Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 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?
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 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.
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. . . .
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Using the 8 dominoes make a square where each of the columns and rows adds up to 8
This Sudoku, based on differences. Using the one clue number can you find the solution?
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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. . . .
There are nasty versions of this dice game but we'll start with the nice ones...
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.
Replace each letter with a digit to make this addition 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?
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.
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?
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 challenge extends the Plants investigation so now four or more children are involved.
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 article suggests some ways of making sense of calculations involving positive and negative numbers.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Find the numbers in this sum
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?
How is it possible to predict the card?
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.
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?
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?
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
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. . . .
What is the sum of all the digits in all the integers from one to one million?
Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.
How can we help students make sense of addition and subtraction of negative numbers?
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. . . .
In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?
Find a great variety of ways of asking questions which make 8.
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.
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
Delight your friends with this cunning trick! Can you explain how it works?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Choose any three by three square of dates on a calendar page. Circle any number on the top row, put a line through the other numbers that are in the same row and column as your circled number. Repeat. . . .
This article for teachers suggests ideas for activities built around 10 and 2010.
Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
Here is a chance to play a fractions version of the classic Countdown Game.
Here is a chance to play a version of the classic Countdown Game.
Can you be the first to complete a row of three?
Find out about Magic Squares in this article written for students. Why are they magic?!