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" .

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

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?

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

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

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 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?

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.

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. . . .

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

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?

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

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?

Number problems at primary level to work on with others.

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

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

Number problems at primary level that may require determination.

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?

Number problems at primary level that require careful consideration.

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!

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?

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

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.

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

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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

Explore the relationship between simple linear functions and their graphs.

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

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

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

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

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?

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?

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

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

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

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

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

Number problems for inquiring primary learners.

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?

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.

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?

There are two forms of counting on Vuvv - Zios count in base 3 and Zepts count in base 7. One day four of these creatures, two Zios and two Zepts, sat on the summit of a hill to count the legs of. . . .