15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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.
Got It game for an adult and child. How can you play so that you know you will always win?
This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.
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?
How many different differences can you make?
This Sudoku, based on differences. Using the one clue number can you find the solution?
Replace each letter with a digit to make this addition correct.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?
This Sudoku requires you to do some working backwards before working forwards.
Investigate the different ways that fifteen schools could have given money in a charity fundraiser.
Delight your friends with this cunning trick! Can you explain how it works?
Can you explain the strategy for winning this game with any target?
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. . . .
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?
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. . . .
Play this game to learn about adding and subtracting positive and negative numbers
Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .
How is it possible to predict the card?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
Use the differences to find the solution to this Sudoku.
Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly Â£100 if the prices are Â£10 for adults, 50p for pensioners and 10p for children.
Here is a chance to play a fractions version of the classic Countdown Game.
Choose any three by three square of dates on a calendar page...
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.
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?
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. . . .
Try out some calculations. Are you surprised by the results?
Find out about Magic Squares in this article written for students. Why are they magic?!
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. . . .
What happens when you add a three digit number to its reverse?
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
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. . . .
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
What is the sum of all the digits in all the integers from one to one million?
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.
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.
By selecting digits for an addition grid, what targets can you make?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.