Each child in Class 3 took four numbers out of the bag. Who had made the highest even number?
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?
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?
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?
This article develops the idea of 'ten-ness' as an important element of place value.
This set of activities focuses on ordering, an important aspect 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.
These tasks will help learners develop their understanding of place value, particularly giving them opportunities to express numbers as amounts.
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.
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E
Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. . . .
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?
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?
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.
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. . . .
Explore the relationship between simple linear functions and their graphs.
This is a game for two players. What must you subtract to remove the rolled digit from your number? The first to zero wins!
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Follow the clues to find the mystery number.
By selecting digits for an addition grid, what targets can you make?
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?
Who said that adding couldn't be fun?
Replace each letter with a digit to make this addition correct.
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.
Try out some calculations. Are you surprised by the results?
In this article, Alf outlines six activities using the Gattegno chart, which help to develop understanding of place value, multiplication and division.
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?
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.
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.
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?
Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?
This article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.
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 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.
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.
Find the sum of all three-digit numbers each of whose digits is odd.
What happens when you add a three digit number to its reverse?
Number problems at primary level that require careful consideration.
There are nasty versions of this dice game but we'll start with the nice ones...
Number problems for inquiring primary learners.
Have a go at balancing this equation. Can you find different ways of doing it?
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...