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?

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

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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

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

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?

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

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 substitute numbers for the letters in these sums?

Number problems at primary level that require careful consideration.

Number problems at primary level that may require resilience.

Number problems at primary level to work on with others.

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?

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

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

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.

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

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?

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

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?

What is the sum of all the digits in all the integers from one to one million?

Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?

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

Find the values of the nine letters in the sum: FOOT + BALL = GAME

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?

Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E

How many solutions can you find to this sum? Each of the different letters stands for a different number.

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

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.

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

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!

This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.

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?

The number 3723(in base 10) is written as 123 in another base. What is that base?

Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .

The Number Jumbler can always work out your chosen symbol. Can you work out how?

Number problems for inquiring primary learners.

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

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

How many positive integers less than or equal to 4000 can be written down without using the digits 7, 8 or 9?

Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?

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

How many six digit numbers are there which DO NOT contain a 5?