Find all the different shapes that can be made by joining five equilateral triangles edge to edge.

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

Investigate these hexagons drawn from different sized equilateral triangles.

Can you find out how the 6-triangle shape is transformed in these tessellations? Will the tessellations go on for ever? Why or why not?

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?

This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

What do these two triangles have in common? How are they related?

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

Can you explain why it is impossible to construct this triangle?

Make an equilateral triangle by folding paper and use it to make patterns of your own.

This interactivity allows you to sort logic blocks by dragging their images.

Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?

Using LOGO, can you construct elegant procedures that will draw this family of 'floor coverings'?

Recreating the designs in this challenge requires you to break a problem down into manageable chunks and use the relationships between triangles and hexagons. An exercise in detail and elegance.