Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Annie and Ben are playing a game with a calculator. What was
Annie's secret number?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
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?
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.
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
Use the information to work out how many gifts there are in each
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
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?
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!
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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. . . .
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
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
There were 22 legs creeping across the web. How many flies? How many spiders?
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.
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!
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
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?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Can you replace the letters with numbers? Is there only one
solution in each case?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
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?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
What is happening at each box in these machines?
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
An old game but lots of arithmetic!
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?
This number has 903 digits. What is the sum of all 903 digits?
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
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?
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?
Can you work out the arrangement of the digits in the square so
that the given products are correct? The numbers 1 - 9 may be used
once and once only.
If you had any number of ordinary dice, what are the possible ways
of making their totals 6? What would the product of the dice be
This task combines spatial awareness with addition and multiplication.
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?