Number problems at primary level that may require resilience.

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.

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

Number problems at primary level to work on with others.

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?

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?

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

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.

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

Number problems at primary level that require careful consideration.

Can you substitute numbers for the letters in these sums?

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?

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?

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

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

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.

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?

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

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

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

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

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.

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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.

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

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

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?

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?

Number problems for inquiring primary learners.

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

More upper primary number sense and place value tasks.

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?

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.

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

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

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

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

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.

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

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" .

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?

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

Investigate the different ways these aliens count in this challenge. You could start by thinking about how each of them would write our number 7.