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.
Replace each letter with a digit to make this addition correct.
Find a great variety of ways of asking questions which make 8.
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
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?
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?
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?
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.
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?
What is the sum of all the digits in all the integers from one to
How can we help students make sense of addition and subtraction of negative numbers?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
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?
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. . . .
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?
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?
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?
Annie cut this numbered cake into 3 pieces with 3 cuts so that the
numbers on each piece added to the same total. Where were the cuts
and what fraction of the whole cake was each piece?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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. . . .
What are the missing numbers in the pyramids?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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 substitute numbers for the letters in these sums?
Find the numbers in this sum
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Who said that adding couldn't be fun?
This article suggests some ways of making sense of calculations involving positive and negative numbers.
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. . . .
Use the numbers in the box below to make the base of a top-heavy
pyramid whose top number is 200.
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.
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Can you explain how this card trick works?
Delight your friends with this cunning trick! Can you explain how
If each of these three shapes has a value, can you find the totals
of the combinations? Perhaps you can use the shapes to make the
Tell your friends that you have a strange calculator that turns
numbers backwards. What secret number do you have to enter to make
141 414 turn around?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Can you follow the rule to decode the messages?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Vera is shopping at a market with these coins in her purse. Which
things could she give exactly the right amount for?
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
What happens when you add the digits of a number then multiply the
result by 2 and you keep doing this? You could try for different
numbers and different rules.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Find out what a Deca Tree is and then work out how many leaves
there will be after the woodcutter has cut off a trunk, a branch, a
twig and a leaf.
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.