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.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
What is the sum of all the three digit whole 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?
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?
Number problems at primary level to work on with others.
Number problems at primary level that may require determination.
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?
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?
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
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?
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).
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.
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 your logical reasoning to work out how many cows and how many
sheep there are in each field.
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.
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?
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?
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?
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?
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?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?
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?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
What is happening at each box in these machines?
Use the information to work out how many gifts there are in each
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Find the next number in this pattern: 3, 7, 19, 55 ...
Number problems at primary level that require careful consideration.
This task combines spatial awareness with addition and multiplication.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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?
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.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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.
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.
This number has 903 digits. What is the sum of all 903 digits?
If the answer's 2010, what could the question be?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received 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
A lady has a steel rod and a wooden pole and she knows the length
of each. How can she measure out an 8 unit piece of pole?
Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?