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Addition & subtraction. Number bases. Multiplication & division. Number operations - generally. Real world. Calculating with ratio & proportion. Calculating with percentages. Ratio. Money. History of measurement.There are 60 results
Broad Topics > Calculations and Numerical Methods > Addition & subtraction
2010: A Year of Investigations
Age 5 to 14
This article for teachers suggests ideas for activities built around 10 and 2010.
Subtraction Surprise
Age 7 to 14 Challenge Level:
Try out some calculations. Are you surprised by the results?
And So on and So On
Age 11 to 14 Challenge Level:
If you wrote all the possible four digit numbers made by using each of the digits 2, 4, 5, 7 once, what would they add up to?
Cayley
Age 11 to 14 Challenge Level:
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
3388
Age 11 to 14 Challenge Level:
Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.
Tis Unique
Age 11 to 14 Challenge Level:
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.
Arrange the Digits
Age 11 to 14 Challenge Level:
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?
Jugs of Wine
Age 11 to 14 Challenge Level:
You have four jugs of 9, 7, 4 and 2 litres capacity. The 9 litre jug is full of wine, the others are empty. Can you divide the wine into three equal quantities?
Got it Article
Age 7 to 14
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
As Easy as 1,2,3
Age 11 to 14 Challenge Level:
When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .
Weights
Age 11 to 14 Challenge Level:
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Pole Star Sudoku 2
Age 11 to 16 Challenge Level:
This Sudoku, based on differences. Using the one clue number can you find the solution?
Countdown
Age 7 to 14 Challenge Level:
Here is a chance to play a version of the classic Countdown Game.
Multiply the Addition Square
Age 11 to 14 Challenge Level:
If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?
Twenty20
Age 7 to 16 Challenge Level:
Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
Making Sense of Positives and Negatives
Age 11 to 14
This article suggests some ways of making sense of calculations involving positive and negative numbers.
Pairs
Age 11 to 14 Challenge Level:
Ann thought of 5 numbers and told Bob all the sums that could be made by adding the numbers in pairs. The list of sums is 6, 7, 8, 8, 9, 9, 10,10, 11, 12. Help Bob to find out which numbers Ann was. . . .
Largest Number
Age 11 to 14 Challenge Level:
What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.
Like Powers
Age 11 to 14 Challenge Level:
Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n $ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.
Pair Sums
Age 11 to 14 Challenge Level:
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Alphabet Soup
Age 11 to 14 Challenge Level:
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.
Digit Sum
Age 11 to 14 Challenge Level:
What is the sum of all the digits in all the integers from one to one million?
Football Sum
Age 11 to 14 Challenge Level:
Find the values of the nine letters in the sum: FOOT + BALL = GAME
The Patent Solution
Age 11 to 14 Challenge Level:
A combination mechanism for a safe comprises thirty-two tumblers numbered from one to thirty-two in such a way that the numbers in each wheel total 132... Could you open the safe?
Adding and Subtracting Positive and Negative Numbers
Age 11 to 14
How can we help students make sense of addition and subtraction of negative numbers?
Chameleons
Age 11 to 14 Challenge Level:
Whenever two chameleons of different colours meet they change colour to the third colour. Describe the shortest sequence of meetings in which all the chameleons change to green if you start with 12. . . .
More Children and Plants
Age 7 to 14 Challenge Level:
This challenge extends the Plants investigation so now four or more children are involved.
Postage
Age 14 to 16 Challenge Level:
The country Sixtania prints postage stamps with only three values 6 lucres, 10 lucres and 15 lucres (where the currency is in lucres).Which values cannot be made up with combinations of these postage. . . .
Have You Got It?
Age 11 to 14 Challenge Level:
Can you explain the strategy for winning this game with any target?
Cunning Card Trick
Age 11 to 14 Challenge Level:
Delight your friends with this cunning trick! Can you explain how it works?
Always the Same
Age 11 to 14 Challenge Level:
Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?
Countdown Fractions
Age 11 to 16 Challenge Level:
Here is a chance to play a fractions version of the classic Countdown Game.
More Plant Spaces
Age 7 to 14 Challenge Level:
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
Making Maths: Double-sided Magic Square
Age 7 to 14 Challenge Level:
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Crossed Ends
Age 11 to 14 Challenge Level:
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
Top-heavy Pyramids
Age 11 to 14 Challenge Level:
Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.
Got it for Two
Age 7 to 14 Challenge Level:
Got It game for an adult and child. How can you play so that you know you will always win?
Nice or Nasty for Two
Age 7 to 14 Challenge Level:
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
Nice or Nasty
Age 7 to 14 Challenge Level:
There are nasty versions of this dice game but we'll start with the nice ones...
Magic Squares
Age 14 to 18
An account of some magic squares and their properties and and how to construct them for yourself.
Number Pyramids
Age 11 to 14 Challenge Level:
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Aba
Age 11 to 14 Challenge Level:
In the following sum the letters A, B, C, D, E and F stand for six distinct digits. Find all the ways of replacing the letters with digits so that the arithmetic is correct.
Connect Three
Age 11 to 16 Challenge Level:
In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?
Score
Age 11 to 14 Challenge Level:
There are exactly 3 ways to add 4 odd numbers to get 10. Find all the ways of adding 8 odd numbers to get 20. To be sure of getting all the solutions you will need to be systematic. What about. . . .
An Introduction to Magic Squares
Age 7 to 16
Find out about Magic Squares in this article written for students. Why are they magic?!
First Connect Three
Age 7 to 14 Challenge Level:
Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?
Two and Two
Age 11 to 14 Challenge Level:
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Number Daisy
Age 11 to 14 Challenge Level:
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
NRICH is part of the family of activities in the Millennium Mathematics Project.