This problem is designed to help children to learn, and to use, the two and three times tables.
A game that tests your understanding of remainders.
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 Chris and Michael are going to share equally.
Can you tell us what each of them will have?
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?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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?
Look at different ways of dividing things. What do they mean? How might you show them in a picture, with things, with numbers and symbols?
Find a great variety of ways of asking questions which make 8.
Resources to support understanding of multiplication and division through playing with number.
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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?
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 design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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.
This number has 903 digits. What is the sum of all 903 digits?
56 406 is the product of two consecutive numbers. What are these
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?
Can you work out what a ziffle is on the planet Zargon?
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
In the multiplication sum, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
What is the sum of all the three digit whole numbers?
Can you see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
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.
A game for 2 or more players with a pack of cards. Practise your
skills of addition, subtraction, multiplication and division to hit
the target score.
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!
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.
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 this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
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.
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Use your logical-thinking skills to deduce how much Dan's crisps
and ice-cream cost altogether.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
How would you count the number of fingers in these pictures?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?