# Fractions

## Introduction to Fractions

Fractions tend to be one of the most challenging topics in primary school. This is largely because of the conventional and dry manner in which they are presented to the students.

## The Big Idea: What is a Fraction?

At their core, a fraction is best thought of as a part of the whole.

**A piece of cake, literally!** Children must use shapes and figures to see what fractions are without resorting to technical terms. They must build familiarity with the idea of **parts of a whole**. Take this cake for example, it looks yummy right? But you can’t possibly eat **all of it**! So, you portion it out, **one slice at a time**, and that is all that a fraction is, **a part of a whole**!

### The Foundational Nature of Fractions

Learnt fractions as **NUMERATOR/DENOMINATOR**? Experts have shown that that’s just about the worst way to understand this topic.

Fractions is not just another math chapter. The concept of fractions is a wonderful mathematical idea that makes our life significantly easier. The familiar numbers like 1, 2, 3... are often not enough to describe certain situations. Especially when division leaves a remainder.

Wait, what has division got to do with fractions? While this may not surprise you too much, math is extremely interconnected. Each concept is intertwined with a bunch of other concepts. Understanding division is critical to understanding fractions.

## How do I understand or visualise fractions?

Through models and pictorial representations, children see that some fractions are less than one, while others can be greater than one.

They figure out that fractions being numbers, can also be added, subtracted, multiplied and divided with each other, and with whole numbers.

For now, before moving on to more complicated topics, let us try creating our own fraction and see how it changes based on the change in the numbers. Take special note of how they are labelled.

## Sub Topics

Here are a few links that will take you through the journey that every Cuemath students undertakes in the pursuit of understanding Fractions along with practice worksheets:

- Equivalent Fractions
- Improper and Mixed Fractions
- Addition and Subtraction of Fractions
- Multiplication of Fractions
- Division of Fractions

## How do you teach fractions?

In a class of approximately 50 students, it sometimes becomes overwhelming for a teacher to give the little extra individual attention that your child requires to fully understand a topic. Here are a few time-tested and effective ways that you can use to help your child out at home:

### Break it down:

Remember that the **big idea** behind fractions is that fractions are **a part of a whole**. When you take a look at the lattice above, you see that topics like division and properties of numbers form a ladder to fractions. Ensure that your child is comfortable performing those operations and with those concepts before starting their fractions journey. This practice is called **Chunking**.

Chunking is a time-tested method that ensures that learning happens at an optimal level. It builds from previously laid down concepts and helps your child connect the dots with newer concepts more easily. To get the most out of your child’s learning ability with chunking, feel free to incorporate a few problems from division and natural and whole numbers in between the fractions problems.

### Flash Cards are your friends:

Prepare flash cards for your child for fractions. Make sure that the flash cards cover all the salient concepts of the topic of fractions that your child is currently learning. Frequent and regular usage of flash cards is an excellent way of solidifying concepts.

Show them the concepts visually:

Being able to visualise or see a concept is the best way to ensure that it is fully understood and absorbed by your child. Use fruits like oranges, props like dice, legos, essentially objects that your child is familiar with to introduce new mathematical concepts.

### Practice makes perfect:

After understanding the concept comes practice. Nothing helps children learn faster than applying the concepts that they are taught. Research has shown that it allows them to cement their concepts and it leads to longer retention.

### Address the common doubts:

Children don’t always speak up in class when they have doubts. It’s due to multiple reasons, however the central problem remains, doubts don’t get cleared. So, when you are teaching your child at home, make sure that these common doubts are always cleared and not allowed to remain behind. This only hinders your child’s understanding, leading to frustration.

- When comparing fractions, you can
**only compare like fractions**. This is primarily because fractions represent parts of the**same whole**, so we utilize the concepts of**Equivalent Fractions**to make them comparable.

- When comparing two fractions and calculating the appropriate equivalent fractions, make sure you find the
**LCM of the denominators**of the fractions in the group.

## Common mistakes or misconceptions

**A common misconception is that just counting the shaded part is enough to identify the fraction**. To correctly identify the fraction, all parts must be equal.

For a part to be \(\frac{1}{4}\)^{th}, 4 such parts should add up to make a whole. But if some parts are smaller, then depending on the shape we take the whole will be different.

**Another misconception:****when finding fraction using area models, children incorrectly believe that the equal sized-piece must also look the same**.

Children say this diagram does not show \(\frac{1}{2}\) of the area of the square coloured because the pieces are “not the same (shape)”. They should know that if the areas of the parts are equal then they are identical. To address this use different geometrical shapes like circle, square, etc. and show how differently these shapes can be divided into the same number of parts.

- Children do not realise that
**while defined as parts of the whole, fractions are numbers**. Children fail to understand that \(\frac{1}{2}\), \(\frac{1}{4}\), etc. are also numbers. To address this, use the number line model to show the children how fractions exist between whole numbers and how even whole numbers can be denoted using fractional form. For instance, show him the following number line. Stress on how \(\frac{5}{8}\) and \(\frac{7}{8}\) lie between 0 and 1 as \(\frac{8}{8}\) is nothing but 1 on the number line written in fractional form since the numbers between 0 and 1 are divided into 8 parts here.

- When just learning fractions, all examples are of fractions less than 1. So,
**children may incorrectly believe that fractions are always less than 1**. This will create a barrier to understand improper fractions. While it may be okay to not address this when fractions are just being introduced, do watch out for this misconception as children build fluency.

## Tips and Tricks

**Tip:****Every time there’s an opportunity to talk about fractions, make use of it**. When you open a pack of biscuits, ask children what fraction each biscuit represents. When eating a pizza or cutting a cake or fruits this exercise can be repeated. Let children see how prevalent fractions are.**Referring to fractions such as \(\frac{3}{4}\) as “three out of four” in addition to “three fourths” helps**reiterate the idea that this fraction indicates 3 parts out of 4. Get students familiar with reading fractions in both these ways.**Don't introduce terms like numerator and denominator till students are completely comfortable**with describing fractions in a simpler language like “three out of four”.