Let us start with the question, what is a fraction?

Fraction is another way of representing a division.

They are represented using fractional notation . Here a is called the numerator and b, the denominator.

Like fractions have the same denominator. Unlike fractions have different denominators.

The line that separates the numerator and the denominator is called a fraction bar.

The different types of fractions are proper, improper and mixed fractions.

Fraction is a representation a part of the whole. It is taught using pictures, fractional models, and the number line.

For example, the colored parts in each of the models represent one part of equally divided parts of a whole.

Another way to represent a fraction is using the number line.  First, a unit of the number line is equally divided into a number equal to the denominator of the fraction. Use the numerator of the fraction to spot them on the number line.

To represent fractions on a number line,  say and   ,  first, divide the part from 0 to 1 into 3 equal parts. Now, each part represents one-third of a unit and thus,    and   can be marked as:

It is important to note that fractions can be defined only if the whole is divided into equal parts.

That is,  does not represent the fraction  .

A Chinese proverb says, “I hear, I forget. I see, I remember. I do, I understand”. Children understand better with pictorial examples. Further practice builds a strong foundation for the concept. This helps them in the advanced learning stages. SplashLearn has well-designed learning activities and worksheets that engage children positively. There, a good count of worksheets for identifying fractions and modeling fractions are available.

After the pictorial definitions, the children learn about comparing fractions. If two fractions have exact equal sizes they are called equivalent fractions.

Children enjoy playing any type of games and a math game is an excellent way to introduce and practice any mathematical concept.

Some of the benefits of using math games for teaching fractions are discussed below.

1. Increased learning: 

Math games provide a better understanding of the topic by intuitive thinking. It enables children to have clear problem-solving strategies. Interactive games for fractions attract children compared to the mere numerical fractional calculations. This results in an increased involvement and thus an increased learning.

2. Computational Fluency: 

Children relate math games more with a fun activity. This leads to a higher frequency of practice that makes calculations faster. The math fraction games for kids would involve a lot of numerical computations. This increases computational fluency.

3. Mathematical Thinking:

These games need a lot of strategic planning for advancing to various levels. This prepares children for a higher level mathematical thinking. This leads to a better problem-solving in studies as well as in life. In equivalent fractions games, the construction, as well as the identification of equivalent fractions, require a good amount of mathematical thinking.

4. Independence: 

Mathematical games designed for children are self-explanatory. It encourages children to try things independently. This enables children to learn independence through these games.

5. Self-Paced Learning: 

By playing math games independently, children can set a comfortable pace for themselves to learn the subject. This not only makes the understanding better, children also connect more with the facts learned. Some children are relatively slower in arithmetic calculations compared to others. This does not affect the fast learners just like in a traditional classroom.

Relatively simple fractions are introduced in Grade 3 with denominators 2, 3, 4, 6 and 8 using pictures, fractional models, and the number line. Once the child is familiar with fractions of numerator 1, they identify a fraction  as the summation of the unit fraction ,  added a times. That is, the fraction   is obtained by adding the two   s or    is obtained by adding four   s using fractional parts.

At this level, the children can compare two fractions based on their sizes and the identify equivalent fractions which are the ones with the same size. That is, they can understand that   and   have exactly the same size or they represent the same point on a number line. So, they are equivalent fractions.

Children also learn to generate equivalent fractions using addition. That is, adding two   results in  and this is the same point on a number line as . So,  and  are equivalent fractions. Fractional strips help children to understand the equivalence between the fractions.

In Grade 4, the children are advanced to more complex fractions. At this level, they understand that an equivalent fraction can be formed by multiplying the numerator and the denominator by the same number. That is,   and  are equivalent fractions.  

The concept of mixed numbers is also introduced. The child learns to add and subtract mixed numbers with like denominators initially. Gradually they solve word problems on the topic. Another concept introduced at this level is the multiplication of a fraction by a whole number. That is,  . Also in Grade 4, children understand the decimal notation for fractions with denominators 10 or 100 and use the concept to convert fraction to decimal, that is, rewriting  as 0.72.

In Grade 5, children learn to use equivalent fractions as a strategy for adding and subtracting fractions with different denominators. For example, to add  and  , the first fraction is rewritten as   and the addition is performed as:

            =

             =

Children learn to use a similar technique for performing subtraction.

Also, the child applies and extends the previous understanding of addition and subtraction to solve word problems involving fractions.

Two fractions are equivalent if they have the same size.

For example, the three fractions below are equivalent as the shaded region is exactly half the circle in all three cases:

While plotting fractions on number line, equivalent fractions are plotted at the exact same place.

The 3rd-grade fractions skills include the understanding that  is obtained by adding the two  s or    is obtained by adding four  s using fractional parts.

Thus,  and  have exactly the same parts shaded and therefore they are equivalent fractions.

In next level, the children can generate equivalent fractions without using any fractional models. The rule is to multiply the numerator and the denominator by the same number. That is,  and   are equivalent fractions.

Equivalent fractions have exactly the same size. So when compared, the result can be connected using equality symbol. For example, .

Comparing fractions with like denominator:

At the introductory stage, the comparing skill is limited to the fractions with the same denominator.

For example:

Five parts out of 8 are clearly more than 3 parts out of 8. So, it is clear that .

Here, children first learn estimating fractions using the benchmark fractions   and 1. That is, children can evaluate and classify the fraction into less than/greater than/equal to  and 1.

When unlike fractions to be compared, the children are supposed to generate equivalent fractions so that they have the same denominators and can be compared by simply comparing the numerators.

For example, to compare   and , first multiply the numerator and the denominator of the first fraction by 2.

Nine parts out of 10 are clearly more than 8 parts of 10. So, .

Since   and  are equivalent fractions,  .

In advanced stages, generating equivalent fractions might require multiplication in both the fractions. For example, to compare   and , first, we need to generate equivalent fractions of both.

Now, there are two fractions with like denominators. It is clear that .

So, .

A good count of comparing fractions with half and one and comparing unlike fractions worksheets are available.

In the next level, children learn to use equivalent fractions as a strategy for subtracting and adding fractions with different denominators.

For example, to add   and , the first fraction is rewritten as an equivalent fraction   and the addition is performed as:

              =  

               =  

[Note that the improper fraction   can also be written as a mixed number  .

The similar technique is used for subtraction as well.

To subtract, say,   from , the two fractions are rewritten with the least common denominator:

Now, there are two fractions with the same denominator and the subtraction can be done in the numerators.

Note that equivalent fractions can also be formed by reducing fractions.

Children also use the above technique to do real-life word problems by solving equations with fractions.