Primary School Division: Easy Methods for Teaching Your Child Division in Years 1 – 6.
Division is one of the trickiest topics for primary school children. Often, this is due to teaching that is focused on memorisation rather than understanding.
Parents are left confused when it comes to homework or if their child does not understand. Many parents ask us “How do I teach my child division?” We’ve outlined some step-by-step easy to do division methods that will have your child practising division at ease in no time!
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What is division?
To divide something is to split or ‘share’ it into parts. In other words, it is the opposite of multiplication. As an example, imagine 3 friends want to share 6 slices of cake equally between them. How many slices of cake would each friend receive? The answer is 2 pieces of cake each – 3 people each have 2 slices of cake for a total of 6 slices.
Another reason division can be confusing is that it uses specific terminology. The key terms that you need to know are:
- Dividend: the number being divided.
- Divisor: the number you are dividing by.
- Quotient: the result of division.
An easy way to remember these terms is the following: dividend ÷ divisor = quotient. Using our example above, the 6 slices of cake represent the dividend, the 3 friends represent the divisor and the slices of cake each person receives (2) is the quotient. So this could be written as: 6 ÷ 3 = 2.
Now that you have recapped what division is and the key terminology surrounding it, lets look at the techniques that are taught in primary school.
Primary school division: what is the chunking method?
Chunking is used once a number is too big to be divided mentally. This method involves calculating how many ‘chunks’ of a number fit into another number, where each ‘chunk’ is a straightforward multiple to calculate, such as 10x, 5x or 2x the divisor. The number of chunks (along with any remainder) will then represent the result of the division (the quotient). An example will help to clarify.
Let’s say you wanted to calculate 163 ÷ 9. First, you could calculate 9 x 10 = 90 and subtract that from 163. That would leave 163 – 90 = 73. Next, let’s calculate 9 x 5 = 45 and subtract that from 73. That would leave 73 – 45 = 28. Finally, we have only 28 left. We should spot that 9 x 3 = 27 and 28 – 27 = 1. Since we have only 1 left, we cannot divide by 9 again.
Okay, now let’s add up how many times we multiplied by 9. First, we did 9 x 10 so that’s 10 lots of 9. Next we did 9 x 5 so that’s 5 lots of nine, meaning we have 15 lots of 9 in total. Finally, we did 9 x 3 for another 3 lots of 9 giving us 18 lots of 9 in total (10 + 5 + 3). Great! However, it is important to remember that the answer is not 18 because we have a remainder of 1. In other words, the number 163 cannot be divided exactly by 9. It can be divided by 9 only 18 times with 1 left over, so the answer is 18 remainder 1.
Why does my child need to learn the chunking division method?
Many parents are confused as to why the chunking method is used when short and long division can be much quicker. The answer is simple and comes back to my earlier point: children need to understand what division really means. Short and long division are great for getting quick answers, but poor at teaching the underlying idea behind division.
How chunking helps to solve division problems:
Chunking, by contrast, gives a better introduction to division. The focus throughout is on the whole calculation and the idea of splitting or sharing, rather than just following rules for generating answers. The less rigid nature of chunking also requires more understanding from the child unlike with short and long division which follow a repeatable procedure, so it is usually easy to spot if a child really understands the method or is just memorising technique.
Primary school short division (bus stop method): definition and the method explained:
Once your child is comfortable with chunking and clearly understands the concepts behind division, it is time to move onto short division, often called the bus stop method. Short division is the single most popular method for children as it is easy to learn and answers can be calculated in just a few steps even with exceptionally large numbers. Short division is often called the ‘bus stop’ method since the calculation looks like a bus stop when drawn on paper.
How to do bus stop division:
Short division does not use the usual divide sign (÷) but instead is written as follows:
quotient
divisor ⟌dividend
We’ll now use an example to illustrate the method. Let’s say that we want to divide 934 by 7. That would be written as follows:
7 ⟌934
Let’s now go through the steps needed to calculate the answer. Starting from the left, we divide each individual number in the dividend by the divisor. So, first we divide 9 by 7, which gives 1 remainder 2, written as follows:
1
7 ⟌9234
Once the division has been performed, the whole number (in this case, 1) is placed above the first digit of the dividend (9), and the remainder is written as a small digit (called a ‘superscript’) to the right of the first digit of the dividend. The superscript number is then combined with the number to its right (in this case forming the number 23) and the process is repeated.
13
7 ⟌92324
We divided 23 by 7 to get 3 remainder 2. The whole number (3) is placed above the second digit and the remainder (2) is written in superscript to the right of the second digit of the dividend (3). So far, so good. We continue to repeat this method until there are no digits left to divide in the dividend.
133 r 3
7 ⟌92324
The final number in the dividend is 4. Combined with the remainder of 2 from the previous division and we make 24. If we divide 24 by 7 we get 3 remainder 3. Since there are no further numbers in the dividend, we write this as ‘remainder 3’ or ‘r 3’.
Now let’s return to the original example and assume that we have been asked to calculate an exact, decimal answer. The way that we do this is to add a decimal point and zeroes as necessary to the right of the dividend. For example:
133
7 ⟌92324.30
We would now need to divide 30 by 7, which gives 4 remainder 2.
133.4
7 ⟌92324.3020
The method remains the same. The whole number answer to the division is placed above, forming part of the quotient, while the remainder is written in superscript to the right of the number that is being divided. This can go on for a long time…
133.4285
7 ⟌92324.30206040
Generally, the most any question will ask for is an accuracy of 2 or 3 decimal places, so don’t worry too much. The point is that the method remains the same regardless of the number of steps it takes to find the answer.
Primary school long division explained:
If a question uses numbers that are too large for short division, then we move on to long division. The key advantage of this method is that it can solve any division problem no matter the size of the numbers involved. The method is like short division but long form and requires more steps. We’ll use an example to illustrate:
15 ⟌824
As we can see, the problem is written in the same form as if we were going to use short division. The first step is also the same as short division:
0
15 ⟌8824
The first digit of the dividend is smaller than the divisor, so we place a 0 above the 8. Now we have to divide 82 by 15 using some mental maths:
05
15 ⟌8824
Here’s where the method of long division diverges from short division. First, we calculate that 15 can only fit into 82 a total of 5 times with a remainder of 7. We then multiply the divisor by 5: 15 x 5 = 75. This number is written below the dividend and then subtracted from the number we just divided (82):
05
15 ⟌8824
-75
07
In other words, the remainder is written below rather the dividend rather than to the side of the quotient, as in short division. The next number in the dividend is then moved down to sit alongside the remainder:
05
15 ⟌8824
-75
074
We now repeat the first step by dividing 74 by 15. This brings an answer of 4 remainder 14:
054
15 ⟌8824
-75
074
-60
14
That makes the final answer 54 remainder 14. We can check if this is correct by multiplying 54 by 15 and then adding 14.
Is division too hard at primary school?
This is the method takes the longest to master. If your child gets stuck, tell them not to panic, but instead to refer to the process. Go back to the last step that you understand and check where you went wrong. Try again and repeat as necessary until you get the answer.
Primary school division methods and what we have learned:
Thank you for sticking with me up to this point. You should feel much more comfortable about what division is and how the different methods of division work. Let’s have a brief recap.
- Chunking is a method where you repeatedly subtract the divisor from the dividend until there is an answer. This method is not always as quick as short or long division but it helps your child to understand the concept of division and is an essential first step before moving on to short division.
- Short division, also known as the bus stop method, is method which breaks down a division problem into a series of easy steps. It is a short form of long division where the products (the results of multiplication) are omitted and the partial remainders are notated as superscripts.
- Long division is a method which begins in the same way as short division but has additional steps which allow children to answer any question by hand regardless of the size of the divisor.
Primary school division tips for parents and kids:
Once you understand all the different division techniques, it is important to understand when to use each method. It is not always easy to choose, but a few guidelines should help:
- Chunking works best with smaller numbers and for teaching the concept of division.
- Short division works best for dividing large numbers by 1-digit numbers.
- Long division works best when dividing large numbers by numbers with more than 1 digit.
These methods will be especially useful for Year 6 SATS as your child will have to answer some division-based questions. The techniques explained in this article will set a solid foundation for them to answer any SATS question. However, questions will often be complicated by multiple layers or unusual wording. It is crucial to practice as many past questions as possible to ensure your child is comfortable applying the methods in tricky situations.
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