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

Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape.

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

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

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

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

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

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 the playing piece?

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

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?

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

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 the butterfly?

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 fit the tangram pieces into the outline of this teacup?

How will you go about finding all the jigsaw pieces that have one peg and one hole?

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

Can you fit the tangram pieces into the outlines of the convex shapes?

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

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

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

Make one big triangle so the numbers that touch on the small triangles add to 10.

Can you fit the tangram pieces into the silhouette of the junk?

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

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 Mah Ling?

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

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

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 the telephone?

What is the best way to shunt these carriages so that each train can continue its journey?

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

Why do you think that the red player chose that particular dot in this game of Seeing Squares?

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

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

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

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

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

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

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

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

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

Read about the adventures of Granma T and her grandchildren in this series of stories, accompanied by interactive tangrams.

Can you fit the tangram pieces into the outlines of the camel and giraffe?

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

Can you logically construct these silhouettes using the tangram pieces?

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