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?

Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?

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

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

Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?

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

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?

Try to picture these buildings of cubes in your head. Can you make them to check whether you had imagined them correctly?

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?

Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.

We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?

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 describe a piece of paper clearly enough for your partner to know which piece it is?

Can you split each of the shapes below in half so that the two parts are exactly the same?

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?

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?

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

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

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

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 fit the tangram pieces into the outline of Mai Ling?

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

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

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?

Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?

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?

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

Can you logically construct these silhouettes using the tangram pieces?

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

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

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

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 Little Ming playing the board game?

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

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

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?

What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.

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

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?

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 outline of these rabbits?

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

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?

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

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