A tessellation is a pattern composed of shapes that perfectly fit together without gaps or overlaps. Math games involving tessellations teach students how to solve problems with multiple possibilities for answers, improve math vocabulary in geometry and spatial sense. Students will also improve mathematical reasoning, recognise patterns and connect what they learn to other disciplines like art.
Ask each student to find five examples of tessellation in the world around them. Examples include bathroom tiles, honeycombs, rug patterns and some quilts. Create a photo file for the students to download and share their photos. A digital camera will make this assignment easier.
For this game, each student needs a 3-inch square sheet of paper, a 12-by-12-inch piece of blank paper, adhesive tape, scissors and coloured pencils or crayons. Have multiple rulers, compasses and protractors available to help students draw shapes. Tell the students to cut a shape out of the square, using one of the sides of the square as part of the shape. For example, draw a triangle originating from the endpoints of one side of the square. Tell the students to tape the cut-out shape to the opposite side of the square to make an interlocking shape to tessellate. Students should trace around their figure to fill the page. When the design is complete, they should colour-in an interesting pattern, or be creative and see if they can make their shape look like an animal. Collect the designs and have a math art show. Invite other classes, and provide slips of paper for visitors to vote on their favourite designs.
Quilts often use tessellation in their design. For this high school age activity, you need several library books featuring colour photographs of quilts, graph paper and coloured pencils or crayons. After allowing the students to browse the books of quilt photos, come up with a class quilt design. Enlarge the pattern and allow students to colour the shapes. If possible, find a seamstress to make the pattern into an actual quilt and donate it to a family in need.
Students can make variety of tessellations using attribute blocks, in various geometric shapes, sizes and colours, and pattern tiles. Each student will need a set of pattern tiles or attribute blocks. Tell the students to use the shapes to make a pattern with no gaps or overlaps. Encourage them to experiment to see which shapes will tessellate and which ones won't.
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