This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube?

Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

What is the shape of wrapping paper that you would need to completely wrap this model?

You want to make each of the 5 Platonic solids and colour the faces so that, in every case, no two faces which meet along an edge have the same colour.

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?

What size square should you cut out of each corner of a 10 x 10 grid to make the box that would hold the greatest number of cubes?

We need to wrap up this cube-shaped present, remembering that we can have no overlaps. What shapes can you find to use?

In this problem you have to place four by four magic squares on the faces of a cube so that along each edge of the cube the numbers match.

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?

What is the largest cuboid you can wrap in an A3 sheet of paper?

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

Each of these solids is made up with 3 squares and a triangle around each vertex. Each has a total of 18 square faces and 8 faces that are equilateral triangles. How many faces, edges and vertices. . . .

Design and construct a prototype intercooler which will satisfy agreed quality control constraints.

Can Jo make a gym bag for her trainers from the piece of fabric she has?

Read all about Pythagoras' mathematical discoveries in this article written for students.

What shape would fit your pens and pencils best? How can you make it?

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