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Mathematics Tools > Sets of shapes

##### Age 5 to 7 Challenge Level:

Here are shadows of some 3D shapes. What shapes could have made them?

##### Age 5 to 7 Challenge Level:

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

##### 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?

##### 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?

##### Age 5 to 7 Challenge Level:

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?

##### Age 7 to 11 Challenge Level:

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

##### Age 7 to 11 Challenge Level:

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.

##### 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?

##### Age 7 to 11 Challenge Level:

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

##### Age 5 to 7 Challenge Level:

This activity challenges you to make collections of shapes. Can you
give your collection a name?

##### Age 7 to 11 Challenge Level:

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

##### Age 5 to 7 Challenge Level:

This problem focuses on Dienes' Logiblocs. What is the same and
what is different about these pairs of shapes? Can you describe the
shapes in the picture?

##### Age 5 to 7 Challenge Level:

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

##### Age 5 to 7 Challenge Level:

How many different shapes can you make by putting four right-
angled isosceles triangles together?

##### Age 7 to 11 Challenge Level:

Find all the different shapes that can be made by joining five
equilateral triangles edge to edge.

##### Age 7 to 11 Challenge Level:

You can trace over all of the diagonals of a pentagon without
lifting your pencil and without going over any more than once. Can
the same thing be done with a hexagon or with a heptagon?

##### Age 7 to 11

Read about David Hilbert who proved that any polygon could be cut up into a certain number of pieces that could be put back together to form any other polygon of equal area.

##### Age 7 to 11 Challenge Level:

Can you make these equilateral triangles fit together to cover the
paper without any gaps between them? Can you tessellate isosceles
triangles?

##### Age 7 to 11 Challenge Level:

This investigation explores using different shapes as the hands of
the clock. What things occur as the the hands move.