Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

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.

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

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

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

This second article in the series refers to research about levels of development of spatial thinking and the possible influence of instruction.

How many different triangles can you make on a circular pegboard that has nine pegs?

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.

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

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?

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 ...

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

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

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

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

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

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

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

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

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

Imagine a 3 by 3 by 3 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will have holes drilled through them?

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

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

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?

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

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

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

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.

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

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!

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

Can you fit the tangram pieces into the outline of the child walking home from school?

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 telephone?

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 Little Fung at the table?

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

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 fit the tangram pieces into the outlines of these clocks?

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 outlines of these people?

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

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