48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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?
Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?
If the answer's 2010, what could the question be?
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 happens when you add the digits of a number then multiply the
result by 2 and you keep doing this? You could try for different
numbers and different rules.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
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?
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.
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?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
Number problems at primary level that may require determination.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
This number has 903 digits. What is the sum of all 903 digits?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
How would you count the number of fingers in these pictures?
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!
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?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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.
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
What is happening at each box in these machines?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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?
Find the next number in this pattern: 3, 7, 19, 55 ...
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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?
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?
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?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Use the information to work out how many gifts there are in each
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
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 is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
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?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
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?