{"id":9282,"date":"2022-03-11T10:27:00","date_gmt":"2022-03-11T10:27:00","guid":{"rendered":"https:\/\/whizz-com.stackstaging.com\/how-to-teach-your-child-advanced-division-using-chunking-short-division-and-long-division\/"},"modified":"2023-03-08T09:56:08","modified_gmt":"2023-03-08T09:56:08","slug":"how-to-teach-your-child-advanced-division-using-chunking-short-division-and-long-division","status":"publish","type":"post","link":"https:\/\/whizz.com\/en-us\/blog\/how-to-teach-your-child-advanced-division-using-chunking-short-division-and-long-division\/","title":{"rendered":"How to: Teach your child Advanced Division (using chunking, short division and long division)"},"content":{"rendered":"\t\t
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We\u2019ve spoken before about how to teach your child the basics of division, here<\/a>.<\/p>

In that article we spoke about the different ways of visualizing division (as \u2018sharing\u2019 sweets between friends or as \u2018grouping\u2019 objects into bags) before introducing an \u2018array\u2019 as a way of arranging objects on the page that helps with multiplication and division. Take a look<\/a> to remind yourself of the important concepts underlying the methods of division before reading on.<\/p>

In this \u2018how to\u2019 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.<\/p>

We\u2019ve 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\u2019re all learning, after all).<\/p>

Re-Capping Division<\/h2>

As our previous article<\/a> on division shows, children now use and visualize 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 memorized and then easily forgotten.<\/p>

Reminder: Division involves a \u2018dividend\u2019 (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).<\/p>

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Before learning written methods of division, it is important to remember the principle of \u2018commutativity\u2019. Put simply, this means that it matters<\/em> where you put the numbers in a division calculation, in a way that is not true for multiplication.<\/p>

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 \u00f7 2 produces a very different answer to 10 \u00f7 5. The divisor and the dividend cannot be switched.<\/p>

Written methods are not always required for division. Sometimes, being able to do mental math 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.<\/p>

Help your child to fill in the gaps below:<\/p>

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\u00a0<\/p>

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Learning written methods of division can become procedural \u2013 students follow the steps without understanding how they follow on from one another \u2013 so it is vital to master foundational mathematical vocabulary and exercises, before moving on to apply the written methods to different problems and contexts.<\/p>

Method 1: Chunking<\/h2>

Chunking uses the method of repeatedly subtracting a divisor from a dividend to see how many times it \u2018fits\u2019 into the number (the quotient).<\/p>

Take, for example, 12 \u00f7 3.<\/p>

The chunking method requires students to repeatedly subtract 3 from 12 until the answer is 0.<\/p>

So, 3 has been subtracted a total of 4 times and 12 \u00f7 3 = 4<\/p>

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.<\/p>

Take, for example, 14 \u00f7 3.<\/p>

So, 3 has been subtracted a total of 4 times and 14 \u00f7 3 = 4r2<\/p>

The term r2 means \u2018remainder 2\u2019 which shows that subtracting any number of threes could not achieve 0. You might think of this as \u2018two left over\u2019. Because 2 is smaller than the divisor, it is impossible to subtract another 3 without going into negative numbers.<\/p>

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.<\/p>

Let\u2019s take 562 \u00f7 12 as a more appropriate example.<\/p>

First, we subtract \u201812 lots of 20\u2019, or 240, from 562 to get 322.<\/p>

Because we have 322 remaining, we can subtract 240 again.<\/p>

Because we have 82 remaining, we can subtract \u20186 lots of 12\u2019, or 72.<\/p>

This is the appropriate written method to use when writing in your exercise book.<\/p>

We can see from the right-hand column in brackets that 12 has been subtracted a total of 46 times.<\/p>

Because 10 is smaller than 12, we have 10 \u2018left over\u2019 at the bottom of the vertical column of subtraction calculations.<\/p>

So, 562 \u00f7 12 = 46r10.<\/p>

This method soon becomes time-consuming and for most division calculations the method of short division, or \u2018the bus stop method\u2019, can be used.<\/p>

Method 2: Short Division (The Bus Stop Method)<\/h2>

Just like chunking, short division answers the question: how many times does the divisor \u2018fit\u2019 into the dividend?<\/p>

Short division is best for calculations using a single-digit divisor and a two- or three-digit dividend.<\/p>

Short division is often referred to as the \u2018bus stop method\u2019 simply because of the shape of the sign used to complete the calculation. Otherwise, teachers generally agree that the analogy is not especially helpful.<\/p>

Let\u2019s take 140 \u00f7 4 as our example to follow.<\/p>

To begin, draw the \u2018bus stop\u2019 and place the divisor on the outside and the dividend on the inside.<\/p>

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.<\/p>

Write \u20180\u2019 above the bus stop and carry across the 1 to the next number.<\/p>

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.<\/p>

Write \u20183\u2019 above the bus stop because \u20183 lots of 4 fit into 14\u2019 and carry across the remaining 2 to the next number (because 14 \u2013 12 = 2).<\/p>

Finally, we need to see how many times 4 fits into 20.<\/p>

4 x 5 = 20, so we write \u20185\u2019 above the bus stop.<\/p>

And we have our answer! 4 fits into 140 a total of 35 times, which we can write as 140 \u00f7 4 = 35.<\/p>

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 recognize factor pairs.<\/p>

You might try the following exercises:<\/p>