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

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

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 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 does the overlap of these two shapes look like? Try picturing it in your head and then use some cut-out shapes to test your prediction.

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?

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?

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

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

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

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 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 outlines of the people?

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?

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 outlines of the convex shapes?

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.

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?

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

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

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

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

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

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

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

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

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

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

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

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

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 outline of this teacup?

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 clock?

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

Why do you think that the red player chose that particular dot in this game of Seeing Squares?

Can you logically construct these silhouettes using the tangram pieces?

What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?

Can you fit the tangram pieces into the outlines of the camel and giraffe?

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