There are **104** NRICH Mathematical resources connected to **Place value**, you may find related items under Numbers and the Number System.

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

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

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

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

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

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 two-digit numbers can you make with these two dice? What can't you make?

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

These spinners will give you the tens and unit digits of a number. Can you choose sets of numbers to collect so that you spin six numbers belonging to your sets in as few spins as possible?

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

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

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?

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

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?

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?

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

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

Evaluate these powers of 67. What do you notice? Can you convince someone what the answer would be to (a million sixes followed by a 7) squared?

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

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

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.

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?

Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number...

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

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

Can you explain the surprising results Jo found when she calculated the difference between square 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?

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.

A 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?

Lee was writing all the counting numbers from 1 to 20. She stopped for a rest after writing seventeen digits. What was the last number she wrote?

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

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.

Number problems at primary level to work on with others.

Number problems for inquiring primary learners.

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

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

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

What is the sum of: 6 + 66 + 666 + 6666 ............+ 666666666...6 where there are n sixes in the last term?

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

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?

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?

Can you find the chosen number from the grid using the clues?

Investigate the different ways these aliens count in this challenge. You could start by thinking about how each of them would write our number 7.

This article for the young and old talks about the origins of our number system and the important role zero has to play in it.

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!

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?