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?
What is the sum of all the three digit whole numbers?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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?
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.
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?
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!
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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!
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
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.
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
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
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Claire thinks she has the most sports cards in her album. "I have
12 pages with 2 cards on each page", says Claire. Ross counts his
cards. "No! I have 3 cards on each of my pages and there are. . . .
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
There were 22 legs creeping across the web. How many flies? How many spiders?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
Use the information to work out how many gifts there are in each
Can you arrange 5 different digits (from 0 - 9) in the cross in the
What is happening at each box in these machines?
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?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Have a go at balancing this equation. Can you find different ways of doing 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?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
This number has 903 digits. What is the sum of all 903 digits?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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?
Can you replace the letters with numbers? Is there only one
solution in each case?
Can you work out some different ways to balance this equation?
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?
This task combines spatial awareness with addition and multiplication.
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.
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?
Find the next number in this pattern: 3, 7, 19, 55 ...
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
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
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.