Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube so that the surface area of the remaining solid is the same as the surface area of the original?

Can you mentally fit the 7 SOMA pieces together to make a cube? Can you do it in more than one way?

Find all the ways to cut out a 'net' of six squares that can be folded into a cube.

A half-cube is cut into two pieces by a plane through the long diagonal and at right angles to it. Can you draw a net of these pieces? Are they identical?

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

A cube is made from smaller cubes, 5 by 5 by 5, then some of those cubes are removed. Can you make the specified shapes, and what is the most and least number of cubes required ?

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

A tennis ball is served from directly above the baseline (assume the ball travels in a straight line). What is the minimum height that the ball can be hit at to ensure it lands in the service area?

This article, written for teachers, looks at the different kinds of recordings encountered in Primary Mathematics lessons and the importance of not jumping to conclusions!

Nicola has lost a piece of her 3D jigsaw. Can you work out the shape of the missing piece?

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?

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

How can we as teachers begin to introduce 3D ideas to young children? Where do they start? How can we lay the foundations for a later enthusiasm for working in three dimensions?

A task which depends on members of the group working collaboratively to reach a single goal.

Which faces are opposite each other when this net is folded into a cube?

A task which depends on members of the group working collaboratively to reach a single goal.

This is the first article in a series which aim to provide some insight into the way spatial thinking develops in children, and draw on a range of reported research. The focus of this article is the. . . .

Can you make a new type of fair die with 14 faces by shaving the corners off a cube?

This article explores ths history of theories about the shape of our planet. It is the first in a series of articles looking at the significance of geometric shapes in the history of astronomy.

The second in a series of articles on visualising and modelling shapes in the history of astronomy.

How can you represent the curvature of a cylinder on a flat piece of paper?

Use trigonometry to determine whether solar eclipses on earth can be perfect.

How would you design the tiering of seats in a stadium so that all spectators have a good view?

Make an accurate diagram of the solar system and explore the concept of a grand conjunction.

This article (the first of two) contains ideas for investigations. Space-time, the curvature of space and topology are introduced with some fascinating problems to explore.