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?

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

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

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?

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.

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

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.

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

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?

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

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

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.

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.

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?

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?

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?

Number problems for inquiring primary learners.

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

Dicey Operations for an adult and child. Can you get close to 1000 than your partner?

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

Number problems at primary level to work on with others.

Number problems at primary level that require careful consideration.

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

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.

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

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

Number problems at primary level that may require determination.

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

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?

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?

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?

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...

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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

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

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

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

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

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.

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