How will you work out which numbers have been used to create this multiplication square?
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.
Can you find different ways of creating paths using these paving slabs?
56 406 is the product of two consecutive numbers. What are these two 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?
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?
Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Number problems at primary level that require careful consideration.
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?
Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
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.
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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?
What is happening at each box in these machines?
How many starfish could there be on the beach, and how many children, if I can see 28 arms?
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!
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
This task offers an opportunity to explore all sorts of number relationships, but particularly multiplication.
Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Use the information to work out how many gifts there are in each pile.
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?
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?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Find the next number in this pattern: 3, 7, 19, 55 ...
This task combines spatial awareness with addition and multiplication.
Can you work out what a ziffle is on the planet Zargon?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
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?
If the answer's 2010, what could the question be?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Number problems at primary level that may require resilience.
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?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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?
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?
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.