Some children were playing a game. Make a graph or picture to show how many ladybirds each child had.

A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

Charlie thinks that a six comes up less often than the other numbers on the dice. Have a look at the results of the test his class did to see if he was right.

Use the two sets of data to find out how many children there are in Classes 5, 6 and 7.

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

Here are four tiles. They can be arranged in a 2 by 2 square so that this large square has a green edge. If the tiles are moved around, we can make a 2 by 2 square with a blue edge... Now try. . . .

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

Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?

Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves. . . .

There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you. . . .

Two buses leave at the same time from two towns Shipton and Veston on the same long road, travelling towards each other. At each mile along the road are milestones. The buses' speeds are constant. . . .

Sketch the graphs of y = sin x and y = tan x and some straight lines. Prove some inequalities.

Draw the graph of a continuous increasing function in the first quadrant and horizontal and vertical lines through two points. The areas in your sketch lead to a useful formula for finding integrals.

Harry and Chiu both reasoned through their solutions clearly, and Chiu demonstrates the power of diagrams.

Derek offered some interesting insights into this problem and explained it nicely too. Chen and Andrei took a slightly different approach.

Angus gives a very good account of how matrices, probability and graph theory are used in his solution.

Written for teachers, this article discusses mathematical representations and takes, in the second part of the article, examples of reception children's own representations.

This article for teachers describes a project which explores thepower of storytelling to convey concepts and ideas to children.

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.

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

This article introduces complex numbers, brings together into one bigger 'picture' some closely related elementary ideas like vectors and the exponential and trigonometric functions and their derivatives and proves that e^(i pi)= -1.