Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
Use this information to work out whether the front or back wheel of
this bicycle gets more wear and tear.
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
What is the sum of all the three digit whole numbers?
The triangles in these sets are similar - can you work out the
lengths of the sides which have question marks?
Mr. Sunshine tells the children they will have 2 hours of homework.
After several calculations, Harry says he hasn't got time to do
this homework. Can you see where his reasoning is wrong?
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?
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.
Resources to support understanding of multiplication and division through playing with number.
After training hard, these two children have improved their
results. Can you work out the length or height of their first
During the third hour after midnight the hands on a clock point in
the same direction (so one hand is over the top of the other). At
what time, to the nearest second, does this happen?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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?
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
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?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
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?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
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?
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?
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
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?
What is happening at each box in these machines?
Put a number at the top of the machine and collect a number at the
bottom. What do you get? Which numbers get back to themselves?
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?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Can you see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
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!
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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?
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?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?