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.

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

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

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

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. . . .

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

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.

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

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

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

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

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

Can you fit the tangram pieces into the outline of this telephone?

Can you fit the tangram pieces into the outline of Little Ming playing the board game?

The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?

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.

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

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

Can you fit the tangram pieces into the outline of Little Fung at the table?

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

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

Can you fit the tangram pieces into the outline of the child walking home from school?

Can you fit the tangram pieces into the outlines of these clocks?

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

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

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.

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 ...

Here's a simple way to make a Tangram without any measuring or ruling lines.

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

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

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

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

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

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

Can you fit the tangram pieces into the outline of Little Ming?

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

How many different ways can I lay 10 paving slabs, each 2 foot by 1 foot, to make a path 2 foot wide and 10 foot long from my back door into my garden, without cutting any of the paving slabs?

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?

Exchange the positions of the two sets of counters in the least possible number of moves

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

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 outline of Wai Ping, Wah Ming and Chi Wing?

Can you fit the tangram pieces into the outline of the telescope and microscope?

Can you fit the tangram pieces into the outline of these rabbits?