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

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

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

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

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

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 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 people?

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

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 Mah Ling?

A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?

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?

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

Try to picture these buildings of cubes in your head. Can you make them to check whether you had imagined them correctly?

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

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

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

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

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

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

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

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 fit the tangram pieces into the outline of the candle?

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 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?

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

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

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

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

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

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

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

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?

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?

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 telephone?

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 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 outline of the dragon?

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

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

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?

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