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?

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

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

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

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. . . .

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.

This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.

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

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

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

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.

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

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

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?

Make a cube out of straws and have a go at this practical challenge.

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?

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.

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

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?

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

Can you find ways of joining cubes together so that 28 faces are visible?

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?

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

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

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?

Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?

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?

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!

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.

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

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?

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 fit the tangram pieces into the outline of Little Fung at the table?

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

Can you fit the tangram pieces into the outlines of these people?

Can you fit the tangram pieces into the outlines of these clocks?

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

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

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?

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

The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?

Can you fit the tangram pieces into the outline of the child walking home from school?

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

Blue Flibbins are so jealous of their red partners that they will not leave them on their own with any other bue Flibbin. What is the quickest way of getting the five pairs of Flibbins safely to. . . .

Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.

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