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?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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.
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.
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?
Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?
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. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
This challenge combines addition, multiplication, perseverance and even proof.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
In this investigation, you are challenged to make mobile phone
numbers which are easy to remember. What happens if you make a
sequence adding 2 each time?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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?
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?
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?
There are four equal weights on one side of the scale and an apple
on the other side. What can you say that is true about the apple
and the weights from the picture?
What is happening at each box in these machines?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
There were 22 legs creeping across the web. How many flies? How many spiders?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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!
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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 see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
This task combines spatial awareness with addition and multiplication.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
At the beginning of May Tom put his tomato plant outside. On the
same day he sowed a bean in another pot. When will the two be the
Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?
Unmultiply is a game of quick estimation. You need to find two numbers that multiply together to something close to the given target - fast! 10 levels with a high scores table.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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.
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?
After training hard, these two children have improved their
results. Can you work out the length or height of their first
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
This activity focuses on doubling multiples of five.
Resources to support understanding of multiplication and division through playing with number.
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
This problem is designed to help children to learn, and to use, the two and three times tables.
Explore Alex's number plumber. What questions would you like to
ask? Don't forget to keep visiting NRICH projects site for the
latest developments and questions.