The purpose of this activity is to engage students in applying transformations to create repeating tiling patterns.

Achievement Objectives
GM4-8: Use the invariant properties of figures and objects under transformations (reflection, rotation, translation, or enlargement).
Description of Mathematics

The background knowledge presumed for this task is outlined in the diagram below:

This activity should be used in a ‘free exploration’ way with an expectation that students will justify the solutions that they find.


Reptiles are shapes that tile to make a larger version of themselves. Here is an example, a trapezium. Notice how the whole is made up of four identical parts.

What transformations (translations, reflections, rotations) map the top trapezium onto the other three?

How might 16 copies of the shape tile to form an even larger copy of itself?

Here are some other reptiles. Four copies of each shape will tile to form a larger copy of itself. Figure out which transformations are needed.

Notice that these shapes are Rep-4 because you need four copies to make a larger whole of the same shape.

Can you find some other Rep-4 shapes?

The arithmetic approach (show more)

  • The student uses trial and error approaches with some acknowledgement of angles and side lengths to tile the shapes.

The procedural approach (show more)

  • The student applies the properties of transformations, including enlargement, to find how four copies of the shape form a larger version of itself.
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Level Four