Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
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?
The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?
Here is a chance to play a fractions version of the classic Countdown Game.
Here is a chance to play a version of the classic Countdown Game.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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?
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .
56 406 is the product of two consecutive numbers. What are these two numbers?
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
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?
Investigate the different ways that fifteen schools could have given money in a charity fundraiser.
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?
Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
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.
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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.
Benâ€™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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Can you find different ways of creating paths using these paving slabs?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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?
Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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?
This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .
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 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!
A number game requiring a strategy.
This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
This Sudoku requires you to do some working backwards before working forwards.
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?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
In this simulation of a balance, you can drag numbers and parts of number sentences on to the trays. Have a play!
This task combines spatial awareness with addition and multiplication.
This challenge combines addition, multiplication, perseverance and even proof.
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
Choose a symbol to put into the number sentence.
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.
This article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.
Alf describes how the Gattegno chart helped a class of 7-9 year olds gain an awareness of place value and of the inverse relationship between multiplication and division.
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
Can you work out what a ziffle is on the planet Zargon?
Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?