Terrific Tesselations

The Activities

  1. Topic: Infinity: Book: The Cat in Numberland by Ekeland, Chapter 2.
  2. Topic: Prime numbers: The kids try to discover which numbers are prime vs composite. We defined prime as any number where it is impossible to make a rectangle out of that many cubes.  The kids then worked on numbers 1 – 70 trying to make rectangles and crossing off numbers that were not prime.
  3. Topic: Tesselations: A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps. Each kid made a tesselation pattern piece by cutting shapes out of two sides of a square and taping the cut-out pieces to the opposite side. Then we repeatedly traced the pattern piece until it covered a big sheet of paper, and colored in the tesselation.

    A tesselation pattern made out of poster board.

    Two mathematical artists.


    This circle required hardly any preparation.  I had posterboard, tape, crayons, and scissors out for the tesselation activity.  For the prime numbers proofs, I got out our set of Base Ten Blocks.

How did it go?

The kids caught on to the prime number activity really quickly. They were allowed to choose any number between 1 and 70. If they could show me a rectangle or square made out of that many cubes, then we know the number is not prime, and the kid got to color in the number’s square on our wall chart.  At first the kids randomly picked numbers, but soon they figured out some patterns.  One girl started working on all the even numbers, making 2 by X rectangles.  Another girl figured out all the multiples of 10s would work if you have 10 to a side.  Several of the kids struggled to find square and rectangles…it took some time before they realized that it is better to try something than to do nothing.  We didn’t finish all the numbers 1 – 70. We’ll come back to this another time.

The Tesselation activity was a big success.  It was a bit hectic at first, when the kids were cutting out their patterns, because I had to carefully tape the pieces to the opposite side.  But once the pattern pieces were complete, it went great.  All the kids were able to trace their pattern pieces, and fill the paper with pretty tesselations.