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

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

Number problems at primary level that require careful consideration.

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

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?

Number problems at primary level to work on with others.

Number problems at primary level that may require resilience.

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?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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

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

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

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

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?

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

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

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

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.

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.

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?

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

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

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?

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

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?

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

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.

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

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?

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.

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

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.

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.

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

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

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

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

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 for inquiring primary learners.

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 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?

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