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

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?

Make a flower design using the same shape made out of different sizes of paper.

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 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 outline of the house?

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

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

Exploring and predicting folding, cutting and punching holes and making spirals.

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

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 ...

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

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

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

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

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

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

Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?

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

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

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

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

Here are more buildings to picture in your mind's eye. Watch out - they become quite complicated!

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

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

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

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 telephone?

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

What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

Can you fit the tangram pieces into the outline of the plaque design?

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?

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

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

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

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

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

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

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

Imagine a 4 by 4 by 4 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will not have holes drilled through them?

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

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

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 Little Ming?

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