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?

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.

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

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

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?

Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?

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?

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

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?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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

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

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

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.

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

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

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

Number problems for inquiring primary learners.

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.

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?

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

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?

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

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?

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

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

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

When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .

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

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.

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

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

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

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

Explore the relationship between simple linear functions and their graphs.

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

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

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?

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.

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?

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

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