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There are 51 NRICH Mathematical resources connected to Place value, you may find related items under Place value and the number system.
Broad Topics > Place value and the number system > Place valueWhere 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...
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?
How many six digit numbers are there which DO NOT contain a 5?
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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.
More upper primary number sense and place value tasks.
These tasks will help learners develop their understanding of place value, particularly giving them opportunities to express numbers as amounts.
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 set of activities focuses on ordering, an important aspect of place value.
This article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.
In this article, Alf outlines six activities using the Gattegno chart, which help to develop understanding of place value, multiplication and division.
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.
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.
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.
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?
Nowadays the calculator is very familiar to many of us. What did people do to save time working out more difficult problems before the calculator existed?
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?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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?
This is a game for two players. What must you subtract to remove the rolled digit from your number? The first to zero wins!
The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?
There are two forms of counting on Vuvv - Zios count in base 3 and Zepts count in base 7. One day four of these creatures, two Zios and two Zepts, sat on the summit of a hill to count the legs of the creatures they could see. The creature looking to the West wrote 122. The creature looking to the East wrote 22. The creature looking to the South wrote 101. The creature looking to the North wrote 41. In which direction are the 2 Zios looking and in which directions are the 2 Zepts looking?
Can you substitute numbers for the letters in these sums?
Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain why this works.
Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E
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" .
The number 3723(in base 10) is written as 123 in another base. What is that base?
Find the sum of all three-digit numbers each of whose digits is odd.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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.
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)?
Suppose you had to begin the never ending task of writing out the natural numbers: 1, 2, 3, 4, 5.... and so on. What would be the 1000th digit you would write down.
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 and so on?
Amazing as it may seem the three fives remaining in the following `skeleton' are sufficient to reconstruct the entire long division sum.
When asked how old she was, the teacher replied: My age in years is not prime but odd and when reversed and added to my age you have a perfect square...
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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 do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?