Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
What is the sum of all the three digit whole numbers?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
56 406 is the product of two consecutive numbers. What are these
In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
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?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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.
On Friday the magic plant was only 2 centimetres tall. Every day it
doubled its height. How tall was it on Monday?
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?
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.
The triangles in these sets are similar - can you work out the
lengths of the sides which have question marks?
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?
Use this information to work out whether the front or back wheel of
this bicycle gets more wear and tear.
After training hard, these two children have improved their
results. Can you work out the length or height of their first
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?
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.
This activity focuses on doubling multiples of five.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Take the number 6 469 693 230 and divide it by the first ten prime
numbers and you'll find the most beautiful, most magic of all
numbers. What is it?
Can you work out what a ziffle is on the planet Zargon?
Resources to support understanding of multiplication and division through playing with number.
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?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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?
This problem is designed to help children to learn, and to use, the two and three times tables.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
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.
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
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!
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?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
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.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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?
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?
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.
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.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?