# Explaining fractions to a child: How to teach fractions to young children

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## How to teach fractions to young children

“I’ll have the smaller half!”

How many times have we said this contradicting statement? Of all the topics in elementary math, fractions is the one that seems to cause the most dread among children and adults alike. Teaching fractions is difficult because for many children, they present the first mathematical stumbling block. Fractions can behave in ways that seem strange at first. For example, every child knows 5 is greater than 4 so they can become confused when told that 1/5 is less than 1/4.

When thinking about how to introduce fractions to your child, it’s important to focus not only on the rules of fractions, but also the meaning behind them. Understanding fractions is the goal.

To understand how to explain fractions to children, we’re going to take a close look at one particular fraction: a half.

#### What is a fraction?

Fractions are used to represent smaller pieces (or parts) of a whole. The parts might make up a ‘whole’, which may be one thing, or more than one thing. Sounds confusing, doesn’t it? Let’s use some tasty treats to get our heads around it all.

Here’s a bar of chocolate (yum!) broken into two identical parts. Each part is one half of the overall amount.

This can also be written as 1/2. Let’s break down this notation – warning: some fancy long words are coming!

#### How to Teach Fractions

When writing a fraction, it helps to get your child to write the denominator first, as this tells us how many equal parts the whole is being divided into (e.g. 2 pieces of chocolate). They can say this out loud as they write it. Then draw the fraction bar (vinculum) which separates the numerator and denominator. Finally, write the numerator which is the top number in a fraction. This shows how many parts we have (e.g. 1 whole chocolate).

Notice how fractions build on simple counting exercises – the key is to know what you are counting at each step. Let’s try another example. This time, our tasty example involves 12 iced biscuits.

There are 12 in all, 6 of which are pink and 6 are blue. We can say that 6 out of 12, or 6/12, are pink. This is the same as 1/2 because one out of every two biscuits is pink. We say that 6/12 and 1/2 are equivalent because they represent the same amount.

#### Use different representations

So far we’ve used groups of objects to represent fractions. We can also use lengths. Here’s a train ambling along the tracks without a care in the world.

We can measure the whole length of the train track and say that the train is half way along. In this case, the fraction 1/2 denotes what proportion of the track the train has travelled (for every 2 meters that cover the whole track, it has covered 1 meter).

You can hopefully see that even a really simple fraction like 1/2 can be modelled in different ways. When children are given the opportunity to visualize fractions (particularly more complicated ones) across different situations, they deepen their understanding of how these strange objects behave.

Very soon, your child will learn to recognize ‘one half’ in everyday situations: half a cake, half past twelve, a glass half full. The key to understanding fractions is to build them into other daily routines. Food is a fantastic resource for fractions. You can use pasta pieces or dried beans in place of counters and then have your child draw them as pictures, coloring in different parts to denote various fractions.

#### Fun ways to teach fractions around the house

You can also collect lots of different objects from around the house – a dressing gown tie, potato, coin, book, glass of water, bunch of grapes, two apples, piece of paper, and so on – and then identify half of each of these objects. A potato is often irregular in its shape so cutting it in half doesn’t necessarily mean each half will be equal. How would you find half?

Activities like these will help build your child’s grasp of mathematical language. Make sure that your child can explain a) why the two parts are equal and b) what the whole is in this situation.

The most important thing to remember when you’re dealing with fractions is to go slowly and use a variety of representations. It’s always worth taking a bit of extra time to hone the basics!

## Learning Fractions — How to Teach Fractions to Kids

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Jessica Kaminski

April 16, 2022

Learning fractions can be hard for many children because it goes beyond basic simple arithmetic calculations. To understand the concept, kids need to practice with examples every day before they can master fractions. This article provides tips on how to learn fractions in a fun and engaging way.

### What is a fraction?

A fraction is a number that indicates a part of a whole. One can write a fraction using two numbers separated by a line instead of a division symbol.

The number above the line is a numerator and represents the number of parts you have. Similarly, the number below the line is called a denominator and represents the total number of parts in the whole area or object.

A simple fraction shows one part that has been partitioned into equal parts. A proper fraction is the one where a numerator is strictly less than a denominator. An improper fraction has a numerator that is greater than or equal to its denominator.

When teaching fractions, you can show kids that 2/5 means that 2 is divided by 5. Each piece that we divide the whole into is called a part, and each part has an equal value. The number on top tells us how many parts we have.

### How to teach fractions to a child?

At what grade do you learn fractions? Kids meet fractions as early as in their first grade. At this stage, you can draw circles or squares with different colors and then divide those shapes into parts. Such pictures will be among the fun ways to teach fractions.

While learning fractions for beginners, you can use colors. For example, you can divide a circle into 2 equal parts and apply blue color for one part and red color for the other part of the circle.

Such an approach will help kids understand that half of the circle is blue and half of it is red, which will let children understand fractions without using any numbers or symbols.

Once children master this concept, you can introduce multiplication. For example, start with simple examples like 1/2 × 1/3 = 1/6 if you are not sure how to teach multiplying fractions.

#### The Nominator

A nominator is a number that indicates how many parts of a whole you have. In other words, a nominator is simply a number that represents the value of the fraction.

A nominator is the first part of a fraction. The other part is called a denominator, which is the bottom number in a fraction.

The purpose of a nominator in fractions is to tell you how many parts you have or what number to count up to. The following is an example of how to teach simplifying fractions:

2/3 means 2 out of 3 parts. So, if you were to cut a cake into 3 equal slices, you would eat 2 of them. Fraction explained, right?

1/2 means 1 out of 2 parts. If you cut that same cake into 2 slices, you would eat 1 slice and leave 1 slice for someone else to eat.

Another example is the following: if you have a pizza and slice it into eight pieces, each piece would be one-eighth of the pizza. You could also say that each piece is “one over eight” or “one/eight” of the whole pizza.

#### The Numerator

A numerator is a term used in mathematics that refers to the number above the line in a common fraction. You can think of a numerator as an indicator representing the number of parts you want to take from the whole.

For example, in the fraction 5/8, “5” is the numerator, while the number below the line (8) is called the denominator.

A numerator represents many equal parts, indicating how many of those parts are taken or considered. In the fraction 7/10, for instance, seven parts are taken out of ten equal parts.

#### Fraction Notation

Fraction notation is a form of writing simple fractions, ratios, and other numbers. It is represented by two digits or numbers separated by a line and placed over each other. In other words, fractional notation is a way to express ratios using the division sign and slashes.

Fractions are usually written using the slash symbol (/) but can also be presented as a division equation with a division sign (÷).

The examples are 3/4, 12/16, 1/3, etc. If you write 3/4, it means that there are three-quarters of something. This thing can be any object or concept. 1/2 is one half, 1/3 is one-third, and so on.

#### Fractions in Everyday Life

There are numerous cases in everyday life where we apply fractions. They not only show up in math class but also can help measure things such as distance or time. For example, when measuring distance, we use fractions of a mile or a kilometer.

When you go to the gas station, you will see pumps that measure gasoline by fractions of gallons. Gallons are divided into halves, quarters, and halves or quarter’s eighths. More importantly, such division makes it easier to fill up a vehicle’s gas tank because some tanks only hold certain amounts of fuel.

Fractions are useful in cooking recipes. We use them when we are measuring ingredients while cooking.  Recipes require you to cut, halve, or double ingredients.

In addition, measurements of liquids may require you to use fractions. Fractions also show up on measuring tapes and rulers to measure parts of an inch and parts of a foot accurately.

Another application of fractions is measuring time. For example, if you have three-quarters of an hour to complete an exam, you will have 45 minutes to complete the exam since there are 60 minutes in one hour.

### Conclusion

The process of learning fractions does not have to be tedious. Numerous useful tips can help make math lessons more interesting and engaging for students. A truly effective math tutor will know how to explain fractions to convey the mathematical concepts in a creative way that children love.

Jessica Kaminski

Jessica is a a seasoned math tutor with over a decade of experience in the field. With a BSc and Master’s degree in Mathematics, she enjoys nurturing math geniuses, regardless of their age, grade, and skills. Apart from tutoring, Jessica blogs at Brighterly. She also has experience in child psychology, homeschooling and curriculum consultation for schools and EdTech websites.

## How to explain fractions to a child?

from Maria Tyunina

Describes a simple and accessible method for explaining fractions.

Of course, children perceive some concrete meanings much better than, for example, abstract ones. And here the question arises: how to explain fractions to a child? How to make him understand what 2/3 is? In order to make it easier for a child to explain what fractions are, it is necessary to follow some rules in the process.

Rules

• The first thing you need to do is to captivate the child.

Let’s say you are walking on the street and you decide to play hopscotch with your child. So instead of all the usual numbers, invite your child to jump 1.5 steps. This will be your first step towards learning fractional numbers. The child will begin to understand that in addition to integer values, there are also fractional ones.

• Show with examples. Pick up an apple or any other fruit and offer it to two children at the same time. Of course, they will unanimously say that this is not possible. Then cut the apple in half and give to each of the children. Thus, emphasize that each number can be divided.

How to explain fractions to a child?

This is certainly not an easy question. But completely solvable.

1. Take six sweets and have your child divide them in half. Then add another candy and ask them to do the same. Of course, he will say that this is impossible. Cut the candy in half and explain to the baby that you can do it like this and then everyone will have an even amount of candies.

2. In addition to all of the above, fractions can be explained to children using a cut circle. Immediately it must be divided into one, two, three, four, six or eight parts.

It is important to explain the notation of fractions: the number below shows how many equal parts, i.e. parts, the whole is divided into, and the number above shows how many such parts the given fraction contains.

Equal parts of the whole: the circle shows how the whole can be divided into different numbers of equal parts.

After that, you need to invite the children to take a circle. Then we divide the circle in half. Even if you exchange halves with a friend, the circle will still remain a circle. After that, we divide the already existing halves in half again. Consequently, in the end it becomes clear that the circle can also be of four parts. Now you need to reflect all the results obtained in the form of a fraction on paper. In this case, it is imperative to explain what the numerator is and what the denominator is. This is how you can easily answer the question: how to explain fractions to a child.

Summing up, it is worth saying that in the process of learning do not forget that in the process of learning you should give your child illustrative examples and accompany everything with your own explanations. This is necessary so that the child can understand exactly how numbers are divided. If you demonstrate this to him clearly, then believe me, he will master the fractions quickly enough.

## Why mathematics in grades 5–6 is the basis of future education

06.12.2022

Irina Kochkova

Teacher, teacher of the Russian language MAXIMUM EDUCATION

The elementary school is over, the child, who has mastered counting perfectly, goes to the fifth grade — and suddenly, for no reason, problems begin with mathematics: instead of the usual integers, some fractions — ordinary, mixed, decimal … A student who has not encountered this before is horrified: mathematics is immediately written down in unloved subjects that cannot be understood and which “will never come in handy”. We tell you how to help a fifth grader fall in love with and understand the “queen of sciences”.

### Mathematics in secondary school: the causes of difficulty

In fact, most students encounter difficulties in one way or another during the transition to secondary school. This happens for a number of reasons:

1. Change of teacher. In four years, the class gets used to one teacher. Having moved to the middle link, some guys start to miss him, so the appearance of new subject teachers is perceived painfully, it is necessary to adapt to it.
2. Change of curriculum. Often in the fifth or sixth grade, students change the line of textbooks. As a result, the children have to get used to a new methodological approach, new explanations, a new way of presenting theoretical material. All this can be accompanied by difficulties in understanding.
3. Psychophysiological changes within the student himself. Fifth graders are already approaching early adolescence, when a lot of behavior and perception begins to change. It’s already difficult for a child to get used to such changes, and then they also couldn’t understand mathematics — self-confidence is rapidly falling.
4. The emergence of new complex topics . In mathematics, it is primarily fractions. Previously, students were used to operating only with integers, so it can be difficult to readjust.

Despite all these difficulties, it is still very important for students of the fifth and sixth grades to understand mathematics, especially fractions. The fact is that in two or three years more complex topics will appear in the program, which simply cannot be dealt with without knowledge of fractions. And even if the child is not going to connect his life with mathematics directly, one way or another he will have to deal with it when studying other disciplines, such as physics, chemistry, biology, etc.

### Why 5th grade math is needed

It is mostly difficult for a child to deal with fractions because they are counted a little differently than whole numbers. The student cannot understand: if 3 is greater than 2, then why is ⅓ less than ½? And why, if 3+2=5, then ⅓+½ is not ⅕ at all?

However, an understanding of the principle by which fractions work will certainly come in handy later, regardless of what specialty he chooses in the future, even if it is not directly related to the exact sciences.

1. So, for students in the natural sciences, for example, for biologists and chemists, fractions are useful for calculating the mass fraction of a substance in mixtures and solutions.
2. For a social and humanitarian profile, it is necessary to be able to calculate statistics and interpret the data obtained. Without working with fractional numbers, this is impossible.
3. Mathematics is necessary even for representatives of creative professions. For example, when learning a complex piece, musicians encounter target notes, halves, quarters, eighth notes, and so on. It is simply impossible to perform a work without the concept of musical beats.

It is very important that the child understands that understanding mathematics at this stage will make it easier for him to continue his studies, no matter what specialty he chooses. This will help motivate you to study the subject further.

### How to explain fractions to a child?

All parents whose children struggle with fractions in the fifth grade are concerned about how to help them deal with this topic in order to avoid problems in the future.

1. Show fractions in real life. If it is difficult for a student to work with abstract numbers in class, you can show illustrative examples at home: a piece of chocolate or fruit. Then he will see for himself: half an apple is larger than a quarter, and if you put them together, you get three quarters.
2. If your child is into music, you can explain fractions using musical beats as an example.
3. To teach your child to compare fractions, you can show him a simple rule “closer to one or farther from one”. So, for example, ⅘ will be greater than ¾, because only ⅕ separates this fraction from a whole number, while the second is ¼.
4. Do not be afraid to use entertainment materials — educational computer and board games, cartoons. Currently, there are quite a few of them.

The restructuring of thinking during the transition to the middle link can be difficult. Children may have problems with math, even if it used to be easy for them. However, it is still necessary to understand it in order to get a good base for mastering high school disciplines.

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