Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?

Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?

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

Eight children each had a cube made from modelling clay. They cut them into four pieces which were all exactly the same shape and size. Whose pieces are the same? Can you decide who made each set?

Can you describe a piece of paper clearly enough for your partner to know which piece it is?

Imagine a 3 by 3 by 3 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will have holes drilled through them?

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

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

Try to picture these buildings of cubes in your head. Can you make them to check whether you had imagined them correctly?

We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?

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

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?

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

Move just three of the circles so that the triangle faces in the opposite direction.

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

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?

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 hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?

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

Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?

An activity centred around observations of dots and how we visualise number arrangement patterns.

How many loops of string have been used to make these patterns?

How many pieces of string have been used in these patterns? Can you describe how you know?

Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.

Can you fit the tangram pieces into the outlines of the workmen?

Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?

A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.

Can you fit the tangram pieces into the outline of this goat and giraffe?

Can you fit the tangram pieces into the outlines of the candle and sundial?

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .

What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.

Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.

Here's a simple way to make a Tangram without any measuring or ruling lines.

Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?

This article looks at levels of geometric thinking and the types of activities required to develop this thinking.

Exploring and predicting folding, cutting and punching holes and making spirals.

Which of these dice are right-handed and which are left-handed?

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

Reasoning about the number of matches needed to build squares that share their sides.

Design an arrangement of display boards in the school hall which fits the requirements of different people.

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

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

An extension of noughts and crosses in which the grid is enlarged and the length of the winning line can to altered to 3, 4 or 5.

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

Can you fit the tangram pieces into the outline of this sports car?

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.