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Investigations. Interactivities. Practical Activity. Combinations. Factors and multiples. Addition & subtraction. Generalising. Working systematically. Visualising. Multiplication & division.There are 124 results
Broad Topics > Calculations and Numerical Methods > Multiplication & division
It Figures
Age 7 to 11 Challenge Level:
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?
The Pied Piper of Hamelin
Age 7 to 11 Challenge Level:
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!
ABC
Age 7 to 11 Challenge Level:
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Route Product
Age 7 to 11 Challenge Level:
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
Forgot the Numbers
Age 7 to 11 Challenge Level:
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?
A-magical Number Maze
Age 7 to 11 Challenge Level:
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!
X Is 5 Squares
Age 7 to 11 Challenge Level:
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Domino Numbers
Age 7 to 11 Challenge Level:
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Dice and Spinner Numbers
Age 7 to 11 Challenge Level:
If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?
Twenty Divided Into Six
Age 7 to 11 Challenge Level:
Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?
Multiplication Series: Illustrating Number Properties with Arrays
Age 5 to 11
This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .
Arranging the Tables
Age 7 to 11 Challenge Level:
There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.
Zargon Glasses
Age 7 to 11 Challenge Level:
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
Rabbits in the Pen
Age 7 to 11 Challenge Level:
Using the statements, can you work out how many of each type of rabbit there are in these pens?
The Clockmaker's Birthday Cake
Age 7 to 11 Challenge Level:
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
How Old?
Age 7 to 11 Challenge Level:
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
Doplication
Age 7 to 11 Challenge Level:
We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
Magic Constants
Age 7 to 11 Challenge Level:
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?
Oh! Harry!
Age 7 to 11 Challenge Level:
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
The Puzzling Sweet Shop
Age 5 to 11 Challenge Level:
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?
Clock Face
Age 7 to 11 Challenge Level:
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
Gift Stacks
Age 7 to 11 Challenge Level:
Use the information to work out how many gifts there are in each pile.
Developing Number Fluency - What, Why and How
Age 5 to 11
In this article for primary teachers, Lynne McClure outlines what is meant by fluency in the context of number and explains how our selection of NRICH tasks can help.
Starfish Spotting
Age 5 to 7 Challenge Level:
How many starfish could there be on the beach, and how many children, if I can see 28 arms?
Place Value as a Building Block for Developing Fluency in the Calculation Process
Age 5 to 11
This article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.
Children's Mathematical Graphics: Understanding the Key Concept
Age 5 to 7
In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
What's Left?
Age 5 to 7 Challenge Level:
Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?
Penta Post
Age 7 to 11 Challenge Level:
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?
Napier's Bones
Age 7 to 11 Challenge Level:
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?
Today's Date - 01/06/2009
Age 5 to 11 Challenge Level:
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
How Much Did it Cost?
Age 7 to 11 Challenge Level:
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Asteroid Blast
Age 7 to 11 Challenge Level:
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Countdown
Age 7 to 14 Challenge Level:
Here is a chance to play a version of the classic Countdown Game.
The Money Maze
Age 7 to 11 Challenge Level:
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
Function Machines
Age 7 to 11 Challenge Level:
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
Cows and Sheep
Age 7 to 11 Challenge Level:
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
Sept03 Sept03 Sept03
Age 7 to 11 Challenge Level:
This number has 903 digits. What is the sum of all 903 digits?
Next Number
Age 7 to 11 Short Challenge Level:
Find the next number in this pattern: 3, 7, 19, 55 ...
Being Resourceful - Primary Number
Age 5 to 11 Challenge Level:
Number problems at primary level that require careful consideration.
Month Mania
Age 5 to 11 Challenge Level:
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
Making Longer, Making Shorter
Age 5 to 7 Challenge Level:
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
Bundles of Cubes
Age 7 to 11 Challenge Level:
Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
Tables Teaser
Age 5 to 7 Challenge Level:
How will you work out which numbers have been used to create this multiplication square?
Throw a 100
Age 7 to 11 Challenge Level:
Can you score 100 by throwing rings on this board? Is there more than way to do it?
Sometimes We Lose Things
Age 7 to 11 Challenge Level:
Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.
The Number Crunching Machine
Age 7 to 11 Challenge Level:
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?
Dividing a Cake
Age 7 to 11 Challenge Level:
Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?
The 24 Game
Age 7 to 11 Challenge Level:
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?
NRICH is part of the family of activities in the Millennium Mathematics Project.