Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number...

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

Think of a number... follow the machine's instructions. I know what your number is! Can you explain how I know?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Think of a number, square it and subtract your starting number. Is the number you’re left with odd or even? How do the images help to explain this?

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.

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?

Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?

We asked what was the most interesting fact that you can find out about the number 2009. See the solutions that were submitted.

Some of the numbers have fallen off Becky's number line. Can you figure out what they were?

In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?

An investigation looking at doing and undoing mathematical operations focusing on doubling, halving, adding and subtracting.

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

Can you find some examples when the number of Roman numerals is fewer than the number of Arabic numerals for the same number?

Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?

This challenge is a game for two players. Choose two of the numbers to multiply or divide, then mark your answer on the number line. Can you get four in a row?

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Is there an efficient way to work out how many factors a large number has?

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?

This activity is best done with a whole class or in a large group. Can you match the cards? What happens when you add pairs of the numbers together?

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

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

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

How would you create the largest possible two-digit even number from the digit I've given you and one of your choice?

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

What happens when you round these numbers to the nearest whole number?

Leah and Tom each have a number line. Can you work out where their counters will land? What are the secret jumps they make with their counters?

This big box adds something to any number that goes into it. If you know the numbers that come out, what addition might be going on in the box?

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

Annie and Ben are playing a game with a calculator. What was Annie's secret number?

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.

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?

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

This problem looks at how one example of your choice can show something about the general structure of multiplication.

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...

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

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

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

Children will love creating their own 'number book'DOWNLOAD HERE.

Play this game and see if you can figure out the computer's chosen number.

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?