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?
What is the sum of all the three digit whole numbers?
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.
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 the information to work out how many gifts there are in each
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
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 happening at each box in these machines?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
In this problem you have to place four by four magic squares on the
faces of a cube so that along each edge of the cube the numbers
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
Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
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?
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.
In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
Fill in the numbers to make the sum of each row, column and
diagonal equal to 34. For an extra challenge try the huge American
Flag magic square.
There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?
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.
This number has 903 digits. What is the sum of all 903 digits?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
Find the next number in this pattern: 3, 7, 19, 55 ...
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Got It game for an adult and child. How can you play so that you know you will always win?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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?
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?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
There were 22 legs creeping across the web. How many flies? How many spiders?
Woof is a big dog. Yap is a little dog.
Emma has 16 dog biscuits to give to the two dogs.
She gave Woof 4 more biscuits than Yap.
How many biscuits did each dog get?
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
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?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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 a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
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?
Cassandra, David and Lachlan are brothers and sisters. They range
in age between 1 year and 14 years. Can you figure out their exact
ages from the clues?
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?
Tell your friends that you have a strange calculator that turns
numbers backwards. What secret number do you have to enter to make
141 414 turn around?
Can you arrange fifteen dominoes so that all the touching domino
pieces add to 6 and the ends join up? Can you make all the joins
add to 7?