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

Number problems at primary level to work on with others.

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" .

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?

Number problems at primary level that may require determination.

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

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

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?

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?

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

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

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

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

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 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.

Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?

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

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

Amazing as it may seem the three fives remaining in the following `skeleton' are sufficient to reconstruct the entire long division sum.

Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. . . .

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?

Number problems at primary level that require careful consideration.

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

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

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

Explore the relationship between simple linear functions and their graphs.

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

Number problems for inquiring primary learners.

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?

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?

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

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?

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

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?

When asked how old she was, the teacher replied: My age in years is not prime but odd and when reversed and added to my age you have a perfect square...

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

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

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?

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

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.

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

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.

There are nasty versions of this dice game but we'll start with the nice ones...

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

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

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!