We’ve spoken before about how to teach your child the basics of division, here.
In that article we spoke about the different ways of visualising division (as ‘sharing’ sweets between friends or as ‘grouping’ objects into bags) before introducing an ‘array’ as a way of arranging objects on the page that helps with multiplication and division. Take a look to remind yourself of the important concepts underlying the methods of division before reading on.
In this ‘how to’ article we go further to outline the ways in which you can help your older children to tackle the division of even larger numbers using three (often dreaded!) written methods: chunking, short division and long division.
We’ve noted that many parents approach division with fear and trepidation. Whizz Education is here to reassure you that homework on division can be enjoyable, if not always super easy and plain-sailing (we’re all learning, after all).
Re-Capping Division
As our previous article on division shows, children now use and visualise solid objects as a way of understanding division early in their schooling. By the time they come to learn written methods of division they have a firm foundation in how, where and why division is important. This means that written methods of division are not simply memorised and then easily forgotten.
Reminder: Division involves a ‘dividend’ (the number to be divided), a divisor (the number by which another number is divided) and a quotient (the result of dividing the divisor by the dividend, or more generally of dividing one number by another).
Before learning written methods of division, it is important to remember the principle of ‘commutativity’. Put simply, this means that it matters where you put the numbers in a division calculation, in a way that is not true for multiplication.
In division, the dividend and divisor must be a certain way around. 2 x 5 and 5 x 2 both equal 10, even when the multipliers are swapped around. In division 10 ÷ 2 produces a very different answer to 10 ÷ 5. The divisor and the dividend cannot be switched.
Written methods are not always required for division. Sometimes, being able to do mental maths is a sufficient skill and will help your child to estimate if they have the correct answer when they move on to calculations with bigger numbers.
Help your child to fill in the gaps below:
Learning written methods of division can become procedural – students follow the steps without understanding how they follow on from one another – so it is vital to master foundational mathematical vocabulary and exercises, before moving on to apply the written methods to different problems and contexts.
Method 1: Chunking
Chunking uses the method of repeatedly subtracting a divisor from a dividend to see how many times it ‘fits’ into the number (the quotient).
Take, for example, 12 ÷ 3.
The chunking method requires students to repeatedly subtract 3 from 12 until the answer is 0, as follows:
So, 3 has been subtracted a total of 4 times and 12 ÷ 3 = 4
Eventually, students will be able to use their times tables to speed-up the process. For example, they might subtract 6 because it is a multiple of 3.
Take, for example, 14 ÷ 3.
Here is another method to visualise it:
So, 3 has been subtracted a total of 4 times and 14 ÷ 3 = 4r2
The term r2 means ‘remainder 2’ which shows that subtracting any number of threes could not achieve 0. You might think of this as ‘two left over’. Because 2 is smaller than the divisor, it is impossible to subtract another 3 without going into negative numbers.
Usually, these kinds of calculations would be demonstrated using a number line, rather than chunking because the numbers we are dealing with are so small. Chunking must also be presented in a very specific way on the page.
Let’s take 562 ÷ 12 as a more appropriate example to follow:
First, we subtract ‘12 lots of 20’, or 240, from 562 to get 322, like so:
Because we have 322 remaining, we can subtract 240 again, like so:
Because we have 82 remaining, we can subtract ‘6 lots of 12’, or 72, like so:
This is the appropriate written method to use when writing in your exercise book.
We can see from the right-hand column in brackets that 12 has been subtracted a total of 46 times.
Because 10 is smaller than 12, we have 10 ‘left over’ at the bottom of the vertical column of subtraction calculations.
So, 562 ÷ 12 = 46r10.
This method soon becomes time-consuming and for most division calculations the method of short division, or ‘the bus stop method’, can be used.
Method 2: Short Division (The Bus Stop Method)
Just like chunking, short division answers the question: how many times does the divisor ‘fit’ into the dividend?
Short division is best for calculations using a single-digit divisor and a two- or three-digit dividend.
Short division is often referred to as the ‘bus stop method’ simply because of the shape of the sign used to complete the calculation. Otherwise, teachers generally agree that the analogy is not especially helpful.
Let’s take 140 ÷ 4 as our example to follow
To begin, draw the ‘bus stop’ and place the divisor on the outside and the dividend on the inside, like so:
The next step is to see how many times 4 fits into the first digit of the dividend. 4 is larger than 1 so it fits a total of 0 times.
Write ‘0’ above the bus stop and carry across the 1 to the next number, like so:
Then we need to see how many times 4 fits into 14. If we know our times-tables we know that 4 x 3 = 12 which is as close to 14 as we can possibly get.
Write ‘3’ above the bus stop because ‘3 lots of 4 fit into 14’ and carry across the remaining 2 to the next number (because 14 – 12 = 2), like so:
Finally, we need to see how many times 4 fits into 20.
4 x 5 = 20, so we write ‘5’ above the bus stop, like so:
And we have our answer! 4 fits into 140 a total of 35 times, which we can write as 140 ÷ 4 = 35.
To help your child to master the bus-stop method, the best thing to do is to ensure that they have a handle on their times-tables and recognise factor pairs.
You might try the following exercises:
- Ask your child questions in daily life, such as how many £1 coins make-up a £10 note or how many seeds each bird would get if there are 100 seeds and 5 birds, or whether you have enough pairs of cutlery in the draw for 8 people. Relate the questions to what you see around you.
- Dedicate 30 minutes a week to speed-testing times tables and factor pairs
- Practice taking a question, say 254 ÷ 4, and putting the digits in the correct place in the bus stop
Method 3: Long Division
Long division follows a similar method to short division but is used for calculations with even larger numbers and when the divisor has two-digits.
Let’s follow the example of 562 ÷ 12.
To begin, draw the ‘bus stop’ and place the divisor on the outside and the dividend on the inside, like so:
12 does not fit into the first digit of the dividend, so we must determine how many times 12 fits into 56.
12 x 4 = 48 which is as close to 56 as we can get. We write ‘4’ above the bus-stop to reflect the fact that ‘4 lots of 12 fit into 56’ and subtract 48 from 56, like so:
Finally, we must work out how many times 12 fits into the remaining 82 (8 tens and 2 ones).
12 x 6 = 72 which is as close to 82 as we can get.
We write ‘6’ above the bus-stop and subtract 72 from 82 so that we know the remainder (see earlier in the article for a discussion of remainders), like so:
And we are left with an answer of 562 ÷ 12 = 46r10 (said forty-six, remainder 10).
The important thing to remember when practicing long division is to go slowly and write neatly so that you keep track of any steps and missteps.
As with all maths skills, learning the basics of division and learning times-tables by heart will help immeasurably when it comes to using written methods for more complex calculations.
If you haven’t already tried them, our free games will help with some of the skills (addition, subtraction, multiplication, doubling, halving, mental calculation or understanding place value) that contribute to an understanding of division – see for Reception through to Year 8.
Important: The nature of describing division in words means that it would be easy to just follow the steps as they are written above. Make sure that you encourage your child to speak about division in all sorts of contexts in order to problem solve. To ensure that they follow the steps in the written methods of division by intuition and understanding, rather than by rote make sure to revisit and talk about the foundational skills of division discussed in our previous article.
