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?

Number problems at primary level that require careful consideration.

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?

Can you substitute numbers for the letters in these sums?

Find the sum of all three-digit numbers each of whose digits is odd.

Number problems at primary level that may require resilience.

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

Number problems at primary level to work on with others.

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

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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

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

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

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?

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?

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.

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

Number problems for inquiring primary learners.

Try out some calculations. Are you surprised by the results?

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

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

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?

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?

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?

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

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

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?

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?

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

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.

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?

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

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

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

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.

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?

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.

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

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!

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" .

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.

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