June 21, 2005

Today the students learned about the concept of tiling and its relationship to planes (flat surfaces). They worked in groups and used cut-out shapes to figure out how to tile a white sheet of paper, thus modeling the tiling concept of using a collection of shapes that fit together with no gaps or overlaps to cover a flat surface.

Next, the students explored the concept of tessellations using the Tessellate! activity. This activity let them discover the myriad of shapes that will tile a plane. Susan then asked questions relating to the number of degrees in a variety of different-sided shapes to get the students thinking about using degrees of angles to determine whether it is possible to tile different shapes or not.

After discussing the significance of using angle degrees to determine what shapes will tile together to form a plane, the students experimented with an applet that shows specifically which shapes will tile a plane. Susan went on to show how dodecagons can be tiled using triangles as connectors.

After several explorations and discussions the students were ready to create their own patterns using construction paper, scissors, colored pencils, and markers.