Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

32 x 38 = 30 x 40 + 2 x 8; 34 x 36 = 30 x 40 + 4 x 6; 56 x 54 = 50 x 60 + 6 x 4; 73 x 77 = 70 x 80 + 3 x 7 Verify and generalise if possible.

Consider all two digit numbers (10, 11, . . . ,99). In writing down all these numbers, which digits occur least often, and which occur most often ? What about three digit numbers, four digit numbers. . . .

The number 27 is special because it is three times the sum of its digits 27 = 3 (2 + 7). Find some two digit numbers that are SEVEN times the sum of their digits (seven-up numbers)?

Carry out cyclic permutations of nine digit numbers containing the digits from 1 to 9 (until you get back to the first number). Prove that whatever number you choose, they will add to the same total.

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .

This activity involves rounding four-digit numbers to the nearest thousand.

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.

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

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

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

The number 3723(in base 10) is written as 123 in another base. What is that base?

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

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?

What happens when you round these three-digit numbers to the nearest 100?

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?

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

Can you replace the letters with numbers? Is there only one solution in each case?

Using balancing scales what is the least number of weights needed to weigh all integer masses from 1 to 1000? Placing some of the weights in the same pan as the object how many are needed?

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

Nowadays the calculator is very familiar to many of us. What did people do to save time working out more difficult problems before the calculator existed?

Each child in Class 3 took four numbers out of the bag. Who had made the highest even number?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Have a go at balancing this equation. Can you find different ways of doing it?

Four strategy dice games to consolidate pupils' understanding of rounding.

Dicey Operations for an adult and child. Can you get close to 1000 than your partner?

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

Can you work out some different ways to balance this equation?

Number problems at primary level that require careful consideration.

This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.

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

Number problems at primary level that may require determination.

Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

Investigate the different ways these aliens count in this challenge. You could start by thinking about how each of them would write our number 7.

Consider all of the five digit numbers which we can form using only the digits 2, 4, 6 and 8. If these numbers are arranged in ascending order, what is the 512th number?

Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?

This article, written for teachers, looks at the different kinds of recordings encountered in Primary Mathematics lessons and the importance of not jumping to conclusions!

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?