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

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?

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

Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

Explore ways of colouring this set of triangles. Can you make symmetrical patterns?

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?

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

Can you each work out what shape you have part of on your card? What will the rest of it look like?

What do you think is the same about these two Logic Blocks? What others do you think go with them in the set?

This activity challenges you to make collections of shapes. Can you give your collection a name?

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

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

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

Which of these triangular jigsaws are impossible to finish?

If the yellow equilateral triangle is taken as the unit for area, what size is the hole ?

Using the interactivity, can you make a regular hexagon from yellow triangles the same size as a regular hexagon made from green triangles ?

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.

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

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?

Nick Lord says "This problem encapsulates for me the best features of the NRICH collection."

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

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.

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

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