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

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

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?

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

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?

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?

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.

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

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?

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?

Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E

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

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?

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

Number problems at primary level to work on with others.

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?

Number problems at primary level that require careful consideration.

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.

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

Number problems at primary level that may require resilience.

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

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

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

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

Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .

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.

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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. . . .

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

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

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

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.

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

The number 27 is special because it is three times the sum of its digits 27 = 3 (2 + 7). Find some two digit numbers that are SEVEN times the sum of their digits (seven-up numbers)?

Can you substitute numbers for the letters in these sums?

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.

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?

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

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

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.

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?

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

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?

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