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

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

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

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.

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

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

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

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.

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?

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

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

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?

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

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

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

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

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?

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

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

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?

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?

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

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

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?

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

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

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?

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

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 ...

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

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?

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 convex shapes?

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

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

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

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

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

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

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