Visualising and representing

problem

Dodecamagic

Age

7 to 11

Challenge level

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?
problem

Child's Play

Age

7 to 11

Challenge level

A toy has a regular tetrahedron, a cube and a base with triangular and square hollows. If you fit a shape into the correct hollow a bell rings. How many times does the bell ring in a complete game?
problem

Green Cube, Yellow Cube

Age

7 to 11

Challenge level

How can you paint the faces of these eight cubes so they can be put together to make a 2 × 2 × 2 cube that is green all over AND a 2 × 2 × 2 cube that is yellow all over?
problem

Map Folding

Age

7 to 11

Challenge level

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?
problem

Trace the Edges

Age

7 to 11

Challenge level

On which of these shapes can you trace a path along all of its edges, without going over any edge twice?
problem

Three Cubed

Age

7 to 11

Challenge level

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

Diagrams

Age

7 to 11

Challenge level

A group activity using visualisation of squares and triangles.
problem

Inside Seven Squares

Age

7 to 11

Challenge level

What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?
problem

A Square in a Circle

Age

7 to 11

Challenge level

What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this area?
problem

A Chain of Eight Polyhedra

Age

7 to 11

Challenge level

Can you arrange the shapes in a chain so that each one shares a face (or faces) that are the same shape as the one that follows it?