Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
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?
These two group activities use mathematical reasoning - one is numerical, one geometric.
Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?
Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.
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.
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.
Can you make square numbers by adding two prime numbers together?
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?
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?
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?
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?
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
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.
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
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?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why?
I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?
There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
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?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
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.
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?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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.
Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?
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?
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?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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 jugs.
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.
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?
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?
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!
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.
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
Are these domino games fair? Can you explain why or why not?
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 way described?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.