Jigsaw puzzles are tessellations with random shapes. For this activity, each student will need a blank jigsaw puzzle, a resealable gallon-size plastic bag and crayons. Encourage the students to color each piece in a way that makes the design interesting. The shapes can be solid colors, have edging or be creative. Allow them to take their finished puzzles home.
You need pictures, or real-life examples, of tessellations and some that appear to be tessellations, but are not. Ideas include, a snake's scales, a turtle's shell, fish scales, a honeycomb, pineapple skin/rind, floor tiles, brick work, soccer ball, fishing nets, some rugs, some tile work from Spain and the Middle East, the works of M.C. Escher and images of microscopic plant cells. Show the pictures one at a time to the students and ask them to vote on whether they think the example is a tessellation. Discuss why each example is, or is not, an example of tessellation.
For this activity, each student needs scissors, a glue stick, access to construction paper and a sheet of paper on which to draw one each of the following shapes: circle, hexagon, kite, oval, parallelogram/rhombus, pentagon, rectangle, semi-circle or triangle. Tell the students to try to design a tessellation using the shape of their choice. Not all of the shapes will work as a tessellation. The interior angles of the polygon must add up to 360 degrees. They can pick whatever color construction paper they wish to cut out their shapes. Use one piece of construction paper as the backing. Share the results with the class.
Semi-regular tessellations use two, or more, regular polygons. Divide the class into seven groups. Each student in a group needs a different colored pencil. Each group needs a piece of chart paper and one of the following sets of shapes cut out of thick cardboard to aid tracing: triangle, hexagon; hexagon, square, triangle; octagon, square; dodecagon, triangle; dodecagon, square, hexagon; square, triangle; or trapezoid, triangle, kite. Not all shapes in the group will make tessellations. Each student should use her own color of pencil when tracing a shape. The group should work together to create the tessellation. Share the results with the class.