On Friday the magic plant was only 2 centimetres tall. Every day it
doubled its height. How tall was it on Monday?
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?
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?
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.
Use the information to work out how many gifts there are in each
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.
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Resources to support understanding of multiplication and division through playing with number.
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
Can you replace the letters with numbers? Is there only one
solution in each case?
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?
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.
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?
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
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 triangles in these sets are similar - can you work out the
lengths of the sides which have question marks?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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?
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?
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
After training hard, these two children have improved their
results. Can you work out the length or height of their first
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?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
This problem is designed to help children to learn, and to use, the two and three times tables.
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
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?
What is the sum of all the three digit whole numbers?
This activity focuses on doubling multiples of five.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
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?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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 game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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 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 work out some different ways to balance this equation?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
This number has 903 digits. What is the sum of all 903 digits?
How would you count the number of fingers in these pictures?
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?
If the answer's 2010, what could the question be?