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

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

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 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?

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

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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?

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

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?

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 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 outline of the house?

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

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

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?

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

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?

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 fit the tangram pieces into the outline of this teacup?

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 ...

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

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

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

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

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

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?

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

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?

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

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

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

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

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

Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

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

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

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

Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube?

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 plaque design?

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

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?