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 see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
This activity focuses on doubling multiples of five.
What is the sum of all the three digit whole numbers?
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?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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 complete this jigsaw of the multiplication square?
Can you replace the letters with numbers? Is there only one
solution in each case?
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?
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.
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.
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
56 406 is the product of two consecutive numbers. What are these
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?
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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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?
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Can you work out what a ziffle is on the planet Zargon?
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
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.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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.
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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!
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.
Claire thinks she has the most sports cards in her album. "I have
12 pages with 2 cards on each page", says Claire. Ross counts his
cards. "No! I have 3 cards on each of my pages and there are. . . .
What is happening at each box in these machines?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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.
After training hard, these two children have improved their
results. Can you work out the length or height of their first
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?
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
Resources to support understanding of multiplication and division through playing with number.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
This task combines spatial awareness with addition and multiplication.
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
Have a go at balancing this equation. Can you find different ways of doing it?
Can you work out some different ways to balance this equation?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?