What two-digit numbers can you make with these two dice? What can't you make?

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

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

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 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?

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

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

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

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

What happens when you round these three-digit numbers to the nearest 100?

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

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.

Number problems at primary level that may require resilience.

Number problems at primary level that require careful consideration.

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?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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?

Can you substitute numbers for the letters in these sums?

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

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

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?

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.

More upper primary number sense and place value tasks.

Dicey Operations for an adult and child. Can you get close to 1000 than your partner?

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

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

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

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.

Number problems for inquiring primary learners.

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.

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,. . . .

This is a game for two players. What must you subtract to remove the rolled 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?

Number problems at primary level to work on with others.

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

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

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?

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

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

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

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

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.