In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?

Can you solve the clues to find out who's who on the friendship graph?

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

There are lots of different methods to find out what the shapes are worth - how many can you find?

Investigate how networks can be used to solve a problem for the 18th Century inhabitants of Konigsberg.

See if you can anticipate successive 'generations' of the two animals shown here.

99% of people who have measles have spots. Ben has spots. Do you think he has measles?

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

Sequences of multiples keep cropping up...

Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?

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

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?

If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?

What's the largest volume of box you can make from a square of paper?

How many winning lines can you make in a three-dimensional version of noughts and crosses?

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.

Can you do a little mathematical detective work to figure out which number has been wiped out?

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?

Match the cumulative frequency curves with their corresponding box plots.

Find the sum of this series of surds.

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

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?

Surprising numerical patterns can be explained using algebra and diagrams...

Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?

Watch the video to see how Charlie works out the sum. Can you adapt his method?

How can you decide if a graph is traversable?

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?

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

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

If you know the perimeter of a right angled triangle, what can you say about the area?

Have you ever wondered what it would be like to race against Usain Bolt?

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

A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?

Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?

Can you use the diagram to prove the AM-GM inequality?

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

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?

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

When I park my car in Mathstown, there are two car parks to choose from. Can you help me to decide which one to use?

Can you work out which spinners were used to generate the frequency charts?

Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?

Can you match each graph to one of the statements?

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

What biological growth processes can you fit to these graphs?

Simple additions can lead to intriguing results...

Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?

Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

Where should runners start the 200m race so that they have all run the same distance by the finish?

Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?