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.

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?

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?

Alf describes how the Gattegno chart helped a class of 7-9 year olds gain an awareness of place value and of the inverse relationship between multiplication and division.

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

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.

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" .

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?

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

Number problems at primary level that may require resilience.

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

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

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?

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

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

Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?

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.

The Number Jumbler can always work out your chosen symbol. Can you work out how?

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

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

Number problems at primary level to work on with others.

Where should you start, if you want to finish back where you started?

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

This article for primary teachers expands on the key ideas which underpin early number sense and place value, and suggests activities to support learners as they get to grips with these ideas.

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?

This article develops the idea of 'ten-ness' as an important element of place value.

One of the key ideas associated with place value is that the position of a digit affects its value. These activities support children in understanding this idea.

These tasks will help learners develop their understanding of place value, particularly giving them opportunities to express numbers as amounts.

This feature aims to support you in developing children's early number sense and understanding of place value.

More upper primary number sense and place value tasks.

Try out some calculations. Are you surprised by the results?

Use your knowledge of place value to try to win this game. How will you maximise your score?

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

Try out this number trick. What happens with different starting numbers? What do you notice?

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E

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

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. . . .

Find the sum of all three-digit numbers each of whose digits is odd.

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.

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?

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

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?

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.

In this article, Alf outlines six activities using the Gattegno chart, which help to develop understanding of place value, multiplication and division.