Sets of shapes

problem

Building with solid shapes

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?

problem

Data shapes

Age

5 to 7

Challenge level

Sara and Will were sorting some pictures of shapes on cards. "I'll collect the circles," said Sara. "I'll take the red ones," answered Will. Can you see any cards they would both want?

problem

Dienes' logiblocs

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?

problem

Skeleton shapes

Age

5 to 7

Challenge level

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

problem

Triangle animals

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?

problem

Shadow play

Age

5 to 7

Challenge level

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

problem

Four-triangle arrangements

Age

5 to 7

Challenge level

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

article

From one shape to another

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.

problem

Tessellating triangles

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?

problem

Tri-five

Age

7 to 11

Challenge level

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

problem

Let us reflect

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?

problem

Cereal packets

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?

problem

Face painting

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.

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

Diagonal trace

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?

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

Cut nets

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?

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?

problem

Clock hands

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.

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Number and algebra

Geometry and measure

Probability and statistics

Working mathematically

Advanced mathematics

For younger learners

Sets of shapes

Building with solid shapes

Data shapes

Dienes' logiblocs

Skeleton shapes

Triangle animals

Shadow play

Four-triangle arrangements

From one shape to another

Tessellating triangles

Tri-five

Let us reflect

Cereal packets

Face painting

Child's play

Diagonal trace

Trace the edges

Cut nets

A chain of eight polyhedra

Clock hands