Can you picture where this letter "F" will be on the grid if you flip it in these different ways?

What is the relationship between these first two shapes? Which shape relates to the third one in the same way? Can you explain why?

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

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

How many different symmetrical shapes can you make by shading triangles or squares?

A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.

Can you work out what kind of rotation produced this pattern of pegs in our pegboard?

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!

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.

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

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 ...

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

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?

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

A triangle ABC resting on a horizontal line is "rolled" along the line. Describe the paths of each of the vertices and the relationships between them and the original triangle.

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?

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

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

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

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

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

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

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

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

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.

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.

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

The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. The task is to move it, without sliding, in a series of turns about the corners so that it. . . .

In how many ways can you fit all three pieces together to make shapes with line symmetry?

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

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

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

Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.

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?

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

When dice land edge-up, we usually roll again. But what if we didn't...?

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.

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 camel and giraffe?

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

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

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?

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