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

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

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.

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

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

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.

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.

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

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

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

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

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

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

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

By selecting digits for an addition grid, what targets can you make?

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

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

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

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

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

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

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

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

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?

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

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 work out some different ways to balance this equation?

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?

Number problems at primary level that may require resilience.

Number problems at primary level that require careful consideration.

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

Number problems for inquiring primary learners.

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

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

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.

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

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

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.

What happens when you add a three digit number to its reverse?

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. . . .

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

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

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. . . .

These tasks will help learners develop their understanding of place value, particularly giving them opportunities to express numbers as amounts.