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 mentally fit the 7 SOMA pieces together to make a cube? Can you do it in more than one way?

Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?

Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.

The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?

To avoid losing think of another very well known game where the patterns of play are similar.

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.

Build gnomons that are related to the Fibonacci sequence and try to explain why this is possible.

Can you mark 4 points on a flat surface so that there are only two different distances between them?

Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?

ABC is an equilateral triangle and P is a point in the interior of the triangle. We know that AP = 3cm and BP = 4cm. Prove that CP must be less than 10 cm.

Can you find a rule which relates triangular numbers to square numbers?

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

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.

Can you see how this picture illustrates the formula for the sum of the first six cube numbers?

Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?

Lyndon Baker describes how the Mobius strip and Euler's law can introduce pupils to the idea of topology.

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

Show that all pentagonal numbers are one third of a triangular number.

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

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

A right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates?

Can you find a rule which connects consecutive triangular numbers?

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

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?

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

Imagine you are suspending a cube from one vertex (corner) and allowing it to hang freely. Now imagine you are lowering it into water until it is exactly half submerged. What shape does the surface. . . .

A 3x3x3 cube may be reduced to unit cubes in six saw cuts. If after every cut you can rearrange the pieces before cutting straight through, can you do it in fewer?

A bus route has a total duration of 40 minutes. Every 10 minutes, two buses set out, one from each end. How many buses will one bus meet on its way from one end to the other end?

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?

Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots and a little about prime knots, crossing numbers and. . . .

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?

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. . . .

Some diagrammatic 'proofs' of algebraic identities and inequalities.

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

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. . . .

What is the shape of wrapping paper that you would need to completely wrap this model?

A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.

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

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?

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?

In the game of Noughts and Crosses there are 8 distinct winning lines. How many distinct winning lines are there in a game played on a 3 by 3 by 3 board, with 27 cells?

When dice land edge-up, we usually roll again. But what if we didn't...?

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

A useful visualising exercise which offers opportunities for discussion and generalising, and which could be used for thinking about the formulae needed for generating the results on a spreadsheet.

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.

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