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. . . .

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?

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. . . .

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

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

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

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?

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

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?

Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?

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...

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

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?

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

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

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

Four strategy dice games to consolidate pupils' understanding of rounding.

Explore the relationship between simple linear functions and their graphs.

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

Number problems for inquiring primary learners.

Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

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

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" .

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.

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.

Number problems at primary level that require careful consideration.

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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?

Number problems at primary level to work on with others.

Number problems at primary level that may require determination.

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

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?

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

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

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

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.

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?

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

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. . . .

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

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

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)?

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?

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!