A combination mechanism for a safe comprises thirty-two tumblers
numbered from one to thirty-two in such a way that the numbers in
each wheel total 132... Could you open the safe?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit
numbers such that their total is close to 1500?
If you wrote all the possible four digit numbers made by using each
of the digits 2, 4, 5, 7 once, what would they add up to?
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.
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?
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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?
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.
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
Replace each letter with a digit to make this addition correct.
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
What is the largest number you can make using the three digits 2, 3
and 4 in any way you like, using any operations you like? You can
only use each digit once.
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?
Find the numbers in this sum
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
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.
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.
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?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
How would you count the number of fingers in these pictures?
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 ...
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
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.
Are these statements always true, sometimes true or never true?
This task combines spatial awareness with addition and multiplication.
Can you follow the rule to decode the messages?
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?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Number problems at primary level to work on with others.
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
What is happening at each box in these machines?
Using 3 rods of integer lengths, none longer than 10 units and not
using any rod more than once, you can measure all the lengths in
whole units from 1 to 10 units. How many ways can you do this?
Use the information to work out how many gifts there are in each
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?
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?
Number problems at primary level that require careful consideration.
Number problems at primary level that may require determination.
Who said that adding couldn't be fun?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?