What can you see? What do you notice? What questions can you ask?

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

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

Bilbo goes on an adventure, before arriving back home. Using the information given about his journey, can you work out where Bilbo lives?

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

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

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

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

A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

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

A game for 2 people. Take turns joining two dots, until your opponent is unable to move.

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

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

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

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?

A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?

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?

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

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

Can you fit the tangram pieces into the outline of Mah Ling?

Can you fit the tangram pieces into the outline of the sports car?

I found these clocks in the Arts Centre at the University of Warwick intriguing - do they really need four clocks and what times would be ambiguous with only two or three of them?

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

Can you logically construct these silhouettes using the tangram pieces?

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

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

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

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

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

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

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

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

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 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 Mah Ling and Chi Wing?

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

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?

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

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

Imagine a 4 by 4 by 4 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will not have holes drilled through them?

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?

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?

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. . . .

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.

Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube so that the surface area of the remaining solid is the same as the surface area of the original?

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