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.

What is the relationship between these first two shapes? Which shape relates to the third one in the same way? Can you explain why?

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

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

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

How many different symmetrical shapes can you make by shading triangles or squares?

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?

Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.

A triangle ABC resting on a horizontal line is "rolled" along the line. Describe the paths of each of the vertices and the relationships between them and the original triangle.

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 work out what kind of rotation produced this pattern of pegs in our pegboard?

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.

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

How many different triangles can you make on a circular pegboard that has nine pegs?

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

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

In how many ways can you fit all three pieces together to make shapes with line symmetry?

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. The task is to move it, without sliding, in a series of turns about the corners so that it. . . .

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 picture where this letter "F" will be on the grid if you flip it in these different ways?

Which of the following cubes can be made from these nets?

Make a flower design using the same shape made out of different sizes of paper.

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

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

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

Here's a simple way to make a Tangram without any measuring or ruling lines.

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

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 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?

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

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

A train leaves on time. After it has gone 8 miles (at 33mph) the driver looks at his watch and sees that the hour hand is exactly over the minute hand. When did the train leave the station?

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!

Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?

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

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

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

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

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

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

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

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

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

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?

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

Can you fit the tangram pieces into the outline of Little Ming playing the board game?