In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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.
Try out this number trick. What happens with different starting numbers? What do you notice?
This is a game for two players. What must you subtract to remove the rolled digit from your number? The first to zero wins!
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Number problems at primary level that may require resilience.
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.
Find the sum of all three-digit numbers each of whose digits is odd.
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?
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. . . .
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 for inquiring primary learners.
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. . . .
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?
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.
Number problems at primary level that require careful consideration.
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Who said that adding, subtracting, multiplying and dividing couldn't be fun?
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?
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?
Who said that adding couldn't be fun?
Can you substitute numbers for the letters in these sums?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
This article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.
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.
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?
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.
Dicey Operations for an adult and child. Can you get close to 1000 than your partner?
Try out some calculations. Are you surprised by the results?
What happens when you add a three digit number to its reverse?
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.
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.
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 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Explore the relationship between simple linear functions and their graphs.
This article develops the idea of 'ten-ness' as an important element of place value.
Can you work out some different ways to balance this equation?
In this article, Alf outlines six activities using the Gattegno chart, which help to develop understanding of place value, multiplication and division.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Have a go at balancing this equation. Can you find different ways of doing it?