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?

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?

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

Explore the relationship between simple linear functions and their graphs.

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?

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 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?

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

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?

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" .

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

Number problems at primary level that may require resilience.

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

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.

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?

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.

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.

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?

Number problems at primary level that require careful consideration.

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

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.

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

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

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

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

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.

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?

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 numbers to the nearest whole number?

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

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

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

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

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?

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

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

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?

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

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