Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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
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.
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?
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
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 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.
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?
What is the sum of all the three digit whole 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?
Use the information to work out how many gifts there are in each
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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?
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.
Number problems at primary level that may require determination.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
What is happening at each box in these machines?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
Find the next number in this pattern: 3, 7, 19, 55 ...
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
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.
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?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
If the answer's 2010, what could the question be?
How can we help students make sense of addition and subtraction of negative numbers?
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.
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
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
This task combines spatial awareness with addition and multiplication.
This number has 903 digits. What is the sum of all 903 digits?
Find a great variety of ways of asking questions which make 8.
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?
We can arrange dots in a similar way to the 5 on a dice and they
usually sit quite well into a rectangular shape. How many
altogether in this 3 by 5? What happens for other sizes?
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
Number problems at primary level to work on with others.
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?
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?
Here is a chance to play a version of the classic Countdown Game.
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
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!