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.
Can you substitute numbers for the letters in these sums?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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 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.
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?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
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?
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?
Can you work out some different ways to balance this equation?
Who said that adding couldn't be fun?
Number problems at primary level that may require resilience.
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.
Can you replace the letters with numbers? Is there only one solution in each case?
Number problems at primary level to work on with others.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Follow the clues to find the mystery number.
Have a go at balancing this equation. Can you find different ways of doing it?
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?
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"?
Try out some calculations. Are you surprised by the results?
Each child in Class 3 took four numbers out of the bag. Who had made the highest even number?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
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 feature aims to support you in developing children's early number sense and understanding of place value.
What happens when you round these numbers to the nearest whole number?
This set of activities focuses on ordering, an important aspect 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.
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.
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
What happens when you round these three-digit numbers to the nearest 100?
What is the sum of all the digits in all the integers from one to one million?
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?
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.
A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Amazing as it may seem the three fives remaining in the following `skeleton' are sufficient to reconstruct the entire long division sum.
Carry out cyclic permutations of nine digit numbers containing the digits from 1 to 9 (until you get back to the first number). Prove that whatever number you choose, they will add to the same total.
Number problems for inquiring primary learners.
Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E
Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?
In this article, Alf outlines six activities using the Gattegno chart, which help to develop understanding of place value, multiplication and division.
Write down a three-digit number Change the order of the digits to get a different number Find the difference between the two three digit numbers Follow the rest of the instructions then try. . . .
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.
These tasks will help learners develop their understanding of place value, particularly giving them opportunities to express numbers as amounts.
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.