How will you go about finding all the jigsaw pieces that have one peg and one hole?

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.

What is the best way to shunt these carriages so that each train can continue its journey?

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

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. . . .

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

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Design an arrangement of display boards in the school hall which fits the requirements of different people.

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

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.

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

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.

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.

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

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?

A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

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

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

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

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

How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?

What is the greatest number of squares you can make by overlapping three squares?

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

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?

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

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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 outlines of the lobster, yacht and cyclist?

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

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

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

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

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

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

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

How many different triangles can you make on a circular pegboard that has nine pegs?

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

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

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

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

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

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 Wai Ping, Wu Ming and Chi Wing?