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.

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?

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

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?

A car's milometer reads 4631 miles and the trip meter has 173.3 on it. How many more miles must the car travel before the two numbers contain the same digits in the same order?

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

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

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.

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

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?

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

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

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

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?

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 at primary level to work on with others.

Number problems at primary level that may require determination.

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

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.

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

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

Carry out cyclic permutations of nine digit numbers containing the digits from 1 to 9 (until you get back to the first number). Prove that whatever number you choose, they will add to the same total.

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

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

Consider all two digit numbers (10, 11, . . . ,99). In writing down all these numbers, which digits occur least often, and which occur most often ? What about three digit numbers, four digit numbers. . . .

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?

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?

Take the numbers 1, 2, 3, 4 and 5 and imagine them written down in every possible order to give 5 digit numbers. Find the sum of the resulting numbers.

The number 27 is special because it is three times the sum of its digits 27 = 3 (2 + 7). Find some two digit numbers that are SEVEN times the sum of their digits (seven-up numbers)?

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

Number problems at primary level that require careful consideration.

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

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.

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.

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

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

Number problems for inquiring primary learners.

Take any four digit number. Move the first digit to the 'back of the queue' and move the rest along. Now add your two numbers. What properties do your answers always have?

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

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

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. . . .

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.

Consider all of the five digit numbers which we can form using only the digits 2, 4, 6 and 8. If these numbers are arranged in ascending order, what is the 512th number?

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