This problem is designed to help children to learn, and to use, the two and three times tables.
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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.
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
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?
Resources to support understanding of multiplication and division through playing with 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?
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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
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 this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
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?
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
On Friday the magic plant was only 2 centimetres tall. Every day it
doubled its height. How tall was it on Monday?
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.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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?
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?
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?
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 complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Can you work out what a ziffle is on the planet Zargon?
Can you work out some different ways to balance this equation?
Have a go at balancing this equation. Can you find different ways of doing it?
This activity focuses on doubling multiples of five.
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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?
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 fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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 triangles in these sets are similar - can you work out the
lengths of the sides which have question marks?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
What is the sum of all the three digit whole numbers?
56 406 is the product of two consecutive numbers. What are these
Find the next number in this pattern: 3, 7, 19, 55 ...
This number has 903 digits. What is the sum of all 903 digits?
Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?
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?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?