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?
A game that tests your understanding of remainders.
Find a great variety of ways of asking questions which make 8.
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
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?
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?
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.
On Friday the magic plant was only 2 centimetres tall. Every day it
doubled its height. How tall was it on Monday?
Can you work out some different ways to balance this equation?
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 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?
Can you see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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?
Resources to support understanding of multiplication and division through playing with number.
Can you work out what a ziffle is on the planet Zargon?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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?
After training hard, these two children have improved their
results. Can you work out the length or height of their first
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
This number has 903 digits. What is the sum of all 903 digits?
The triangles in these sets are similar - can you work out the
lengths of the sides which have question marks?
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?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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'.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Can you replace the letters with numbers? Is there only one
solution in each case?
Have a go at balancing this equation. Can you find different ways of doing it?
What is the sum of all the three digit whole 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?
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?
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?
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
56 406 is the product of two consecutive numbers. What are these
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
At the beginning of May Tom put his tomato plant outside. On the
same day he sowed a bean in another pot. When will the two be the
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?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
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?