Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
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?
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?
Find out about Magic Squares in this article written for students. Why are they magic?!
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
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?
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.
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.
Whenever two chameleons of different colours meet they change colour to the third colour. Describe the shortest sequence of meetings in which all the chameleons change to green if you start with 12. . . .
What is the sum of all the three digit whole numbers?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Can you score 100 by throwing rings on this board? Is there more than way to do it?
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.
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?
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?
Use the information to work out how many gifts there are in each pile.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
What is happening at each box in these machines?
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?
Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?
Here is a chance to play a version of the classic Countdown Game.
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?
This Sudoku, based on differences. Using the one clue number can you find the solution?
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?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
This number has 903 digits. What is the sum of all 903 digits?
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.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
This article suggests some ways of making sense of calculations involving positive and negative numbers.
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.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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?
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?
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
Find the next number in this pattern: 3, 7, 19, 55 ...
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.
Delight your friends with this cunning trick! Can you explain how it works?
Can you explain how this card trick works?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
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?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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?
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?