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

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

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?

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?

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

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

Number problems at primary level to work on with others.

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?

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 article, written for teachers, looks at the different kinds of recordings encountered in Primary Mathematics lessons and the importance of not jumping to conclusions!

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" .

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

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?

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.

There are two forms of counting on Vuvv - Zios count in base 3 and Zepts count in base 7. One day four of these creatures, two Zios and two Zepts, sat on the summit of a hill to count the legs of. . . .

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

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

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

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.

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

When asked how old she was, the teacher replied: My age in years is not prime but odd and when reversed and added to my age you have a perfect square...

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.

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?

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

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.

Number problems at primary level that may require resilience.

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.

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?

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?

Number problems at primary level that require careful consideration.

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

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"?

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

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

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

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

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 for inquiring primary learners.

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

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?

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

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

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?