Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
There are nasty versions of this dice game but we'll start with the nice ones...
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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.
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 the sum of all the three digit whole numbers?
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 possible?
The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Here is a chance to play a version of the classic Countdown Game.
Find the next number in this pattern: 3, 7, 19, 55 ...
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?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Use the information to work out how many gifts there are in each pile.
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.
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?
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?
Find the sum of all three-digit numbers each of whose digits is odd.
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.
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?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
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?
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?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
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?
This article suggests some ways of making sense of calculations involving positive and negative numbers.
Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
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.
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.
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?
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?
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?
Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.
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?
What is happening at each box in these machines?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
The picture shows a lighthouse and many underwater creatures. If you know the markings on the lighthouse are 1m apart, can you work out the distances between some of the different creatures?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
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 given totals?
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 the 'double-3 down' dominoes to make a square so that each side has eight dots.
Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.