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?

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?

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.

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?

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

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

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. . . .

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. . . .

Explore the relationship between simple linear functions and their graphs.

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?

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

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.

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

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?

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?

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

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?

Number problems at primary level to work on with others.

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 that may require resilience.

Number problems at primary level that require careful consideration.

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.

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.

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

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?

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

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.

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 challenge is to make up YOUR OWN alphanumeric. Each letter represents a digit and where the same letter appears more than once it must represent the same digit each time.

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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

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

Can you substitute numbers for the letters in these sums?

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

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

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

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

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

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

What happens when you round these numbers to the nearest whole number?

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

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

More upper primary number sense and place value tasks.

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

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