See if you can anticipate successive 'generations' of the two animals shown here.

Can you work out how these polygon pictures were drawn, and use that to figure out their angles?

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.

How can you make an angle of 60 degrees by folding a sheet of paper twice?

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

Join pentagons together edge to edge. Will they form a ring?

The image in this problem is part of a piece of equipment found in the playground of a school. How would you describe it to someone over the phone?

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

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?

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

Can you maximise the area available to a grazing goat?

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

A cheap and simple toy with lots of mathematics. Can you interpret the images that are produced? Can you predict the pattern that will be produced using different wheels?

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

Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.

Given a 2 by 2 by 2 skeletal cube with one route `down' the cube. How many routes are there from A to B?

A rectangular field has two posts with a ring on top of each post. There are two quarrelsome goats and plenty of ropes which you can tie to their collars. How can you secure them so they can't. . . .

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. . . .

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

Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of. . . .

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

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 fit the tangram pieces into the outlines of Wai Ping, Wu Ming and Chi Wing?

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.

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

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

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?

Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?

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

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

ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.

If you move the tiles around, can you make squares with different coloured edges?

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

A half-cube is cut into two pieces by a plane through the long diagonal and at right angles to it. Can you draw a net of these pieces? Are they identical?

Can you fit the tangram pieces into the outline of the playing piece?

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?

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

Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?

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

At the time of writing the hour and minute hands of my clock are at right angles. How long will it be before they are at right angles again?

Can you fit the tangram pieces into the outlines of Mah Ling and Chi Wing?

Can you fit the tangram pieces into the silhouette of the junk?

Can you fit the tangram pieces into the outline of the plaque design?

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

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.

Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?

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