## Division Methods for Primary School

Posted on January, 2024

### What is Division?

Division is the action of separating something into smaller parts.

It is one of the four operations in maths and is the inverse of multiplication.

These methods change as children get older and move from key stage 1 to 2.

In time, children eventually learn advanced division methods such as long division.

## Visual and Tactile Division Methods

In key stage one, children who are around 5 or 6 will usually need to first understand the concept of division.

The easiest way to teach children at this young age is by using realia (real objects) and sharing them.

For instance, getting them to share counters equally is a great way to show the main aim of division.

Once students have a handle on these basics, then they can start using a written pictorial method to perform basic divisions.

Take a look at this visual division gif below:

Once students become confident with this visual method, they can be introduced to the concept of a remainder, when there is one counter/object left over.

Students should start learning their 1, 2, and 5 multiplications before attempting division problems.

## Repeated Subtraction

Division can also be understood as repeated subtraction.

Let’s explore this idea with a couple of examples.

#### Example 1: 12÷4

Repeated Subtraction: Think of 12÷4 as repeatedly subtracting 4 from 12 until you can’t subtract anymore.

1. 12−4=8
2. 8−4=4
3. 4−4=0

So, 12÷4 equals 3 because you could subtract 4 three times from 12.

#### Example 2: 15÷3

Repeated Subtraction: Consider 15÷3 as subtracting 3 from 15 repeatedly.

1. 15−3=12
2. 12−3=9
3. 9−3=6
4. 6−3=3
5. 3−3=0

So, 15÷3 is 5 because you could subtract 3 five times from 15.

#### Conceptual Understanding:

This way of thinking about division helps to visualise the process and reinforces the idea that division is about distributing a quantity into equal parts.

It’s a foundational concept that can be especially helpful for introducing division to learners and building a solid understanding of the operation.

## Bus Stop Division Method (Short)

Once children get confident with a visual method, they can move on to a more adaptable method called bus stop method.

This method is the most important division method that a child can master.

Mastery of this method will allow your child to approach most division sums with confidence. Children need to master this method before taking the 11 plus, GCSE maths, and entering secondary school.

Short division works as a method best when the number you divide by (divisor), is a single digit. Short division can, however, be used to work out more difficult sums with larger divisors.

Check out this graphic which shows the division of 84 by 3.

### Remainders

Students also need to be aware that when a number ends up left over, we call this a remainder. We indicate that there is a remainder by placing an “r” on top of the bus stop after our answer.

For instance:

## The Layout of Division Sums

Division sums can be presented in several different ways.

Traditionally, division is shown with a special sign called an obelus. Division sums can also be presented as fractions and at a bus stop. Students should be able to recognise each situation.

Look at the graphic below to see how the presentation of the division sum can vary:

## The Wordings of Division Sums

Division sums can be worded in different ways. Students need to become familiar with these different wordings. Here are some of the scenarios that students need to know about:

1. Quotient Unknown:
• Divide 15 by 3.
• What is the result when you divide 24 by 4?
• If you have 27 apples and share them equally among 9 friends, how many does each friend get?
2. Dividend Unknown:
• If you divide a number by 5 and get 8 as the quotient, what is the original number?
• There are 21 candies in total, and each student gets 7 candies. How many students are there?
3. Divisor Unknown:
• If you have 18 cookies and want to divide them equally among some friends, how many friends should there be if each friend gets 3 cookies?
• If a number is divided by 9, and the result is 6, what is the original number?
4. Remainder or Fractional Part:
• If you divide 17 by 5, what is the remainder?
• What is the result when you divide 10 by 3, expressed as a mixed number?
5. Problem Solving:
• John has $45. He wants to buy books that cost$9 each. How many books can he buy?
• A farmer has 36 eggs and wants to pack them into cartons. If each carton holds 6 eggs, how many cartons will he need?
6. Real-life Scenarios:
• A baker made 60 cupcakes and wants to distribute them equally among 12 children. How many cupcakes will each child get?
• If a car travels 240 miles and takes 4 hours to do so, what is its average speed?

These are just a few examples, and the wording can vary based on the context and the complexity of the problem. The essence remains the same: division involves distributing a quantity into equal parts, and the answer is expressed as the quotient.

## Conclusion

In conclusion, division is a fundamental mathematical operation that involves separating a quantity into smaller, equal parts. It serves as the inverse of multiplication and is crucial for various mathematical concepts. This blog has explored different methods to teach division, from visual and tactile approaches in the early stages to more advanced techniques like the bus stop method.

The concept of repeated subtraction has been emphasised, offering a practical understanding of division. The importance of mastering division with remainders, the layout of division sums, and the various wordings of division problems were also discussed.

With a solid grasp of these concepts, learners can confidently approach division problems in real-life scenarios and problem-solving situations, dividing a versatile and essential skill in mathematical understanding.

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