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.

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.

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.

Write down a three-digit number Change the order of the digits to get a different number Find the difference between the two three digit numbers Follow the rest of the instructions then try. . . .

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.

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?

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

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

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. . . .

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.

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?

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

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

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

This feature aims to support you in developing children's early number sense and understanding of place value.

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.

This article for primary teachers expands on the key ideas which underpin early number sense and place value, and suggests activities to support learners as they get to grips with these ideas.

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. . . .

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

One of the key ideas associated with place value is that the position of a digit affects its value. These activities support children in understanding this idea.

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

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.

More upper primary number sense and place value tasks.

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?

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?

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

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

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

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?

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

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

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

This article develops the idea of 'ten-ness' as an important element of place value.

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

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

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?

Try out this number trick. What happens with different starting numbers? What do you notice?

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.

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?

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

The number 27 is special because it is three times the sum of its digits 27 = 3 (2 + 7). Find some two digit numbers that are SEVEN times the sum of their digits (seven-up numbers)?

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

Find the sum of all three-digit numbers each of whose digits is odd.

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!