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?

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

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. . . .

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?

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?

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

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

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?

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

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

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?

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 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?

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

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

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" .

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

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?

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

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?

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.

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

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

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?

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.

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

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?

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

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

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

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

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

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 activity involves rounding four-digit numbers to the nearest thousand.

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.

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. . . .

What happens when you round these numbers to the nearest whole 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...

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.

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.

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

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