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,. . . .

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.

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

A school song book contains 700 songs. The numbers of the songs are displayed by combining special small single-digit boards. What is the minimum number of small boards that is needed?

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

Number problems for inquiring primary learners.

You have two sets of the digits 0 – 9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?

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

This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.

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?

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?

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?

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.

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

Number problems at primary level to work on with others.

Number problems at primary level that require careful consideration.

Number problems at primary level that may require determination.

This activity involves rounding four-digit numbers to the nearest thousand.

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?

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

How would you create the largest possible two-digit even number from the digit I've given you and one of your choice?

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

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

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

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

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

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

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 find the chosen number from the grid using the clues?

A church hymn book contains 700 hymns. The numbers of the hymns are displayed by combining special small single-digit boards. What is the minimum number of small boards that is needed?

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

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?

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

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?

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

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?

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

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

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

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

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

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

This article for the young and old talks about the origins of our number system and the important role zero has to play in it.