Resources tagged with: Multiplication & division

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Broad Topics > Calculations and Numerical Methods > Multiplication & division

Activities on the Gattegno Chart

Age 5 to 11

In this article, Alf outlines six activities using the Gattegno chart, which help to develop understanding of place value, multiplication and division.

Fingers and Hands

Age 7 to 11 Challenge Level:

How would you count the number of fingers in these pictures?

Being Resourceful - Primary Number

Age 5 to 11 Challenge Level:

Number problems at primary level that require careful consideration.

Odds and Threes

Age 7 to 11 Challenge Level:

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.

Number Tracks

Age 7 to 11 Challenge Level:

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?

Method in Multiplying Madness?

Age 7 to 14 Challenge Level:

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

Making Pathways

Age 7 to 11 Challenge Level:

Can you find different ways of creating paths using these paving slabs?

Square Subtraction

Age 7 to 11 Challenge Level:

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?

Numbers Numbers Everywhere!

Age 5 to 11

Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.

Largest Number

Age 11 to 14 Challenge Level:

What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.

Surprising Split

Age 7 to 11 Challenge Level:

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

A Mixed-up Clock

Age 7 to 11 Challenge Level:

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

Journeys on the Gattegno Tens Chart

Age 5 to 11

Alf describes how the Gattegno chart helped a class of 7-9 year olds gain an awareness of place value and of the inverse relationship between multiplication and division.

Sumo

Age 7 to 11 Challenge Level:

A number game requiring a strategy.

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.

One Million to Seven

Age 7 to 11 Challenge Level:

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?

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?

Can You Make 100?

Age 11 to 14 Challenge Level:

How many ways can you find to put in operation signs (+ - x ÷) to make 100?

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,. . . .

Fair Feast

Age 5 to 11 Challenge Level:

Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?

Wild Jack

Age 7 to 11 Challenge Level:

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.

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.

What's My Weight?

Age 7 to 11 Short Challenge Level:

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?

As Easy as 1,2,3

Age 11 to 14 Challenge Level:

When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .

Compare the Calculations

Age 7 to 11 Challenge Level:

Can you put these four calculations into order of difficulty? How did you decide?

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!

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?

Product Sudoku

Age 11 to 16 Challenge Level:

The clues for this Sudoku are the product of the numbers in adjacent squares.

Looking at Lego

Age 7 to 11 Challenge Level:

This task offers an opportunity to explore all sorts of number relationships, but particularly multiplication.

A First Product Sudoku

Age 11 to 14 Challenge Level:

Given the products of adjacent cells, can you complete this Sudoku?

X Marks the Spot

Age 11 to 14 Challenge Level:

When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .

Ducking and Dividing

Age 7 to 11 Challenge Level:

Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?

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?

Difficulties with Division

Age 5 to 11

This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.

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?

Oh! Hidden Inside?

Age 11 to 14 Challenge Level:

Find the number which has 8 divisors, such that the product of the divisors is 331776.

Repeaters

Age 11 to 14 Challenge Level:

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

Divide it Out

Age 7 to 11 Challenge Level:

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

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?

Book Codes

Age 7 to 11 Challenge Level:

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?

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.

Jumping

Age 7 to 11 Challenge Level:

After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?

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?

Funny Factorisation

Age 11 to 16 Challenge Level:

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?

Six Numbered Cubes

Age 7 to 11 Challenge Level:

This task combines spatial awareness with addition and multiplication.

Six Ten Total

Age 7 to 11 Challenge Level:

This challenge combines addition, multiplication, perseverance and even proof.

Four Go for Two

Age 7 to 11 Challenge Level:

Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?

Gabriel's Problem

Age 11 to 14 Challenge Level:

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

Which Symbol?

Age 7 to 11 Challenge Level:

Choose a symbol to put into the number sentence.

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.