How many balls of modelling clay and how many straws does it take to make these skeleton shapes?
Here are shadows of some 3D shapes. What shapes could have made them?
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?
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?
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?
Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?
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?
How many pieces of string have been used in these patterns? Can you describe how you know?
How many loops of string have been used to make these patterns?
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?
Try to picture these buildings of cubes in your head. Can you make them to check whether you had imagined them correctly?
A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?
A variant on the game Alquerque
Move just three of the circles so that the triangle faces in the opposite direction.
Can you cover the camel with these pieces?
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 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?
This second article in the series refers to research about levels of development of spatial thinking and the possible influence of instruction.
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
An activity centred around observations of dots and how we visualise number arrangement patterns.
On which of these shapes can you trace a path along all of its edges, without going over any edge twice?
Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?
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!
What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.
Here's a simple way to make a Tangram without any measuring or ruling lines.
This article looks at levels of geometric thinking and the types of activities required to develop this thinking.
These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?
Can you fit the tangram pieces into the outline of this sports car?
Can you fit the tangram pieces into the outline of this goat and giraffe?
Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?
Can you fit the tangram pieces into the outlines of the workmen?
Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!
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.
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
Which of these dice are right-handed and which are left-handed?
A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.
Reasoning about the number of matches needed to build squares that share their sides.
Can you fit the tangram pieces into the outlines of the watering can and man in a boat?
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?
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 candle and sundial?
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
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.
Can you fit the tangram pieces into the outline of the telescope and microscope?