Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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?
After training hard, these two children have improved their
results. Can you work out the length or height of their first
Resources to support understanding of multiplication and division through playing with number.
This problem is designed to help children to learn, and to use, the two and three times tables.
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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?
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?
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?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Can you work out some different ways to balance this equation?
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?
On Friday the magic plant was only 2 centimetres tall. Every day it
doubled its height. How tall was it on Monday?
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?
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?
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 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?
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?
Can you see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
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?
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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?
Can you work out what a ziffle is on the planet Zargon?
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?
This activity focuses on doubling multiples of five.
56 406 is the product of two consecutive numbers. What are these
Have a go at balancing this equation. Can you find different ways of doing it?
If you had any number of ordinary dice, what are the possible ways
of making their totals 6? What would the product of the dice be
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
These eleven shapes each stand for a different number. Can you use
the multiplication sums to work out what they are?
We can arrange dots in a similar way to the 5 on a dice and they
usually sit quite well into a rectangular shape. How many
altogether in this 3 by 5? What happens for other sizes?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Find the next number in this pattern: 3, 7, 19, 55 ...
If the answer's 2010, what could the question be?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
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!
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?