Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
These eleven shapes each stand for a different number. Can you use
the multiplication sums to work out what they are?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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.
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!
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 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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
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 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?
Use the information to work out how many gifts there are in each
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?
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?
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
Annie and Ben are playing a game with a calculator. What was
Annie's secret number?
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
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 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?
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?
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?
All the girls would like a puzzle each for Christmas and all the
boys would like a book each. Solve the riddle to find out how many
puzzles and books Santa left.
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
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. . . .
There were 22 legs creeping across the web. How many flies? How many spiders?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
Find the next number in this pattern: 3, 7, 19, 55 ...
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?
An old game but lots of arithmetic!
Choose a symbol to put into the number sentence.
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
Can you order the digits from 1-6 to make a number which is
divisible by 6 so when the last digit is removed it becomes a
5-figure number divisible by 5, and so on?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
This number has 903 digits. What is the sum of all 903 digits?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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.
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?