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.

Create a pattern on the left-hand grid. How could you extend your pattern on the right-hand grid?

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?

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

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 picture where this letter "F" will be on the grid if you flip it in these different ways?

Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

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

What is the relationship between these first two shapes? Which shape relates to the third one in the same way? Can you explain why?

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

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

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

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

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

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

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?

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?

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

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?

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

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

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

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 Wai Ping, Wah Ming and Chi Wing?

Here are shadows of some 3D shapes. What shapes could have made them?

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

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

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

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

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.

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

Mathematics is the study of patterns. Studying pattern is an opportunity to observe, hypothesise, experiment, discover and create.

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 these people?

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

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

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 Ming?

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

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

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?