Division is one of the four operations a child is introduced to after learning to count, recognize and write numbers. They are addition, subtraction, multiplication, and division. These operations are used to manipulate numbers. They open up a whole new world of possibilities for students as they progress through the academic ladder.
Division is usually the last of the four to be taught. This is because it's a little more involved than others. It comes with additional rules outside of what the other three offers.
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For instance, the concept of remainder usually appears alien to students at first acquaintance, but as they attempt more exercise, they get conversant with it.
Division is also more complex because a part of it involves the iteration of the other operations. Long division, for example, is a combination of addition, multiplication and subtraction.
It can get overwhelming for new learners. Therefore, learning the concept has to follow a progressive learning structure.
This article presents a simple strategy for learning division from ground up.
History of Division
Thinking of how close division is to man and his activities, you'd want to believe that division dates as far back as man. There are chances the ancestors of our ancestors performed division without actually having a name for it. Of course, when you share things equally or unequally, you have performed division.
However, for subjects like this, which are part of man's existence, the credit usually goes to the person who finds a name or formalizes it.
For division, the credit went to a Swiss mathematician named Johann Heinrich Rahn, who introduced the division symbol (÷) – a horizontal line with a point each, above and below.
He introduced the symbol in a work he published in 1659. Although the symbol is widely known today, it was not accepted in his own country, Switzerland. They said it was too graphical. They expected something simpler to write than even the plus sign.
However, the symbol was welcomed by countries like the United States, Canada, and Great Britain. It got popular so much so that you'd find it on calculators, business and academic papers.
A German mathematician, Gottfried W Leibniz, later introduced another symbol. It was less graphical and had since become the most universally accepted symbol of division. It is called the two points (:) symbol.
Application of Division
Thinking about the application of division answers questions like why is it important to learn it.
Like many other math topics, such as fractions, division is practical. In fact, operations like division and multiplication are what make numbers make sense. learn more about fractions here.
Here are a few applications of division:
Sharing: Sharing is the most basic application of division. Division as a whole means sharing. We share things every day: food, money, objects, resources, etc.; division helps us share accordingly.
Percentage: Percentage is a highly visual form of communicating numbers and quantities. It is perhaps the most sensational application of division. It has gone on to become a globally accepted form of stating numbers for both math junkies and non-junkies alike. It involves division by 100.
Recipes: Recipes are always in small quantities measured in parts. "3/4 of a tablespoon", 50% water", etc.
Budget and Planning: We plan our expenses upfront and allocate funds to them accordingly. Sometimes the allocations are in the form of percentages.
Division of Labor: Division of labor is common to all workforce. Different people mean different aspects of the production. When you divide labor, you do not only divide work, you divide time.
Prerequisite for Learning Division
Learning to divide is not all that sexy like repeating the English Alphabets. It's not what a grade 1 or grade 2 student will joyfully jump at. To have a seamless experience with division, students should have mastered the following:
Counting Numbers: While this may seem too basic, it's the fundamental of every mathematical operation. Students should be able to recognize, count, and write numbers before attempting division.
Addition, Subtraction, and Multiplication: They are all basic operations for manipulating numbers. Division is the fourth one. It is also the most involving. It is a game of its own. Students must be grounded in the first three before attempting division
Learning Division the Easy Way
Let's take a step-by-step approach on how to learn division effectively. Division, however, is not like counting numbers or reciting the English alphabets that could be mastered even by mindless repetitions. The concept and logic must be internalized. A picture must be seen and comprehended to be able to tackle any division problem whatsoever.
Here are some steps:
The first step in learning to divide is to grasp the concept and internalize the logic. It's like multiplication. You have to know how it works to work out 2x2 and 4x5 on your own. If you don't understand the procedure, much of what you'd do would be largely memorization.
How many can you memorize?
This first step of introducing division is pretty much about how it's presented to the students. It depends on the analogies, the metaphors, the examples and the illustrations.
Here are some suggestions:
Dividing: Dividing is one of the most popular ways of learning division. 10/5 can be explained by asking learners to divide 10 pens between 5 people, in which case each gets 2. With enough repetition of diving items and objects into several places, they understand the background logic of division.
Grouping: Explaining division through grouping is similar to sharing. Instead of giving out what's been shared, it's grouped. For an experienced person, the two methods may have no difference whatsoever, but it offers a new language of explaining the concept. 15/5 here would be presented as grouping 15 balls into 5 groups, in which case, each group has 3 members(balls) each.
In grades 2 and 3 texts, these concepts are presented as illustrations and pictures. It is important because, at that level, school children are visual learners, still trying to picture the world. Teachers are however encouraged to practically engage students when teaching.
Division Without Remainder
After a student internalizes the logic of division, the next step is performing simple integer division that does not involve remainder—divisions like 10/2, 50/5, 20/4, etc., without the use of diagrams. However, at this beginning level, you'd often see students drawing strokes and grouping them in an attempt to divide.
It's fine. We all did it. It takes some amount of practice to become conversant with the whole idea.
Division With Remainder
Next step? Division with remainder.
For many students, division is interesting until there's a remainder. At first, it may be challenging, but they soon fit all the parts together into one giant ball.
What students find most challenging about remainders is what to do with them. How would they represent them mathematically? That's where fractions come in.
5/2 is 2 remainder 1. That makes it 2 ½. The remainder is represented as a fraction.
This is where it gets interesting. This is because it's where division meets multiplication, addition, and subtraction. While long division is a progressive aspect of division, students are not immediately taught the concepts. It's a grade 4 and 5 coursework.
While you can easily divide small numbers like 100/10, 100/50, you need long division to perform complex divisions like 1573/43, 523/13, 519/121, etc.
Long division gives you the ability and confidence to perform any division, no matter how complex.
The beauty of any knowledge is in its subconscious application. You need to master division to the point where it becomes part of your internal math skills.
Here are a few ways to do so:
Get a personal tutor: Digging through all the exercises and disciplining yourself not to give up on tough exercises may not be easy if you're doing it all on your own. A tutor keeps you on your toes while encouraging and challenging you at the same time. He also helps you skyrocket your learning process.
Here at Superprof, we have qualified tutors who are passionate about helping students grow.
Practice website/Apps: There are several websites and apps that can help you learn and master division. Websites like Homeschoolmath, have division exercises for all academic levels. They also have worksheets to get you busy in real-time. Other websites like weareteachers have visual exercises to help you build your division skill with fun.
Read more about the best websites for math revision.
Division Games: There are games for almost every educational topic. Many math topics have been broken down into games, including division. While it doesn't feel like you're in the class, these games involve you mentally. They get more challenging as you ascend from stage to stage.
Have Fun Dividing
Division is one of the several approaches to learning math in school. It's also one of the math operations we perform every day. Learning and mastering it goes beyond passing exams. You don't want to be at the groceries and get stuck trying to figure 90/9.
Start from the basics, then work your way up. See why the times table is significant.
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