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?

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.

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?

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

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

Number problems for inquiring primary learners.

Number problems at primary level that require careful consideration.

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

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

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?

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?

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?

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

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.

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?

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

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

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

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

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?

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?

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

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 work out some different ways to balance this equation?

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

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

Use two dice to generate two numbers with one decimal place. 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?

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

Number problems at primary level that may require resilience.

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

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

Number problems at primary level to work on with others.

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.

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

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.

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?

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" .

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.

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

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

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!