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In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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