Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
What is the sum of all the three digit whole numbers?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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?
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?
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 complete this jigsaw of the multiplication square?
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 put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Can you replace the letters with numbers? Is there only one
solution in each case?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Here is a chance to play a version of the classic Countdown Game.
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?
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.
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.
This challenge is a game for two players. Choose two numbers from the grid and multiply or divide, then mark your answer on the number line. Can you get four in a row before your partner?
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
Can you work out the arrangement of the digits in the square so
that the given products are correct? The numbers 1 - 9 may be used
once and once only.
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
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 article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
What is happening at each box in these machines?
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
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!
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Use the information to work out how many gifts there are in each
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 why 2 by 2 could be 5? Can you predict what 2 by 10
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
This problem is designed to help children to learn, and to use, the two and three times tables.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Unmultiply is a game of quick estimation. You need to find two numbers that multiply together to something close to the given target - fast! 10 levels with a high scores table.
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?
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.
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 complete this calculation by filling in the missing numbers? In how many different ways can you do it?