Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Investigate the different ways that fifteen schools could have given money in a charity fundraiser.
Can you explain the strategy for winning this game with any target?
Got It game for an adult and child. How can you play so that you know you will always win?
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
Can you explain how this card trick works?
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?
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.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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?
Choose any three by three square of dates on a calendar page...
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.
Replace each letter with a digit to make this addition correct.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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?
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.
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
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?
By selecting digits for an addition grid, what targets can you make?
How many solutions can you find to this sum? Each of the different letters stands for a different 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?
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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. . . .
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?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
This Sudoku requires you to do some working backwards before working forwards.
Delight your friends with this cunning trick! Can you explain how it works?
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. . . .
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?
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?
Find the numbers in this sum
Play this game to learn about adding and subtracting positive and negative numbers
How many different differences can you make?
This Sudoku, based on differences. Using the one clue number can you find the solution?
Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
How is it possible to predict the card?
This article suggests some ways of making sense of calculations involving positive and negative numbers.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
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. . . .
Here is a chance to play a fractions version of the classic Countdown Game.
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?
Find out about Magic Squares in this article written for students. Why are they magic?!
Special clue numbers related to the difference between numbers in two adjacent cells and values of the stars in the "constellation" make this a doubly interesting problem.
Can you crack these cryptarithms?
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.
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.
Try out some calculations. Are you surprised by the results?