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?

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

A cylindrical helix is just a spiral on a cylinder, like an ordinary spring or the thread on a bolt. If I turn a left-handed helix over (top to bottom) does it become a right handed helix?

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 explain why it is impossible to construct this triangle?

Triangles are formed by joining the vertices of a skeletal cube. How many different types of triangle are there? How many triangles altogether?

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. . . .

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.

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

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?

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

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 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.

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

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

Can you fit the tangram pieces into the outline of this shape. How would you describe it?

Mathematics is the study of patterns. Studying pattern is an opportunity to observe, hypothesise, experiment, discover and create.

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

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

Show that among the interior angles of a convex polygon there cannot be more than three acute angles.

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

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

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

Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?

Blue Flibbins are so jealous of their red partners that they will not leave them on their own with any other bue Flibbin. What is the quickest way of getting the five pairs of Flibbins safely to. . . .

The second in a series of articles on visualising and modelling shapes in the history of astronomy.

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

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

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 fit the tangram pieces into the outline of Little Ming?

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

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

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?

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

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 ...

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

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?

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

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

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

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 this goat and giraffe?

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

This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .