats (obtainable from the Association of Teachers of Mathematics or seeResources section at the end of this booklet)• computer software packages which allow children to investigate tiling and tessellationactivities;• real-life examples of tessellation patterns (such as works of art (e.g. by Escher),fabrics, wrapping papers, wallpapers, floor and wall tilings, brickwork patterns);• sets of different kinds of triangles• sets of different kinds of quadrilaterals• sets of irregular shapes (some of which tessellate and some of which do not)• protractorsProgression in Learning about TessellationSeveral distinct stages can be identified in learning about the mathematics of tessellation. Asprogress is made through these stages the degree of regularity of the shapes under considerationreduces. The suggested stages in the progression are:1 Tessellations involving repeated use of ONE regular polygon;2 Tessellations involving repeated use of a unit of shape made up of TWO OR MOREdifferent regular polygons;3 Tessellations involving triangles or quadrilaterals;4 Tessellations of irregular shapes obtained by transformation of other ‘more regular’,tessellating shapes ;5 Tessellations involving other irregular shapes.The Mathematics of Tessellation 5 © 2000 Andrew Harris

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