How can we help students make sense of addition and subtraction of negative numbers?
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.
Find out about Magic Squares in this article written for students. Why are they magic?!
This number has 903 digits. What is the sum of all 903 digits?
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?
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?
Replace each letter with a digit to make this addition correct.
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. . . .
Number problems at primary level that may require determination.
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
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?
Number problems at primary level to work on with others.
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Find the numbers in this sum
Use the information to work out how many gifts there are in each
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?
Here is a chance to play a version of the classic Countdown Game.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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
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?
Find the next number in this pattern: 3, 7, 19, 55 ...
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?
Max and Mandy put their number lines together to make a graph. How
far had each of them moved along and up from 0 to get the counter
to the place marked?
In sheep talk the only letters used are B and A. A sequence of
words is formed by following certain rules. What do you notice when
you count the letters in each word?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
This is an adding game for two players.
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.
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?
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
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
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?
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.
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.
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
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?
Investigate the different distances of these car journeys and find
out how long they take.
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?
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.
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?
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
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.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).