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. . . .

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

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

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

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

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?

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.

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.

This article for the young and old talks about the origins of our number system and the important role zero has to play in it.

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

Number problems for inquiring primary learners.

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. . . .

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?

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?

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.

We are used to writing numbers in base ten, using 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Eg. 75 means 7 tens and five units. This article explains how numbers can be written in any number base.

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

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 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?

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

Number problems at primary level to work on with others.

Number problems at primary level that may require resilience.

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?

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

Amazing as it may seem the three fives remaining in the following `skeleton' are sufficient to reconstruct the entire long division sum.

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!

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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?

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

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

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?

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

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

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

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.

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?

Number problems at primary level that require careful consideration.

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

Explore the relationship between simple linear functions and their graphs.

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

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

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.