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" .

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?

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?

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 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?

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

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

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.

Number problems at primary level that require careful consideration.

Number problems at primary level that may require determination.

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...

Number problems at primary level to work on with others.

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

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. . . .

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

Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?

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

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?

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?

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

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.

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?

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?

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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.

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?

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!

Explore the relationship between simple linear functions and their graphs.

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

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?

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?

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

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

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

Use two dice to generate two numbers with one decimal place. 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?

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.

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

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

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.