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Escher Tessellations

Age 7 to 11
Challenge Level Yellow starYellow star
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I've been seeing tessellations in lots of different places and realise that they are being used in so many situations such as tiling on both walls and floors.
At visits to various garages and big buildings I've seen one particular style of tile that's good to create and tessellate. Here's how it goes.
A - You start with a rectangle that is twice as long as it is wide.
B - Then you make a roof shape at one end - this one happens to be as high as a quarter of the base of the triangle it has made.
C - You then put the same triangle on the other end.
D - On one side you take a bite out just the same size as the roof triangle.
E - Then do the same at the other end of the opposite side.
5tiles


Now you have the tile shape for tessellating like the floors I've seen.
One way I've seen is like this:

garage Tiles1

At another garage I saw a tile like this:
2ndTile
These were put together like this [I've coloured them to see the pattern more easily]:

easy2ndTile
or

2ndTilesB


Now it's time for you to try and find some ways of putting shapes - like these two examples - together!

Let us know how you made your shape and do send us some pictures of your tessellations.


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Penta Place

Penta people, the Pentominoes, always build their houses from five square rooms. I wonder how many different Penta homes you can create?

Tessellating Triangles

Can you make these equilateral triangles fit together to cover the paper without any gaps between them? Can you tessellate isosceles triangles?

Two by One

An activity making various patterns with 2 x 1 rectangular tiles.

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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