Challenge Level

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

Challenge Level

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

Challenge Level

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.

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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.

Challenge Level

Under what circumstances can you rearrange a big square to make three smaller squares?

Challenge Level

Using a ruler, pencil and compasses only, it is possible to construct a square inside any triangle so that all four vertices touch the sides of the triangle.

Challenge Level

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

Challenge Level

Can you make sense of these three proofs of Pythagoras' Theorem?

Challenge Level

Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?

Challenge Level

Can you work out how to produce different shades of pink paint?

Challenge Level

The length AM can be calculated using trigonometry in two different ways. Create this pair of equivalent calculations for different peg boards, notice a general result, and account for it.

Challenge Level

Can you find an efficent way to mix paints in any ratio?

Challenge Level

Medieval stonemasons used a method to construct octagons using ruler and compasses... Is the octagon regular? Proof please.

Challenge Level

Move the point P to see how P' moves. Then use your insights to calculate a missing length.

Challenge Level

Some of the numbers have fallen off Becky's number line. Can you figure out what they were?

Challenge Level

Kyle and his teacher disagree about his test score - who is right?

Challenge Level

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?

Challenge Level

Complex numbers can be represented graphically using an Argand diagram. This problem explains more...

Challenge Level

The farmers want to redraw their field boundary but keep the area the same. Can you advise them?

Week 2

How well can you estimate angles? Playing this game could improve your skills.

Challenge Level

A dot starts at the point (1,0) and turns anticlockwise. Can you estimate the height of the dot after it has turned through 45 degrees? Can you calculate its height?

Challenge Level

The sine of an angle is equal to the cosine of its complement. Can you explain why and does this rule extend beyond angles of 90 degrees?

Challenge Level

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

Use the applet to explore the area of a parallelogram and how it relates to vectors.

Challenge Level

Use these four dominoes to make a square that has the same number of dots on each side.

Challenge Level

Can you devise a system for making sense of complex multiplication?

Challenge Level

Let's go further and see what happens when we multiply two complex numbers together!

Challenge Level

What happens when we multiply a complex number by a real or an imaginary number?

Use the applet to make some squares. What patterns do you notice in the coordinates?

Challenge Level

Can you explain what is happening and account for the values being displayed?

Challenge Level

Can you work out the fraction of the original triangle that is covered by the inner triangle?

Challenge Level

A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .

Move the corner of the rectangle. Can you work out what the purple number represents?

Challenge Level

Take any triangle, and construct squares on each of its sides. What do you notice about the areas of the new triangles formed?

Challenge Level

Draw some angles inside a rectangle. What do you notice? Can you prove it?

Challenge Level

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

Challenge Level

If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.

Challenge Level

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?

Challenge Level

Can you find triangles on a 9-point circle? Can you work out their angles?

Challenge Level

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?

Challenge Level

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Challenge Level

Make five different quadrilaterals on a nine-point pegboard, without using the centre peg. Work out the angles in each quadrilateral you make. Now, what other relationships you can see?

Challenge Level

An environment that enables you to investigate tessellations of regular polygons