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?
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?
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
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?
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?
Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.
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?
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?
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.
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Can you work out some different ways to balance this equation?
Have a go at balancing this equation. Can you find different ways of doing it?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
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.
Number problems at primary level that may require determination.
Find the next number in this pattern: 3, 7, 19, 55 ...
If the answer's 2010, what could the question be?
What is the sum of all the three digit whole numbers?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
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?
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
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?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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!
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
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?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Use the information to work out how many gifts there are in each pile.
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?
Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?
What is happening at each box in these machines?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
This number has 903 digits. What is the sum of all 903 digits?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Number problems at primary level that require careful consideration.