What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

The clues for this Sudoku are the product of the numbers in adjacent squares.

Take any four digit number. Move the first digit to the 'back of the queue' and move the rest along. Now add your two numbers. What properties do your answers always have?

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

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

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

What does this number mean ? Which order of 1, 2, 3 and 4 makes the highest value ? Which makes the lowest ?

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

A car's milometer reads 4631 miles and the trip meter has 173.3 on it. How many more miles must the car travel before the two numbers contain the same digits in the same order?

The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.

Can you explain the surprising results Jo found when she calculated the difference between square numbers?

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

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

All CD Heaven stores were given the same number of a popular CD to sell for £24. In their two week sale each store reduces the price of the CD by 25% ... How many CDs did the store sell at. . . .

In a three-dimensional version of noughts and crosses, how many winning lines can you make?

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

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. . . .

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

Different combinations of the weights available allow you to make different totals. Which totals can you make?

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?

Five children went into the sweet shop after school. There were choco bars, chews, mini eggs and lollypops, all costing under 50p. Suggest a way in which Nathan could spend all his money.

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

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

The number 2.525252525252.... can be written as a fraction. What is the sum of the denominator and numerator?

Use the differences to find the solution to this Sudoku.

Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?

Some 4 digit numbers can be written as the product of a 3 digit number and a 2 digit number using the digits 1 to 9 each once and only once. The number 4396 can be written as just such a product. Can. . . .

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

The area of a square inscribed in a circle with a unit radius is, satisfyingly, 2. What is the area of a regular hexagon inscribed in a circle with a unit radius?

A game for 2 or more people, based on the traditional card game Rummy. Players aim to make two `tricks', where each trick has to consist of a picture of a shape, a name that describes that shape, and. . . .

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

Find the decimal equivalents of the fractions one ninth, one ninety ninth, one nine hundred and ninety ninth etc. Explain the pattern you get and generalise.

Show that is it impossible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units...

Which set of numbers that add to 10 have the largest product?

Which has the greatest area, a circle or a square inscribed in an isosceles, right angle triangle?