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?

Try out this number trick. What happens with different starting numbers? What do you notice?

Number problems at primary level that require careful consideration.

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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 may require resilience.

Can you substitute numbers for the letters in these sums?

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

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

Number problems at primary level to work on with others.

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?

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?

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

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?

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 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?

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

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.

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

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?

Write down a three-digit number Change the order of the digits to get a different number Find the difference between the two three digit numbers Follow the rest of the instructions then try. . . .

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

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?

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.

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

Number problems for inquiring primary learners.

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

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

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.

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.

32 x 38 = 30 x 40 + 2 x 8; 34 x 36 = 30 x 40 + 4 x 6; 56 x 54 = 50 x 60 + 6 x 4; 73 x 77 = 70 x 80 + 3 x 7 Verify and generalise if possible.

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

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

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

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

Carry out cyclic permutations of nine digit numbers containing the digits from 1 to 9 (until you get back to the first number). Prove that whatever number you choose, they will add to the same total.

The Number Jumbler can always work out your chosen symbol. Can you work out how?

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

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

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?

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