Number problems at primary level that may require resilience.
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?
Number problems at primary level to work on with others.
Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.
Here is a chance to play a version of the classic Countdown Game.
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.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
If you have only four weights, where could you place them in order to balance this equaliser?
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
You have 5 darts and your target score is 44. How many different ways could you score 44?
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
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.
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
Choose a symbol to put into the number sentence.
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?
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
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?
This task follows on from Build it Up and takes the ideas into three dimensions!
Find a great variety of ways of asking questions which make 8.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
Can you make square numbers by adding two prime numbers together?
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.
This is an adding game for two players.
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 challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Investigate the different distances of these car journeys and find out how long they take.
Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
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?
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?
Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?
Investigate what happens when you add house numbers along a street in different ways.
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?
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?
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!
Try out this number trick. What happens with different starting numbers? What do you notice?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
A lady has a steel rod and a wooden pole and she knows the length of each. How can she measure out an 8 unit piece of pole?
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?
Investigate the totals you get when adding numbers on the diagonal of this pattern in threes.
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?