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

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

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

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

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

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

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

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

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

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?

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

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

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 outline of the house?

Can you visualise what shape this piece of paper will make when it is folded?

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

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?

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

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

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?

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

Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?

This article looks at levels of geometric thinking and the types of activities required to develop this thinking.

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 the sports car?

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 Little Fung at the table?

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

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 plaque design?

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

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

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

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 Mah Ling and Chi Wing?

Can you fit the tangram pieces into the outline of the playing piece?

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

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

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

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

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

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

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

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