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 ?

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

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

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?

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

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?

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

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

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

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

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?

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

Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400. . . .

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?

The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false?

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?

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, B & C own a half, a third and a sixth of a coin collection. Each grab some coins, return some, then share equally what they had put back, finishing with their own share. How rich are they?

A cyclist and a runner start off simultaneously around a race track each going at a constant speed. The cyclist goes all the way around and then catches up with the runner. He then instantly turns. . . .

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.

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

Let S1 = 1 , S2 = 2 + 3, S3 = 4 + 5 + 6 ,........ Calculate S17.

How good are you at finding the formula for a number pattern ?

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?

Fifteen students had to travel 60 miles. They could use a car, which could only carry 5 students. As the car left with the first 5 (at 40 miles per hour), the remaining 10 commenced hiking along the. . . .

Robert noticed some interesting patterns when he highlighted square numbers in a spreadsheet. Can you prove that the patterns will continue?

Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?

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

Find the five distinct digits N, R, I, C and H in the following nomogram

A moveable screen slides along a mirrored corridor towards a centrally placed light source. A ray of light from that source is directed towards a wall of the corridor, which it strikes at 45 degrees. . . .

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?

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?

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

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

Semicircles are drawn on the sides of a rectangle. Prove that the sum of the areas of the four crescents is equal to the area of the rectangle.

My train left London between 6 a.m. and 7 a.m. and arrived in Paris between 9 a.m. and 10 a.m. At the start and end of the journey the hands on my watch were in exactly the same positions but the. . . .

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

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.

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

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?

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

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

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}.

This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?

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

Can you find a rule which relates triangular numbers to square numbers?