There are nasty versions of this dice game but we'll start with the nice ones...
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
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?
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.
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?
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.
Can you draw a continuous line through 16 numbers on this grid so
that the total of the numbers you pass through is as high as
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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.
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?
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.
Find the sum of all three-digit numbers each of whose digits is
Tim had nine cards each with a different number from 1 to 9 on it.
How could he have put them into three piles so that the total in
each pile was 15?
What is happening at each box in these machines?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Use the information to work out how many gifts there are in each
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.
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?
Susie took cherries out of a bowl by following a certain pattern.
How many cherries had there been in the bowl to start with if she
was left with 14 single ones?
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
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?
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?
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?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Find the numbers in this sum
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
A game for 2 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.
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?
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
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?
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
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?
Use the 'double-3 down' dominoes to make a square so that each side
has eight dots.
If each of these three shapes has a value, can you find the totals
of the combinations? Perhaps you can use the shapes to make the
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
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?
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?
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Investigate the different distances of these car journeys and find out how long they take.
This article suggests some ways of making sense of calculations involving positive and negative numbers.