There were 22 legs creeping across the web. How many flies? How many spiders?
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?
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!
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.
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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!
This number has 903 digits. What is the sum of all 903 digits?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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. . . .
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Use the information to work out how many gifts there are in each
At the beginning of May Tom put his tomato plant outside. On the
same day he sowed a bean in another pot. When will the two be the
Find the next number in this pattern: 3, 7, 19, 55 ...
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
What is happening at each box in these machines?
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?
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.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
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?
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?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
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?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
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.
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?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
These sixteen children are standing in four lines of four, one
behind the other. They are each holding a card with a number on it.
Can you work out the missing numbers?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
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?