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. . . .
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
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?
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.
This challenge extends the Plants investigation so now four or more children are involved.
This Sudoku, based on differences. Using the one clue number can you find the solution?
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.
Using the 8 dominoes make a square where each of the columns and rows adds up to 8
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?
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?
How is it possible to predict the card?
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. . . .
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
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. . . .
Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.
Delight your friends with this cunning trick! Can you explain how it works?
Can you explain how this card trick works?
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?
This article suggests some ways of making sense of calculations involving positive and negative numbers.
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?
Try out some calculations. Are you surprised by the results?
An account of some magic squares and their properties and and how to construct them for yourself.
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. . . .
Got It game for an adult and child. How can you play so that you know you will always win?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Here is a chance to play a fractions version of the classic Countdown Game.
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 brief article written for pupils about mathematical symbols.
Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
This article for teachers suggests ideas for activities built around 10 and 2010.
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?
Here is a chance to play a version of the classic Countdown Game.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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.
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.
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. . . .
Can you explain the strategy for winning this game with any target?
This Sudoku requires you to do some working backwards before working forwards.
What is the sum of all the digits in all the integers from one to one million?
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?
How can we help students make sense of addition and subtraction of negative numbers?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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?
Find out about Magic Squares in this article written for students. Why are they magic?!
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?
Investigate the different ways that fifteen schools could have given money in a charity fundraiser.
In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?
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.