Where can you draw a line on a clock face so that the numbers on both sides have the same total?
Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
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 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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
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?
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
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!
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.
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 is happening at each box in these machines?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?
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.
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.
Can you score 100 by throwing rings on this board? Is there more than way to do it?
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?
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?
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!
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.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
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.
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?
In this article for primary teachers, Lynne McClure outlines what is meant by fluency in the context of number and explains how our selection of NRICH tasks can help.
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 article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
If the answer's 2010, what could the question be?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Find the next number in this pattern: 3, 7, 19, 55 ...
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?
What is the sum of all the three digit whole numbers?
Number problems at primary level that require careful consideration.
This number has 903 digits. What is the sum of all 903 digits?
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?
This task offers an opportunity to explore all sorts of number relationships, but particularly multiplication.
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
This task combines spatial awareness with addition and multiplication.
This challenge combines addition, multiplication, perseverance and even proof.
Number problems at primary level that may require resilience.
Can you find different ways of creating paths using these paving slabs?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left.