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 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?

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?

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...

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. . . .

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

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

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

This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.

four strategy dice games to consolidate pupils' understanding of rounding.

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

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?

Explore the relationship between simple linear functions and their graphs.

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?

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

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!

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

You have two sets of the digits 0 – 9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?

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

We are used to writing numbers in base ten, using 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Eg. 75 means 7 tens and five units. This article explains how numbers can be written in any number base.

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

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.

Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?

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" .

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.

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

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

There are nasty versions of this dice game but we'll start with the nice ones...

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.

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.

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

Nowadays the calculator is very familiar to many of us. What did people do to save time working out more difficult problems before the calculator existed?

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

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

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

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

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

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

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

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

Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

Take any four digit number. Move the first digit to the 'back of the queue' and move the rest along. Now add your two numbers. What properties do your answers always have?

A church hymn book contains 700 hymns. The numbers of the hymns are displayed by combining special small single-digit boards. What is the minimum number of small boards that is needed?

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.

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.

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.