A cheap and simple toy with lots of mathematics. Can you interpret the images that are produced? Can you predict the pattern that will be produced using different wheels?

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

The image in this problem is part of a piece of equipment found in the playground of a school. How would you describe it to someone over the phone?

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.

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

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

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

What can you see? What do you notice? What questions can you ask?

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?

Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?

What is the shape of wrapping paper that you would need to completely wrap this model?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

I found these clocks in the Arts Centre at the University of Warwick intriguing - do they really need four clocks and what times would be ambiguous with only two or three of them?

This is the first article in a series which aim to provide some insight into the way spatial thinking develops in children, and draw on a range of reported research. The focus of this article is the. . . .

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

Can you fit the tangram pieces into the outlines of the convex shapes?

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?

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.

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

Lyndon Baker describes how the Mobius strip and Euler's law can introduce pupils to the idea of topology.

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

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

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

Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

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 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?

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.

Mathematics is the study of patterns. Studying pattern is an opportunity to observe, hypothesise, experiment, discover and create.

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

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

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this area?

Can you fit the tangram pieces into the outline of this teacup?

How will you go about finding all the jigsaw pieces that have one peg and one hole?

Why do you think that the red player chose that particular dot in this game of Seeing Squares?

Can you fit the tangram pieces into the outline of the plaque design?

Can you fit the tangram pieces into the silhouette of the junk?

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

Can you fit the tangram pieces into the outline of the playing piece?

Can you fit the tangram pieces into the outline of the clock?

Can you fit the tangram pieces into the outline of Granma T?

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

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

Can you fit the tangram pieces into the outline of the dragon?

Can you fit the tangram pieces into the outlines of Wai Ping, Wu Ming and Chi Wing?

Read about the adventures of Granma T and her grandchildren in this series of stories, accompanied by interactive tangrams.

Can you fit the tangram pieces into the outlines of the camel and giraffe?