Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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!
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!
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
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
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?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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.
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
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?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
If the answer's 2010, what could the question be?
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
How would you count the number of fingers in these pictures?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
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.
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Number problems at primary level that require careful consideration.
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 your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Number problems at primary level that may require determination.
This number has 903 digits. What is the sum of all 903 digits?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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?
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.
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?
What is happening at each box in these machines?
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 ...
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?
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?
Use the information to work out how many gifts there are in each
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?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?
This challenge combines addition, multiplication, perseverance and even proof.
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?