How can we help students make sense of addition and subtraction of negative numbers?
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 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.
Find a great variety of ways of asking questions which make 8.
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?
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
Find out about Magic Squares in this article written for students. Why are they magic?!
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. . . .
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?
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.
What is the sum of all the digits in all the integers from one to
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?
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?
In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Who said that adding couldn't be fun?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
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?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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. . . .
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 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 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.
Find the sum of all three-digit numbers each of whose digits is
This number has 903 digits. What is the sum of all 903 digits?
This article suggests some ways of making sense of calculations involving positive and negative numbers.
What are the missing numbers in the pyramids?
The picture shows a lighthouse and many underwater creatures. If
you know the markings on the lighthouse are 1m apart, can you work
out the distances between some of the different creatures?
Can you substitute numbers for the letters in these sums?
Use the 'double-3 down' dominoes to make a square so that each side has eight dots.
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?
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
Use these four dominoes to make a square that has the same number of dots on each side.
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
Find the numbers in this sum
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?
Number problems at primary level to work on with others.
Use the numbers in the box below to make the base of a top-heavy
pyramid whose top number is 200.
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.
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
Investigate what happens when you add house numbers along a street
in different ways.
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
The Scot, John Napier, invented these strips about 400 years ago to
help calculate multiplication and division. Can you work out how to
use Napier's bones to find the answer to these multiplications?
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?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
What is happening at each box in these machines?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
Vera is shopping at a market with these coins in her purse. Which
things could she give exactly the right amount for?