Resources to support understanding of multiplication and division through playing with number.
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?
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?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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.
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
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?
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 see why 2 by 2 could be 5? Can you predict what 2 by 10
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
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
Given the products of adjacent cells, can you complete this Sudoku?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
Can you replace the letters with numbers? Is there only one solution in each case?
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?
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
Can you complete this jigsaw of the multiplication square?
Here is a chance to play a version of the classic Countdown Game.
If you take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Choose a symbol to put into the number sentence.
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?
Number problems at primary level that require careful consideration.
Can you work out what a ziffle is on the planet Zargon?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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!
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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 Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.
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?
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
Use the information to work out how many gifts there are in each
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.
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
What is happening at each box in these machines?
Use this information to work out whether the front or back wheel of
this bicycle gets more wear and tear.
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
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?
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.
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?