2. E12 Students will be expected to recognize, name, and represent figures that tessellate.

3. A tessellation is a tiling of the plane using one or more shapes in a repeated pattern with no holes or gaps. A 2-D figure is said to tessellate if an arrangement of replications of it can cover a surface without gaps or overlapping. What is a tessellation?

4. E12.1 Do you think that the green equilateral triangle in the set of pattern blocks will tessellate? Start by trying to trace the triangle in a repeated way so that there are no gaps or overlapping in your design. Will this type of triangle tessellate? Next, use the other pieces in the set of pattern blocks one at a time to check their ability to tessellate. Which 2-Dimensional Figures Will Tessellate?

5.  E12.2 Now fold a sheet of paper in half again and again until you have 8 sections.  With it completely folded, draw any triangle on the exposed surface and cut it out going through all 8 sections.  Using the 8 congruent triangles, test to see if your triangle tessellates.  Did everyone’s triangle tessellate? Did we have different triangles – acute, obtuse, right, isosceles, scalene?  What conclusion might we make about the tessellating ability of any triangle?

6.  E12.3 Using any of the pattern blocks and half of a sheet of plain paper, trace the block to completely cover this paper.  Colour one block in the centre of your paper blue. Colour the rest of the shapes following these rules: if two shapes share a common side, they must be a different color (sharing a common vertex is okay); use as few colors as you can. Two shapes share a common side Two shapes share a common vertex

7.  Now let’s check to see if any other shapes will tessellate? What about a regular pentagon? A regular octogon?  What shape could be used to fill in the gaps because the octagon does not tessellate?  Did you know that octagon is the shape often used when tiling floors. Squares are used to fill the gaps because octagonal tiles won’t tessellate. What about some other shapes?

8. Investigating Tessellations on the Web http://mathforum.org/ http://ck022.k12.sd.us/ (Montrose Mathematics)