Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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.
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
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
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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?
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
A game for 2 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.
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?
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?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Find the next number in this pattern: 3, 7, 19, 55 ...
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?
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?
If the answer's 2010, what could the question be?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
This is an adding game for two players.
There are 78 prisoners in a square cell block of twelve cells. The
clever prison warder arranged them so there were 25 along each wall
of the prison block. How did he do it?
Number problems at primary level that may require determination.
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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.
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?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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.
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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.
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?
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.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
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?
Use the information to work out how many gifts there are in each
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Got It game for an adult and child. How can you play so that you know you will always win?
Claire thinks she has the most sports cards in her album. "I have
12 pages with 2 cards on each page", says Claire. Ross counts his
cards. "No! I have 3 cards on each of my pages and there are. . . .
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?