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

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

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

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

Sequences of multiples keep cropping up...

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

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

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.

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

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?

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.

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?

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

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

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.

Various solids are lowered into a beaker of water. How does the water level rise in each case?

Infographics are a powerful way of communicating statistical information. Can you come up with your own?

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

Which numbers can we write as a sum of square numbers?

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

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

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.

Six samples were taken from two distributions but they got muddled up. Can you work out which list is which?

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

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

Match the cumulative frequency curves with their corresponding box plots.

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

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

Can you find the area of a parallelogram defined by two vectors?

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

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?

Can you see how this picture illustrates the formula for the sum of the first six cube numbers?

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

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

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

We are given a regular icosahedron having three red vertices. Show that it has a vertex that has at least two red neighbours.

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

How much of the field can the animals graze?

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?

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