Education Technology

Tessellations and Tile Patterns

Published on 06/09/2008

Activity Overview

Students understand that a tessellation is covering of a plane with a pattern of figures so there are no overlaps or gaps. They draw quadrilaterals and triangles and explore monohedral, dihedral, and trihedral tessellating patterns.

Before the Activity

  • See the attached PDF file for detailed instructions for this activity
  • Print page 25 from the attached PDF file for your class
  • During the Activity

    Distribute the page to the class.

    Follow the Activity procedures:

  • Draw a regular polygon
  • Reflect the polygon across its own sides and observe the pattern
  • Observe that triangles, squares, and hexagons tesselate a plane with monhedral pattern
  • Note that dihedral tiling patterns are formed by a regular pentagon together with a rhombus, a regular pentagon with a heptagon, a regular octagon with a square, and a dodecagon with a triangle
  • Drag the original figure around the screen and note that the pattern remains unchanged
  • Use transformational tools to check if isosceles or scalene right triangles always tessellate the plane
  • Determine the methods by which a plane can be tessellated by a rectangle
  • Experiment with ways to tessellate the plane with a trapezoid
  • Understand that any quadrilateral tessellates the plane by a 180° rotation about the midpoint of its sides
  • After the Activity

    Review student results:

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary