Where can you draw a line on a clock face so that the numbers on both sides have the same total?
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.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?
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.
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?
Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?
Use the information to work out how many gifts there are in each pile.
What is the sum of all the three digit whole numbers?
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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.
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?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Find the next number in this pattern: 3, 7, 19, 55 ...
Number problems at primary level that may require resilience.
If the answer's 2010, what could the question be?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
This task combines spatial awareness with addition and multiplication.
What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
Can you score 100 by throwing rings on this board? Is there more than way 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?
What is happening at each box in these machines?
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?
Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.
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?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
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?
This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?
This number has 903 digits. What is the sum of all 903 digits?
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?
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.
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?
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?
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.
Vera is shopping at a market with these coins in her purse. Which things could she give exactly the right amount for?
Can you follow the rule to decode the messages?
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?
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
This is an adding game for two players.
Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?
I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?
Start with four numbers at the corners of a square and put the total of two corners in the middle of that side. Keep going... Can you estimate what the size of the last four numbers will be?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).