Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.
Choose any three by three square of dates on a calendar page...
Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do. . . .
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. . . .
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.
Using the 8 dominoes make a square where each of the columns and rows adds up to 8
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?
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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. . . .
Can you each work out the number on your card? What do you notice? How could you sort the cards?
Find out about Magic Squares in this article written for students. Why are they magic?!
Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?
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. . . .
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.
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.
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?
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.
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.
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
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?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
Replace each letter with a digit to make this addition correct.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
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.
The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?
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.
Here is a chance to play a fractions version of the classic Countdown Game.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Find the numbers in this sum
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. . . .
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
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.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
This article suggests some ways of making sense of calculations involving positive and negative numbers.
What are the missing numbers in the pyramids?
Find a great variety of ways of asking questions which make 8.
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
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 explain how this card trick works?
Delight your friends with this cunning trick! Can you explain how it works?
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
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?
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?
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?