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?

Design an arrangement of display boards in the school hall which fits the requirements of different people.

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?

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

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

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

What is the best way to shunt these carriages so that each train can continue its journey?

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

Can you make a 3x3 cube with these shapes made from small cubes?

Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

Can you fit the tangram pieces into the outlines of the candle and sundial?

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

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

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.

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

A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?

Here are more buildings to picture in your mind's eye. Watch out - they become quite complicated!

What is the greatest number of squares you can make by overlapping three squares?

Can you fit the tangram pieces into the outline of Mai Ling?

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

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,. . . .

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

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

Can you cut up a square in the way shown and make the pieces into a triangle?

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

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

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

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!

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?

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 ...

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

Can you work out what is wrong with the cogs on a UK 2 pound coin?

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

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

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.

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?

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

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

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 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 outline of this telephone?

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

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.