First of all, pick the number of times a week that you would like to eat chocolate. Multiply this number by 2...

Can you find the lap times of the two cyclists travelling at constant speeds?

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

Can you hit the target functions using a set of input functions and a little calculus and algebra?

Brian swims at twice the speed that a river is flowing, downstream from one moored boat to another and back again, taking 12 minutes altogether. How long would it have taken him in still water?

Derive an equation which describes satellite dynamics.

Fancy learning a bit more about rates of reaction, but don't know where to look? Come inside and find out more...

What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?

Attach weights of 1, 2, 4, and 8 units to the four attachment points on the bar. Move the bar from side to side until you find a balance point. Is it possible to predict that position?

If a sum invested gains 10% each year how long before it has doubled its value?

If a two digit number has its digits reversed and the smaller of the two numbers is subtracted from the larger, prove the difference can never be prime.

Prove that 3 times the sum of 3 squares is the sum of 4 squares. Rather easier, can you prove that twice the sum of two squares always gives the sum of two squares?

Account of an investigation which starts from the area of an annulus and leads to the formula for the difference of two squares.

Use algebra to reason why 16 and 32 are impossible to create as the sum of consecutive numbers.

Find relationships between the polynomials a, b and c which are polynomials in n giving the sums of the first n natural numbers, squares and cubes respectively.

For which values of n is the Fibonacci number fn even? Which Fibonnaci numbers are divisible by 3?

Prove that the product of the sum of n positive numbers with the sum of their reciprocals is not less than n^2.

Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.

Show there are exactly 12 magic labellings of the Magic W using the numbers 1 to 9. Prove that for every labelling with a magic total T there is a corresponding labelling with a magic total 30-T.

This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.

A 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?

The sums of the squares of three related numbers is also a perfect square - can you explain why?

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

Take a few whole numbers away from a triangle number. If you know the mean of the remaining numbers can you find the triangle number and which numbers were removed?

A task which depends on members of the group noticing the needs of others and responding.

In turn 4 people throw away three nuts from a pile and hide a quarter of the remainder finally leaving a multiple of 4 nuts. How many nuts were at the start?

A sequence of polynomials starts 0, 1 and each poly is given by combining the two polys in the sequence just before it. Investigate and prove results about the roots of the polys.

The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target?

Five equations... five unknowns... can you solve the system?

Janine noticed, while studying some cube numbers, that if you take three consecutive whole numbers and multiply them together and then add the middle number of the three, you get the middle number. . . .

To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...

What is the total number of squares that can be made on a 5 by 5 geoboard?

An algebra task which depends on members of the group noticing the needs of others and responding.

Take a complicated fraction with the product of five quartics top and bottom and reduce this to a whole number. This is a numerical example involving some clever algebra.

A mother wants to share a sum of money by giving each of her children in turn a lump sum plus a fraction of the remainder. How can she do this in order to share the money out equally?

There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?

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

By proving these particular identities, prove the existence of general cases.

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

A circle of radius r touches two sides of a right angled triangle, sides x and y, and has its centre on the hypotenuse. Can you prove the formula linking x, y and r?

Take any two numbers between 0 and 1. Prove that the sum of the numbers is always less than one plus their product?

Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.

What would you get if you continued this sequence of fraction sums? 1/2 + 2/1 = 2/3 + 3/2 = 3/4 + 4/3 =

To break down an algebraic fraction into partial fractions in which all the denominators are linear and all the numerators are constants you sometimes need complex numbers.

Can you find the value of this function involving algebraic fractions for x=2000?