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?
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?
Number problems at primary level to work on with others.
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Number problems at primary level that may require determination.
What is the sum of all the three digit whole numbers?
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?
Who said that adding couldn't be fun?
Number problems at primary level that require careful consideration.
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?
This number has 903 digits. What is the sum of all 903 digits?
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.
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?
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?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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.
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?
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?
What is happening at each box in these machines?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
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.
I throw three dice and get 5, 3 and 2. Add the scores on the three
dice. What do you get? Now multiply the scores. What do you notice?
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?
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?
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.
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?
This task combines spatial awareness with addition and multiplication.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
Got It game for an adult and child. How can you play so that you know you will always win?
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?
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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?
Find the next number in this pattern: 3, 7, 19, 55 ...
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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
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.
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
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
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three