How would you find out how many football cards Catrina has collected?
It's Sahila's birthday and she is having a party. How could you answer these questions using a picture, with things, with numbers or symbols?
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!
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?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?
Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?
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?
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.
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?
How will you work out which numbers have been used to create this multiplication square?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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.
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.
Can you find different ways of creating paths using these paving slabs?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
How many starfish could there be on the beach, and how many children, if I can see 28 arms?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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?
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?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Number problems at primary level that require careful consideration.
56 406 is the product of two consecutive numbers. What are these two numbers?
What is the sum of all the three digit whole numbers?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
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?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
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?
Can you each work out the number on your card? What do you notice? How could you sort the cards?
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
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?
A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.
Can you work out what a ziffle is on the planet Zargon?
Resources to support understanding of multiplication and division through playing with number.
Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
This challenge combines addition, multiplication, perseverance and even proof.
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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?
This task combines spatial awareness with addition and multiplication.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
This number has 903 digits. What is the sum of all 903 digits?
Here is a chance to play a version of the classic Countdown Game.
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?