Course Guide - USAID Teacher Education Project

d) Distribute the pattern block cutouts and have students work in their groups to findthe regular shapes that tessellate. They should find that the triangles, squares, andhexagons can tessellate. Describe these as regular tessellations.e) Next, ask them if the triangle and square be used together to create a tessellation.If a group discovers only one way that the shapes can form a tessellation, challengethem to find another. (These will be shown in the handouts for the for the nextactivity.)Explain that a tessellation that occurs when more than one regular polygon can createa tessellation is called a semi-regular tessellation. Even though there is no patternblock for a regular octagon, have students sketch a lattice of regular octagons that areconnected to each other. What do they notice about the spaces between the octagons?What type of tessellation is this?f) Give students the opportunity to work with the remaining pattern blocks to see ifthey can create tessellations with them. Since the two rhombuses and the trapezoidare quadrilaterals, they can tessellate. However, because they are not regularpolygons (equilateral and equiangular) the results are neither regular nor semiregular.These types of tessellations are termed non-regular.g) To follow up on activity e), where students used equilateral triangles and squaresto create semi-regular tessellations, distribute the following two worksheets wheretwo different designs result from triangles and squares: http://tinyurl.com/Tessel-Coloring-SheetsHave students circle one 360-degree angle on each sheet, then note the polygons thatcreate the angle. How many sides does each have? Have students write that numberin the shape. What do they notice about the numbers? (There are four "3"s and two"4"s.)What is different about the numbers on the two sheets. (They are in a different order.)Have students note the header on each page, explaining that they just discovered thenotation by which a particular arrangement of equilateral triangles and squares can bespecified.