Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. . . .

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

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

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

Can you create a Latin Square from multiples of a six digit 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?

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

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

32 x 38 = 30 x 40 + 2 x 8; 34 x 36 = 30 x 40 + 4 x 6; 56 x 54 = 50 x 60 + 6 x 4; 73 x 77 = 70 x 80 + 3 x 7 Verify and generalise if possible.

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" .

There are two forms of counting on Vuvv - Zios count in base 3 and Zepts count in base 7. One day four of these creatures, two Zios and two Zepts, sat on the summit of a hill to count the legs of. . . .

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?

When asked how old she was, the teacher replied: My age in years is not prime but odd and when reversed and added to my age you have a perfect square...

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 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?

Number problems for inquiring primary learners.

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

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

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?

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

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

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.

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?

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

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.

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?

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

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?

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

Number problems at primary level that may require determination.

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

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

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?

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

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

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

Using balancing scales what is the least number of weights needed to weigh all integer masses from 1 to 1000? Placing some of the weights in the same pan as the object how many are needed?

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

Number problems at primary level that require careful consideration.

Number problems at primary level to work on with others.

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 strategy dice games to consolidate pupils' understanding of rounding.

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. . . .

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

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

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!