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,. . . .

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 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?

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?

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?

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

Number problems at primary level that may require resilience.

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?

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

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

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?

Number problems for inquiring primary learners.

Number problems at primary level that require careful consideration.

Number problems at primary level to work on with others.

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?

Can you substitute numbers for the letters in these sums?

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?

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

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

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?

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?

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

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?

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.

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

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

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

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

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

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

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

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?

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.

This article, written for teachers, looks at the different kinds of recordings encountered in Primary Mathematics lessons and the importance of not jumping to conclusions!

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?

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.

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

Nowadays the calculator is very familiar to many of us. What did people do to save time working out more difficult problems before the calculator existed?