What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.

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?

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?

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?

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape.

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

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

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?

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?

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

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

What shape is made when you fold using this crease pattern? Can you make a ring design?

Can you visualise what shape this piece of paper will make when it is folded?

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

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

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.

Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?

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

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?

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

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

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

Create a pattern on the left-hand grid. How could you extend your pattern on the right-hand grid?

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

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

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

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

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

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

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?

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

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

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

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

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

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

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

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

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

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

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

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 outlines of the workmen?

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?