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

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?

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

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

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

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

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.

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 work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

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

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

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

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?

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

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

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?

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!

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?

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

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

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

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

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

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

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?

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

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

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

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

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?

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

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.

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?

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?

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.

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

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.

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?