Tessellations

Goal:  The student will create 10 shapes, all identical, which fit together with no negative space between the pieces.  This is called a tessellated shape.

Tessellation- A tessellation is a shape which when repeated will fit together side-by-side with NO negative space between pieces.  Any parallelogram will tessellate.  Think of a tile floor.  Any triangle will tessellate, as it is merely ½ of a parallelogram.

Materials:

      pencil                        stiff paper for the template            scissors                      clear tape

      9” X 12” scratch paper       9” X 12”white paper

Steps:

1.    Watch the demonstrations and take notes at all times.      Much of what is taught here is visual and not written down yet.  Your job is to write it down to learn it.

2.    We will use only the triangle to make our tessellations.

* You must always have perfectly straight edges.

* Be sure to color one side to indicate the back of the template so as not to accidentally turn over the shape when taping it to a new space.

3.    Label one edge as A, with hatch marks, one as B, with cross hatch marks, and one as C, with spirals.

4.    Find the middle by folding one corner to the other corner, or by using a piece of paper to duplicate the dimension and then folding that.  This bisects the side A, now all you need do is draw a line at the midpoint.  Do this on both remaining sides, as well.

5.    Draw a shape from the left corner of side A to the midpoint of side A.  Cut it out and rotate it about the midpoint.  Use the tape to firmly reattach it at its new location, ON THE SAME SIDE of the triangle, on side “A”.  (This piece is rotated 180 degrees and placed at the other end of side “A”.)

6.    Do the same thing on sides B and C.

7.    Keep all measurements from the midpoint exact and there should be no problems with your shape tessellating.  Creativity is the name of the game with this assignment.

A special note:  Remember the scribbling from step #2 above?  At any time you can turn your shape over and see how the lines match.  They will always match each other EXCEPT where you’ve matched the sides of the shape as in step #5.

Items required for your grade:

Your proper original pattern, the template

Your 10 shapes cut properly

Your shape traced to cover all

Your 10 shapes colored neatly

Grading Rubric:

      A  All 10 shapes in and neatly cut, no sloppiness anywhere.        

They must fit and have no gaps, or practically none.

The design must fit the shape well with the coloring done neatly.  Your hard work must be plainly visible.   

The student would have no trouble teaching another how to do this assignment.

B All 10 shapes in and neatly done, little sloppiness (if any).  They must fit very well, with little room to spare.  Done neatly.  The design must fit the shape coloring done well.

Your work must be plainly visible.  The student could probably teach the project to another.

C All 10 shapes in and done, average to poor neatness, so-so design.  The student understands but couldn’t teach it to another very well, if at all.

D All or some shapes in, but poorly done, or only some of the shapes in.  The student is lost.

F No shapes in, or one shape in but done so poorly that it is wrong!  The student has not learned.

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FOLLOWING DIRECTIONS is the primary criteria for this assignment, followed closely by correct time use.  Original and creative designing of the resulting tessellated shape is also a must.  Enjoy and learn!

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17 October 2008