We have a box of cubes, triangular prisms, cones, cuboids, cylinders and tetrahedrons. Which of the buildings would fall down if we tried to make them?

Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?

How many balls of modelling clay and how many straws does it take to make these skeleton shapes?

If you had 36 cubes, what different cuboids could you make?

Can you make a 3x3 cube with these shapes made from small cubes?

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

Make a cube out of straws and have a go at this practical challenge.

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

The image in this problem is part of a piece of equipment found in the playground of a school. How would you describe it to someone over the phone?

Try making 3D patterns in two dimensions with LOGO

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.

Imagine you are suspending a cube from one vertex (corner) and allowing it to hang freely. Now imagine you are lowering it into water until it is exactly half submerged. What shape does the surface. . . .

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?

A 3x3x3 cube may be reduced to unit cubes in six saw cuts. If after every cut you can rearrange the pieces before cutting straight through, can you do it in fewer?

Learn how to use lookup functions to create exciting interactive Excel spreadsheets.

A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.

Take any whole number between 1 and 999, add the squares of the digits to get a new number. Use a spreadsheet to investigate this sequence.

In a three-dimensional version of noughts and crosses, how many winning lines can you make?

What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse?

Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.

You add 1 to the golden ratio to get its square. How do you find higher powers?

Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.