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?

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?

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.

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?

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.

Number problems at primary level to work on with others.

Number problems at primary level that may require resilience.

Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain. . . .

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?

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. . . .

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

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?

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.

Explore the relationship between simple linear functions and their graphs.

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?

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?

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

Number problems at primary level that require careful consideration.

By selecting digits for an addition grid, what targets can you make?

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

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

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 work out some different ways to balance this equation?

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

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

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

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

What happens when you add a three digit number to its reverse?

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

More upper primary number sense and place value tasks.

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

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

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.

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

This article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.

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

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

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

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

Can you substitute numbers for the letters in these sums?

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

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" .

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?

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.

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. . . .