An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

Ever thought of playing three dimensional Noughts and Crosses? This problem might help you visualise what's involved.

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

Libby Jared helped to set up NRICH and this is one of her favourite problems. It's a problem suitable for a wide age range and best tackled practically.

Lyndon chose this as one of his favourite problems. It is accessible but needs some careful analysis of what is included and what is not. A systematic approach is really helpful.

It looks like we may have some budding bellringers in our midst.

Toni Beardon has chosen this article introducing a rich area for practical exploration and discovery in 3D geometry

Alf Coles writes about how he tries to create 'spaces for exploration' for the students in his classrooms.