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

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

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 workmen?

Can you fit the tangram pieces into the outlines of the watering can and man in a boat?

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

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

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

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

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?

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?

What shape is made when you fold using this crease pattern? Can you make a ring design?

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

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?

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

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 Fung at the table?

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

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 Mai Ling?

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

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

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 Mai Ling and Chi Wing?

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 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?

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 chairs?

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

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

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

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

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

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

Imagine a 4 by 4 by 4 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will not have holes drilled through them?

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?

I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?

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?

Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?

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

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

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 the rocket?

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