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

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.

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.

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

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?

The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

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

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 butterfly?

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. . . .

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

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.

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

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

A Hamiltonian circuit is a continuous path in a graph that passes through each of the vertices exactly once and returns to the start. How many Hamiltonian circuits can you find in these graphs?

This article is based on some of the ideas that emerged during the production of a book which takes visualising as its focus. We began to identify problems which helped us to take a structured view. . . .

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

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

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

If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.

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

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?

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.

A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.

This article for teachers discusses examples of problems in which there is no obvious method but in which children can be encouraged to think deeply about the context and extend their ability to. . . .

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

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

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

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?

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

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

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

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 Granma T?

Can you cross each of the seven bridges that join the north and south of the river to the two islands, once and once only, without retracing your steps?

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

The reader is invited to investigate changes (or permutations) in the ringing of church bells, illustrated by braid diagrams showing the order in which the bells are rung.

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

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 the camel and giraffe?

Can you logically construct these silhouettes using the tangram pieces?

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?

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

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

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

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

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

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

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