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

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?

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

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

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?

This article for teachers describes a project which explores thepower of storytelling to convey concepts and ideas to children.

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

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?

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?

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

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

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?

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

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

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

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,. . . .

Can you fit the tangram pieces into the outline of this shape. How would you describe it?

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

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

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

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

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 the lobster, yacht and cyclist?

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.

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 outlines of the chairs?

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

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

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!

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

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.

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?

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

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

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.

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

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?

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 Mai Ling and Chi Wing?

Can you fit the tangram pieces into the outlines of the watering can and man in a boat?

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!

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.

Can you fit the tangram pieces into the outline of the telescope and microscope?

Find your way through the grid starting at 2 and following these operations. What number do you end on?