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

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?

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?

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

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?

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?

Number problems at primary level to work on with others.

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

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

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

A school song book contains 700 songs. The numbers of the songs are displayed by combining special small single-digit cards. What is the minimum number of small cards that is needed?

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" .

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?

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

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?

Can you substitute numbers for the letters in these sums?

Number problems at primary level that require careful consideration.

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.

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

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

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

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

Explore the relationship between simple linear functions and their graphs.

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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.

Number problems for inquiring primary learners.

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?

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

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

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

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?

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. . . .

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

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

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

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?

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

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 any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?

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. . . .