After training hard, these two children have improved their
results. Can you work out the length or height of their first
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.
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.
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?
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?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
Resources to support understanding of multiplication and division through playing with number.
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?
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?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
56 406 is the product of two consecutive numbers. What are these
The triangles in these sets are similar - can you work out the
lengths of the sides which have question marks?
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?
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.
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?
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?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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?
Can you work out what a ziffle is on the planet Zargon?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Can you see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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?
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?
What is the sum of all the three digit whole numbers?
Annie cut this numbered cake into 3 pieces with 3 cuts so that the
numbers on each piece added to the same total. Where were the cuts
and what fraction of the whole cake was each piece?
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.
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
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
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?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
When I type a sequence of letters my calculator gives the product
of all the numbers in the corresponding memories. What numbers
should I store so that when I type 'ONE' it returns 1, and when I
type. . . .
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
What is happening at each box in these machines?
Can you arrange 5 different digits (from 0 - 9) in the cross in the