Find the numbers in this sum
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?
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. . . .
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?
In this game the winner is the first to complete a row of three.
Are some squares easier to land on than others?
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 a great variety of ways of asking questions which make 8.
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?
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 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?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
This number has 903 digits. What is the sum of all 903 digits?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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.
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 sum of all the three digit whole numbers?
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.
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 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.
There are over sixty different ways of making 24 by adding,
subtracting, multiplying and dividing all four numbers 4, 6, 6 and
8 (using each number only once). How many can you find?
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.
Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.
Using 3 rods of integer lengths, none longer than 10 units and not
using any rod more than once, you can measure all the lengths in
whole units from 1 to 10 units. How many ways can you do this?
Fill in the numbers to make the sum of each row, column and
diagonal equal to 34. For an extra challenge try the huge American
Flag magic square.
Replace each letter with a digit to make this addition correct.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
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?
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
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?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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.
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
On a calculator, make 15 by using only the 2 key and any of the
four operations keys. How many ways can you find to do it?
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
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?
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
Rocco ran in a 200 m race for his class. Use the information to
find out how many runners there were in the race and what Rocco's
finishing position was.
On the table there is a pile of oranges and lemons that weighs
exactly one kilogram. Using the information, can you work out how
many lemons there are?
Mr. Sunshine tells the children they will have 2 hours of homework.
After several calculations, Harry says he hasn't got time to do
this homework. Can you see where his reasoning is wrong?
Amy has a box containing domino pieces but she does not think it is
a complete set. She has 24 dominoes in her box and there are 125
spots on them altogether. Which of her domino pieces are missing?
In this game, you can add, subtract, multiply or divide the numbers
on the dice. Which will you do so that you get to the end of the
number line first?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
Can you make square numbers by adding two prime numbers together?
There are three buckets each of which holds a maximum of 5 litres.
Use the clues to work out how much liquid there is in each bucket.
Well now, what would happen if we lost all the nines in our number
system? Have a go at writing the numbers out in this way and have a
look at the multiplications table.
What are the missing numbers in the pyramids?
What is happening at each box in these machines?