Can you substitute numbers for the letters in these sums?

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

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

Number problems at primary level to work on with others.

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?

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

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 that may require resilience.

Number problems at primary level that require careful consideration.

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In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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

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

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?

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

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.

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

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

More upper primary number sense and place value tasks.

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

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

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

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?

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

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?

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.

A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.

Lee was writing all the counting numbers from 1 to 20. She stopped for a rest after writing seventeen digits. What was the last number she wrote?

Can you find the chosen number from the grid using the clues?

I am less than 25. My ones digit is twice my tens digit. My digits add up to an 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?

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

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

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

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

More activities which will help you get a better of sense of numbers and understand what we mean by place value.

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

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.

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

These tasks will help children understand the 'ten-ness' of ten, a fundamental part of place value.

Once a basic number sense has developed for numbers up to ten, a strong 'sense of ten' needs to be developed as a foundation for both place value and mental calculations.

Marion Bond recommends that children should be allowed to use 'apparatus', so that they can physically handle the numbers involved in their calculations, for longer, or across a wider ability band,. . . .

These spinners will give you the tens and unit digits of a number. Can you choose sets of numbers to collect so that you spin six numbers belonging to your sets in as few spins as possible?