The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

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

Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

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?

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.

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

A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

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.

A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

Move just three of the circles so that the triangle faces in the opposite direction.

Eight children each had a cube made from modelling clay. They cut them into four pieces which were all exactly the same shape and size. Whose pieces are the same? Can you decide who made each set?

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.

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

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 happens when you try and fit the triomino pieces into these two grids?

A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.

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

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?

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

Make one big triangle so the numbers that touch on the small triangles add to 10.

Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?

A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?

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. . . .

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

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

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

Can you find a way of representing these arrangements of balls?

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

Create a pattern on the left-hand grid. How could you extend your pattern on the right-hand grid?

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

Can you use the interactive to complete the tangrams in the shape of butterflies?

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?

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 Mai Ling and Chi Wing?

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

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

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!

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

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?

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.