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.

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

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

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

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.

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?

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?

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

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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

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

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

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

Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?

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

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

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

Number problems at primary level that require careful consideration.

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

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

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?

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

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 at primary level to work on with others.

Number problems for inquiring primary learners.

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

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

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?

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.

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

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.

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. . . .

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

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" .

Number problems at primary level that may require determination.

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?

Who said that adding, subtracting, multiplying and dividing couldn't be fun?

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

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

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

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

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

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

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

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. . . .