Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
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.
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?
Use the information to work out how many gifts there are in each pile.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
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 at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.
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?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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?
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?
What is the sum of all the three digit whole numbers?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
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?
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?
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?
You have 5 darts and your target score is 44. How many different ways could you score 44?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Can you score 100 by throwing rings on this board? Is there more than way to do it?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
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.
Max and Mandy put their number lines together to make a graph. How far had each of them moved along and up from 0 to get the counter to the place marked?
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.
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?
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.
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
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?
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?
What is happening at each box in these machines?
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
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?
Vera is shopping at a market with these coins in her purse. Which things could she give exactly the right amount for?
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?
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?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
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?
Ben has five coins in his pocket. How much money might he have?
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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?
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 group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
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.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
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?