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

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

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

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

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

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

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

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

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

Can you work out what is wrong with the cogs on a UK 2 pound coin?

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

This article for teachers describes a project which explores the power of storytelling to convey concepts and ideas to children.

What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.

Can you find a way of counting the spheres in these arrangements?

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?

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

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

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

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.

Which of these dice are right-handed and which are left-handed?

Can you arrange the shapes in a chain so that each one shares a face (or faces) that are the same shape as the one that follows it?

An extension of noughts and crosses in which the grid is enlarged and the length of the winning line can to altered to 3, 4 or 5.

Reasoning about the number of matches needed to build squares that share their sides.

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.

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?

ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR?

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

On which of these shapes can you trace a path along all of its edges, without going over any edge twice?

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

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

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

Can you make a 3x3 cube with these shapes made from small cubes?

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

I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?

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 chairs?

Have a look at these photos of different fruit. How many do you see? How did you count?

Can you logically construct these silhouettes using the tangram pieces?

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.

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?

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

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

Can you fit the tangram pieces into the outline of Granma T?

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