As most teachers will know, finding the right long division method for KS2 can take time and often prove difficult in the classroom, but it doesn’t have to if you have the right strategy in place. In this blog, Sophie Bee (@_MissieBee) talks you through the long division technique she has used with great success with her Year 6 primary school class, and talks you through how you can use it too.
Long division: long and divisive, right? Wrong!
Long division is probably one of my favourite things to teach Year 6 in maths (I know, I know – but bear with me).
When children watch you do it, they think it looks complicated, difficult and unnecessary, and it almost instantly turns them off – until they realise how systematic and logical it is.
Long Division Plays An Important Role In The SATs
We all know that the arithmetic paper is the one in which we expect the children to score the highest marks, and often, those crucial marks are lost because of inaccuracies in the children’s answers.
In all three SATs papers that have been released so far under the new curriculum, there have been two ‘long division’ (dividing by a 2-digit number) questions – that’s 10% of the arithmetic paper marks.
It is therefore crucial that children are fluent in division and confident with the accuracy of their answers, and this means finding the right KS2 long division method for your class.
According to the National Curriculum, Year 6 children should be taught to:
“Divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context”.
The Mathematics Appendix 1: Examples of formal written methods for addition, subtraction, multiplication and division “sets out some examples of formal written methods for all four operations to illustrate the range of methods that could be taught”, as shown below for long division. (Note that it also says, “For division, some pupils may include a subtraction symbol when subtracting multiples of the divisor”.)
The first two methods depicted are what have often been called the ‘chunking’ method; the third method is the one we shall be investigating (my favourite!).
But Wait….That Long Division Method Looks Too Hard I Hear You Shout!
I admit, when I first started teaching Year 6, I shied away from the long division method for a long time.
I’d never understood it properly, yet always considered myself a competent mathematician, so didn’t really understand the need for it.
It wasn’t until I sat down and decided to teach myself the method that I realised how systematic it was, and how it really embedded what was happening in each step of the division process – something that would be really useful for those that struggle with mathematical concepts.
A short personal story to show you that this technique can work is that during Year 6 SATs last year, I was very conscious of one of my ‘boundary’ children – you know the ones – who really struggled with confidence and general understanding in maths.
I took a sneak peek at them completing a long division question in the arithmetic paper and watched them methodically work their way through it to achieve the correct answer. This was someone who didn’t know their times tables at the start of the year, and I could’ve burst with pride! It was a case of long division made easy for this primary pupil, all thanks to the method we will be looking at below!
But Doesn’t Long Division Take Too…Well…Long?
Okay, so the name of the method doesn’t really help in selling itself, but, once you’re fluent, it should take the same amount of time (if not less) than ‘short division’. See the examples below, dividing 45,041 by 73 using firstly the short division method and then the long division method.
With short division, children still need to work out the remainders.
Many will need to do this via written subtraction anyway, and even if they can calculate them mentally, we all know how many mistakes are made by overconfident children when working at speed – especially when they refuse to write their workings-out!
If anything, the long division method took less time as I didn’t have to repeat myself by writing out the numbers again elsewhere on the page when calculating the remainders.
How Third Space Learning uses its interactive classroom to bring long division to life
With long division often proving troublesome to teach in the classroom, at Third Space we take full advantage of the interactive element of our online workspace. Here, our expert 1-to-1 tutors can break down the process and logic behind long division and present it in an easily digestible (and most importantly visual) manner for pupils.
Book your no commitment 10 minute demo to discover the impact our 1-to-1 interventions can have for your pupils – it’s never been easier or more affordable. Call us on 0203 771 0095 or contact us here to learn more about how we can help turbocharge maths in your school!
How Does This Method Of Long Division Work In The Primary Classroom?
Fear not! This is my tried and tested KS2 long division method of how to approach the topic with Year 6.
On average, it would take me around three days, but as we all know, this completely depends on the cohort, so I’ve broken the process down into ‘steps’ instead, to be spread across as many lessons as needed.
Using The Long Division Method: Step 1
Recap short division, ensuring children can talk through the process. Do they understand what’s happening at each step? For example, you could ask:
• What is the divisor?
• Why is it important to know multiples of the divisor?
• What is a remainder?
• How have you calculated the remainder?
• What happens if you get a remainder at the end of the question?
• How can you check your calculation is correct?
Once children are confident with short division, they can move onto long division.
Using The Long Division Method: Step 2
Dividing by 3 isn’t so scary, but dividing by 97 (as in 2018’s paper) is much more intimidating!
I’ll always start this lesson by asking children to list the first nine multiples of a ‘difficult’ number (such as 86) and watch them groan and do lots of column addition or counting on fingers or something else equally as inefficient. (Of course, there are occasionally those that can whizz through these – I know a few children who would quickly list multiples of 97 by adding 100 and subtracting 3 each time, but until we have a class full of children that can do that without prompting, this method will be worth it!)
I then show them how to do it by partitioning and it’s sometimes one of those moments where if a cartoon lightbulb could appear above their heads, it would (cue a chorus of “Ohhhhhh yeahhhhhh!”s).
(Another anecdote: the first time I did this, it was one of those lessons which on the face of it looked intensely boring, but the children got so carried away with it that they even asked to stay into their lunchtime to finish the questions! This just proves that engagement isn’t created from bells and whistles, but listing multiples in preparation for long division – you heard it here first!)
I ask the children to list nine multiples every time – asking them why you would only need nine multiples for any long division question is a good way of obtaining their understanding of the division process. Obviously, as they gain confidence in the method, they only need list as many as necessary.
Using The Long Division Method: Step 3
This is where I bring in the good old ‘me, we, you’ process.
Firstly, I show them a completed modelled example:
Then, I complete the division myself (next to the modelled example) to show them how I achieved it, always talking through each step as I go. This is usually when you get the “What?”, “Miss, I don’t get it”, or, “That’s impossible” comments; it doesn’t take much to change their minds!
Explaining This Long Division Method As You Go Is Very Important To Cement Understanding Of It
It’s important to explain the steps broken down: to divide, multiply, subtract, then bring the next number down.
I encourage the children to write the four symbols down on their page to remind themselves of the steps. They should have a solid understanding of these steps as, apart from the last one, they are the same as the short division process:
• Divide: how many times does the divisor fit into the number without remainder? (use the list of multiples)
• Multiply: multiply the answer to your previous division by the divisor to reach the multiple needed to calculate the remainder (use the list of multiples)
• Subtract: subtract the multiple from the original number to calculate the remainder
• Bring the next digit down: this replaces the ‘write the remainder just before the next number’ step in short division
(Numbers 2-5 come from this YouTube video:
This is purely because after watching this, it’s impossible to forget the order of the steps! Advance warning notice: Whilst this song is great to use in the classroom, it will be stuck in your head for a week if not longer…)
This method is far more coherently explained in the context of a specific question. Sometimes it’s appropriate to apply it to a division by a 1-digit number, to show how ‘long division’ is just a different way of setting out what they know as ‘short division’, but otherwise you can go straight into dividing by 2-digit number.
Let’s take the modelled long division example, 13,032 ÷ 24 (assuming we’ve already listed the multiples as in the modelled example in Step 3):
1: Divide: 130 ÷ 24 → 24 goes into 130 five times (I can see by looking through my list of multiples that 130 would be placed between 120, the 5th multiple, and 144, the 6th multiple). Note: as we’re working digit by digit from left to right, we can see that 24 doesn’t fit into 1 (the 1st digit), therefore a 0 is placed above it; it also doesn’t fit into 13 (the 1st and 2nd digit combined), therefore another 0 is placed above it. We are now working with 130 (the first three digits combined) which has ensured that all the place values are correctly aligned.
2: Multiply: 5 lots of 24 is 120 (I should know this from the answer to the previous step, but I can also count down my list of multiples to find the 5th multiple of 24). This is the number we need to work out the remainder to our first division (130 ÷ 24).
3: Subtract: 130 – 120 = 10, so this is the remainder to the first division (130 ÷ 24). This needs to be included in our next step
4: Bring the next digit down: bringing the 3 down makes my new number 103. I’ll then repeat the process again
5: Divide: 103 ÷ 24 → 24 goes into 103 four times (I can see by looking through my list of multiples that 103 would be placed between 96, the 4th multiple, and 120, the 5th multiple)
6: Multiply: 4 lots of 24 is 96 (I should know this from the answer to the previous step, but I can also count down my list of multiples to find the 4th multiple of 24). This is the number we need to work out the remainder from the second division (103 ÷ 24)
7: Subtract: 103 – 96 = 7, so this is the remainder to the second division (103 ÷ 24). This needs to be included in our next step
8: Bring the next digit down: bringing the final digit down creates my final number to work with: 72
9: Divide: 72 ÷ 24 = 3
10: Multiply: 3 x 24 = 72
11: Subtract: 72 – 72 = 0. There is no remainder, so we know that the divisor must fit into the original number exactly.
How You Can Get Your Class To Check Their Own Work
Of course, like in any activity the children do, it’s important to encourage them to check their own work.
They can do this by multiplying their answer by the divisor to see if the original number is produced. In this case, 543 x 24 = 13,032, so we know that we are correct.
If they don’t get the original number as their answer, I’ve found that the most common mistake the children make is either listing the multiples incorrectly or misaligning the place values (meaning they may have calculated one of the steps with the wrong numbers).
Using The Long Division Method: Step 4
Repetition, repetition, repetition.
Do loads of questions together on whiteboards and slowly take away the help. Then, when the children are ready, they can work independently.
In my classroom, this works as a ‘peeling away’ process, which often looks like this: input to the whole class for 5 minutes – 2 or 3 children set off to work independently; input to the rest of the class for a further 5 minutes – another few children set off to work independently; input to the rest of the class for a further 5 minutes – another group of children set off to work independently.
I’m then left with those requiring the most support, with whom I stay whilst my TA circulates the class, or with whom I ask my TA to stay whilst I circulate the class.
Using The Long Division Method: Step 5
Once children are confident with this method of long division, reasoning activities can then be introduced, such as long division with missing digits, or ‘spot the mistake/s’.
Of course, ultimately, if you don’t feel confident with this method, it will never translate effectively to the children; as with anything in teaching, it must work for you and your class.
However, knowing that this is often a topic hotly debated on Edu-Twitter and -Facebook, I hope I’ve converted some people to the long-division-loving side! In which case, please download and use this resource (including some free long division worksheets) to help with long division learning in your classroom.
It can be tricky to find the right long division method for KS2, but this is certainly a great place to start!
If you are looking for further help with long division, or any other element of KS2 maths in your school, take a look at our how our 1-to-1 interventions can make a difference for your target pupils.