Straight lines are drawn from each corner of a square to the mid points of the opposite sides. Express the area of the octagon that is formed at the centre as a fraction of the area of the square.

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

Follow the instructions and you can take a rectangle, cut it into 4 pieces, discard two small triangles, put together the remaining two pieces and end up with a rectangle the same size. Try it!

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. . . .

Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?

On the grid provided, we can draw lines with different gradients. How many different gradients can you find? Can you arrange them in order of steepness?

Investigate what happens to the equation of different lines when you translate them. Try to predict what will happen. Explain your findings.

How far have these students walked by the time the teacher's car reaches them after their bus broke down?

Collect as many diamonds as you can by drawing three straight lines.

Investigate what happens to the equations of different lines when you reflect them in one of the axes. Try to predict what will happen. Explain your findings.

I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?

Explore the relationship between resistance and temperature

Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?

When I park my car in Mathstown, there are two car parks to choose from. Which car park should I use?

Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.

How does the position of the line affect the equation of the line? What can you say about the equations of parallel lines?

You can move the 4 pieces of the jigsaw and fit them into both outlines. Explain what has happened to the missing one unit of area.

In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

Two cyclists, practising on a track, pass each other at the starting line and go at constant speeds... Can you find lap times that are such that the cyclists will meet exactly half way round the. . . .

Can you adjust the curve so the bead drops with near constant vertical velocity?

Looking at the graph - when was the person moving fastest? Slowest?

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.

Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its vertical and horizontal movement at each stage.

In a snooker game the brown ball was on the lip of the pocket but it could not be hit directly as the black ball was in the way. How could it be potted by playing the white ball off a cushion?

If you take two tests and get a marks out of a maximum b in the first and c marks out of d in the second, does the mediant (a+c)/(b+d)lie between the results for the two tests separately.