How many loops of string have been used to make these patterns?

How many pieces of string have been used in these patterns? Can you describe how you know?

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?

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

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

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?

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 fit the tangram pieces into the outline of these rabbits?

A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

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

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 outline of Little Fung at the table?

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.

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

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

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 the child walking home from school?

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

How many balls of modelling clay and how many straws does it take to make these skeleton shapes?

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

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

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

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 Little Ming playing the board game?

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

A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.

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

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 plaque design?

A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?

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?

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

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

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

What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.

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 this goat and giraffe?

Can you fit the tangram pieces into the outline of this sports car?

A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.

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

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 fit the tangram pieces into the outline of the rocket?

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

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

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

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