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?

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

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

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.

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

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. . . .

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!

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

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?

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

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

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 these people?

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

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 Little Fung at the table?

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

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

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

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

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

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

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?

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

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

Can you fit the tangram pieces into the outline of these convex shapes?

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?

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?

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

Can you fit the tangram pieces into the outline of these rabbits?

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

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

At the time of writing the hour and minute hands of my clock are at right angles. How long will it be before they are at right angles again?

Exchange the positions of the two sets of counters in the least possible number of moves

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

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

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?

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

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

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

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

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 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.

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