This article suggests some ways of making sense of calculations involving positive and negative numbers.
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?
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?
Find the numbers in this sum
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?
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
In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?
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?
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?
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.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
What is the sum of all the three digit whole numbers?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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.
Susie took cherries out of a bowl by following a certain pattern.
How many cherries had there been in the bowl to start with if she
was left with 14 single ones?
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.
Find the sum of all three-digit numbers each of whose digits is
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. . . .
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?
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?
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?
Can you draw a continuous line through 16 numbers on this grid so
that the total of the numbers you pass through is as high as
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
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.
Investigate the different distances of these car journeys and find out how long they take.
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?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
In this problem you have to place four by four magic squares on the
faces of a cube so that along each edge of the cube the numbers
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Cassandra, David and Lachlan are brothers and sisters. They range
in age between 1 year and 14 years. Can you figure out their exact
ages from the clues?
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Can you explain how this card trick works?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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?
Use the 'double-3 down' dominoes to make a square so that each side
has eight dots.
Delight your friends with this cunning trick! Can you explain how
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?
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.
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?