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?

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

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

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?

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

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.

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?

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

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

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.

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

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

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

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

Number problems at primary level that may require determination.

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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?

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. . . .

Number problems at primary level to work on with others.

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

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

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

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?

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

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

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

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?

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

Number problems for inquiring primary learners.

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?

Number problems at primary level that require careful consideration.

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?

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

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

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

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

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?

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)?

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

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

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. . . .