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?

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.

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.

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

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

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?

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

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?

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

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. . . .

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

A useful visualising exercise which offers opportunities for discussion and generalising, and which could be used for thinking about the formulae needed for generating the results on a spreadsheet.

This article is based on some of the ideas that emerged during the production of a book which takes visualising as its focus. We began to identify problems which helped us to take a structured view. . . .

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

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

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

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?

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

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?

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

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

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

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?

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

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?

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

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.

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

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

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?

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

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

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.

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

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?

Can you find a way of counting the spheres in these arrangements?

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

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

This article for teachers discusses examples of problems in which there is no obvious method but in which children can be encouraged to think deeply about the context and extend their ability to. . . .

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 game for 2 people. Take turns joining two dots, until your opponent is unable to move.

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

Think of a number, square it and subtract your starting number. Is the number youâ€™re left with odd or even? How do the images help to explain this?

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

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