What is the sum of all the digits in all the integers from one to one million?

A church hymn book contains 700 hymns. The numbers of the hymns are displayed by combining special small single-digit boards. What is the minimum number of small boards that is 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"?

Number problems at primary level to work on with others.

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 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?

How many six digit numbers are there which DO NOT contain a 5?

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

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

Number problems at primary level that may require determination.

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?

Find the values of the nine letters in the sum: FOOT + BALL = GAME

Number problems at primary level that require careful consideration.

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

A school song book contains 700 songs. The numbers of the songs are displayed by combining special small single-digit boards. What is the minimum number of small boards that is needed?

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

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

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

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

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?

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

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?

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.

How many positive integers less than or equal to 4000 can be written down without using the digits 7, 8 or 9?

Take the numbers 1, 2, 3, 4 and 5 and imagine them written down in every possible order to give 5 digit numbers. Find the sum of the resulting numbers.

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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

When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .

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

Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.

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?

Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?

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

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

There are six numbers written in five different scripts. Can you sort out which is which?

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

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

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

Number problems for inquiring primary learners.

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

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

You have two sets of the digits 0 – 9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?

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.

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

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?