On Friday the magic plant was only 2 centimetres tall. Every day it
doubled its height. How tall was it on Monday?
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.
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?
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?
Annie and Ben are playing a game with a calculator. What was
Annie's secret number?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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?
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
On a calculator, make 15 by using only the 2 key and any of the
four operations keys. How many ways can you find to do it?
Find another number that is one short of a square number and when
you double it and add 1, the result is also a square number.
There are three buckets each of which holds a maximum of 5 litres.
Use the clues to work out how much liquid there is in each bucket.
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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?
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 this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
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?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Use the information to work out how many gifts there are in each
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
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.
The triangles in these sets are similar - can you work out the
lengths of the sides which have question marks?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
After training hard, these two children have improved their
results. Can you work out the length or height of their first
This activity focuses on doubling multiples of five.
These eleven shapes each stand for a different number. Can you use
the multiplication sums to work out what they are?
What is the sum of all the three digit whole numbers?
This problem is designed to help children to learn, and to use, the two and three times tables.
Can you replace the letters with numbers? Is there only one
solution in each case?
Resources to support understanding of multiplication and division through playing with number.
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.
Can you work out some different ways to balance this equation?
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 group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
How would you count the number of fingers in these pictures?
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?
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Claire thinks she has the most sports cards in her album. "I have
12 pages with 2 cards on each page", says Claire. Ross counts his
cards. "No! I have 3 cards on each of my pages and there are. . . .
What is happening at each box in these machines?
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?
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!
This number has 903 digits. What is the sum of all 903 digits?
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.