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

Use your knowledge of place value to try to win this game. How will you maximise your score?

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.

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

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

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

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.

Where should you start, if you want to finish back where you started?

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

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.

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

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

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

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.

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

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.

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

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

More upper primary number sense and place value tasks.

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?

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.

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.

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

Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?

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

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. . . .

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.

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.

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. . . .

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!

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

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 work out some different ways to balance this equation?

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

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

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?

Alf describes how the Gattegno chart helped a class of 7-9 year olds gain an awareness of place value and of the inverse relationship between multiplication and division.

This article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.

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)?

Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?

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

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

Number problems for inquiring primary learners.