Moira is late for school. What is the shortest route she can take from the school gates to the entrance?

Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?

The graph below is an oblique coordinate system based on 60 degree angles. It was drawn on isometric paper. What kinds of triangles do these points form?

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

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?

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?

Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?

Can you give the coordinates of the vertices of the fifth point in the patterm on this 3D grid?

A square of area 3 square units cannot be drawn on a 2D grid so that each of its vertices have integer coordinates, but can it be drawn on a 3D grid? Investigate squares that can be drawn.

Find all the turning points of y=x^{1/x} for x>0 and decide whether each is a maximum or minimum. Give a sketch of the graph.

Plot the graph of x^y = y^x in the first quadrant and explain its properties.

This polar equation is a quadratic. Plot the graph given by each factor to draw the flower.

Amy takes us step-by-step through her solution so we can see exactly how she approached it.

Lucy and Hayley present their solution in a clear way which helps to show the order of the operations they used.

Fred and Matt show that with a little thought, problems that at first seem obscure often can be tackled if we use our imagination and don't panic!

This article describes a practical approach to enhance the teaching and learning of coordinates.

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.

This introduction to polar coordinates describes what is an effective way to specify position. This article explains how to convert between polar and cartesian coordinates and also encourages the creation of some attractive curves from some relatively easy equations.

Scientist Bryan Rickett has a vision of the future - and it is one in which self-parking cars prowl the tarmac plains, hunting down suitable parking spots and manoeuvring elegantly into them.