Can you substitute numbers for the letters in these sums?
Try out this number trick. What happens with different starting numbers? What do you notice?
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?
Find the sum of all three-digit numbers each of whose digits is odd.
Number problems at primary level that may require resilience.
Number problems at primary level to work on with others.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
This is a game for two players. What must you subtract to remove the rolled digit from your number? The first to zero wins!
By selecting digits for an addition grid, what targets can you make?
Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E
Number problems at primary level that require careful consideration.
This article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.
Who said that adding couldn't be fun?
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 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?
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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.
Can you replace the letters with numbers? Is there only one solution in each case?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Use your knowledge of place value to try to win this game. How will you maximise your score?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
There are nasty versions of this dice game but we'll start with the nice ones...
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
More upper primary number sense and place value tasks.
Each child in Class 3 took four numbers out of the bag. Who had made the highest even number?
Try out some calculations. Are you surprised by the results?
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?
What happens when you add a three digit number to its reverse?
Who said that adding, subtracting, multiplying and dividing couldn't be fun?
Dicey Operations for an adult and child. Can you get close to 1000 than your partner?
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.
In this article, Alf outlines six activities using the Gattegno chart, which help to develop understanding of place value, multiplication and division.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
These tasks will help learners develop their understanding of place value, particularly giving them opportunities to express numbers as amounts.
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. . . .
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?
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.
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.
Have a go at balancing this equation. Can you find different ways of doing it?
This set of activities focuses on ordering, an important aspect of place value.
Number problems for inquiring primary learners.
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?
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?
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.
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.