What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

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

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

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?

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

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?

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?

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?

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 Little Fung at the table?

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

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

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?

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

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?

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

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

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

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

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

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

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 ...

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

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

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

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

How can you paint the faces of these eight cubes so they can be put together to make a 2 x 2 cube that is green all over AND a 2 x 2 cube that is yellow all over?

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

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

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

Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.

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

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

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

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?

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 chairs?

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

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

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

One face of a regular tetrahedron is painted blue and each of the remaining faces are painted using one of the colours red, green or yellow. How many different possibilities are there?

What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?

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

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

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?

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?