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.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
What is the sum of all the three digit whole numbers?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
56 406 is the product of two consecutive numbers. What are these
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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?
Find a great variety of ways of asking questions which make 8.
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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?
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.
What is happening at each box in these machines?
Can you see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
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 looks at how teachers can use problems from the NRICH site to help them teach division.
Use this information to work out whether the front or back wheel of
this bicycle gets more wear and tear.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
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?
Mr. Sunshine tells the children they will have 2 hours of homework.
After several calculations, Harry says he hasn't got time to do
this homework. Can you see where his reasoning is wrong?
On the table there is a pile of oranges and lemons that weighs
exactly one kilogram. Using the information, can you work out how
many lemons there are?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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.
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?
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
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?
Use the information to work out how many gifts there are in each
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
After training hard, these two children have improved their
results. Can you work out the length or height of their first
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.
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? What do you think is happening to the numbers?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Can you work out what a ziffle is on the planet Zargon?
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? Don't forget to keep visiting NRICH projects site for the
latest developments and questions.
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
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.
When I type a sequence of letters my calculator gives the product
of all the numbers in the corresponding memories. What numbers
should I store so that when I type 'ONE' it returns 1, and when I
type. . . .
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?