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

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

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?

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?

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?

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

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?

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

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

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

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?

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

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

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

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

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?

Number problems for inquiring primary learners.

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.

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

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.

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.

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

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?

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

Can you substitute numbers for the letters in these sums?

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

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

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

More upper primary number sense and place value tasks.

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.

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

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.

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

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.

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,. . . .

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

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

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?

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

Number problems at primary level to work on with others.

Number problems at primary level that require careful consideration.