Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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.
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
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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.
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?
What is the sum of all the three digit whole numbers?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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
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?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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?
If the answer's 2010, what could the question be?
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?
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.
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.
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
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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?
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
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.
Number problems at primary level that require careful consideration.
Find the next number in this pattern: 3, 7, 19, 55 ...
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
Use the information to work out how many gifts there are in each
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?
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?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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?
Got It game for an adult and child. How can you play so that you know you will always win?
Put a number at the top of the machine and collect a number at the
bottom. What do you get? Which numbers get back to themselves?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
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?
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?
Investigate what happens when you add house numbers along a street
in different ways.
Can you find all the ways to get 15 at the top of this triangle of numbers?
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?
This task follows on from Build it Up and takes the ideas into three dimensions!
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.
This is an adding game for two players.