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.
On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
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?
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?
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
Winifred Wytsh bought a box each of jelly babies, milk jelly bears,
yellow jelly bees and jelly belly beans. In how many different ways
could she make a jolly jelly feast with 32 legs?
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?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
What is happening at each box in these machines?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
There were 22 legs creeping across the web. How many flies? How many spiders?
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 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
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.
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
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!
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.
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?
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?
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
Find all the numbers that can be made by adding the dots on two dice.
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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?
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 make square numbers by adding two prime numbers together?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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!
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?
Find the next number in this pattern: 3, 7, 19, 55 ...
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
This activity is best done with a whole class or in a large group. Can you match the cards? What happens when you add pairs of the numbers together?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Are these domino games fair? Can you explain why or why not?
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
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?
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 dice train has been made using specific rules. How many different trains can you make?
Got It game for an adult and child. How can you play so that you know you will always win?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.