Fractions represent a foundation for many more advanced fields of math and science overall. In fact, it’s shown that children’s knowledge of fractions in elementary school can serve as an early predictor of their math achievement in high school.

Yet, many students continue to struggle with understanding fractions, and one major reason behind this is that understanding quantity *a *is much simpler than understanding relation *a/b*.

So when fourth graders begin to learn about fraction equivalence, they must already be fluent in precisely understanding this relation a/b to be able to show why a fraction a/b is equivalent to a fraction (n × a) (n × b).

There are many ways in which you as a math teacher can support your students in this process. To this end, we’ve outlined several teaching tips that will help your students master fraction equivalence in no time!

## How to Teach Fraction Equivalence

### Review Decomposing Fractions

Remind students that decomposing a fraction means dividing it into smaller parts, i.e. smaller fractions. However, when we decompose a fraction into smaller parts, we must always be able to obtain the initial fraction by adding these smaller parts.

You can remind children that we can decompose ^{4}⁄_{8} as a sum of unit fractions:

^{1}⁄_{8} + ^{1}⁄_{8} + ^{1}⁄_{8} + ^{1}⁄_{8} = ^{4}⁄_{8}

As well as as a sum of smaller fractions that are not unit fractions:

^{2}⁄_{8} + ^{2}⁄_{8} = ^{4} ⁄ _{8}

For additional information, you can also have a look at our article with free guidelines and resources on decomposing fractions. Understanding how to decompose fractions is useful to help students understand how to determine whether two fractions are equivalent.

### Define Fraction Equivalence

You can start by writing the word “equivalence” on the whiteboard. Some children might know it already, but there’s a good chance that many never came across it. Ask students if this word rings any bells. Does it remind them of some other word?

Once they notice that this word is similar to the word “equal”, you can explain that equivalence refers to the state or fact of being equal in amount, quantity, value, etc. Point out that the same applies to fractions – equivalent fractions are simply equal fractions, even though they look different.

You can proceed by asking children if they would prefer to spend ^{1}⁄_{2} or ^{3}⁄_{6} of their money on candy. Allow a few minutes for students to reflect. They might observe that these fractions are in fact equal, or equivalent. But how can we determine this?

### Finding Equivalent Fractions Using Area Model

The best and easiest way to demonstrate to students that two given fractions are equivalent is by using the area model. To use this model, you can draw two circles on the whiteboard. If you have the possibility, you can also use construction paper instead of the whiteboard.

Split one circle in half, and color one half of it. Ask children if they can tell which fraction is shown on this circle? Once they identify that we’re showing the first fraction in this circle, that is, ^{1}⁄_{2}, you can write ^{1}⁄_{2} next to it.

Now draw a second circle next to the first one. Just make sure the second one has the same size as the first one. Split this second circle into six equal parts. Color three parts of it (corresponding to one half of it) and tell students that this second circle shows the fraction ^{3}⁄_{6}.

Now students can visualize that these two fractions are equivalent because the amount colored on both circles didn’t change; the only thing that changed on the second circle was that it was divided into more parts. So we can conclude that these fractions are equivalent.

### Finding Equivalent Fractions Using Multiplication

Since we can’t always use area models, as this would be too time-consuming, point out that we can determine whether fractions are equivalent or not by multiplying the numerator and the denominator by the same number.

For example, let’s say that we want to prove that ^{1}⁄_{2} = ^{3}⁄_{6}

We’ll start by turning ^{1}⁄_{2} into ^{3}⁄_{6}. Remind children that when we multiply a number by 1, the value of this number doesn’t change. Remind them also that if a fraction has the same numerator and denominator, this equals 1. For example: ^{2}⁄_{2} = 1, ^{4}⁄_{4} = 1, ^{5}⁄_{5} = 1.

Therefore, if we multiply ^{1}⁄_{2} by 1, the value won’t change, it will equal ^{1}⁄_{2}.

^{1}⁄_{2} × 1 = ^{1}⁄_{2}

And since we know that ^{3}⁄_{3} = 1, if we multiply ^{1}⁄_{2} by ^{3}⁄_{3}, the value of the fraction will also stay the same:

^{1}⁄_{3} × ^{2}⁄_{3} = ^{3}⁄_{6}

And there you have it, you’ve demonstrated to students that ^{1}⁄_{2} = ^{3}⁄_{6}!

But why did we decide to multiply ^{1}⁄_{2} by ^{3}⁄_{3} in the first place? You can explain that when we want to determine if two fractions are equivalent, we can first look at their denominators. We’ll choose the bigger denominator, which in this case is 6.

^{1}⁄_{2} = ^{3}⁄_{6} ?

Then we look at the denominator from the other fraction, which is 2 and we ask ourselves – how can we get to 6 from 2 by multiplying? Well, to get from 2 to 6, we need to multiply by 3. With equivalent fractions, we have to do the same to the numerator and multiply 1 by 3 also.

^{1}⁄_{2} × ^{3}⁄_{3} = ^{3}⁄_{6}

By multiplying both the denominator and numerator of ^{1}⁄_{2}, we can observe that ^{1}⁄_{2} and ^{3}⁄_{6} are indeed equivalent.

### Finding Equivalent Fractions Using Division

Point out that another way of determining if fractions are equivalent or not is by using division. We can determine whether fractions are equivalent or not by dividing the numerator and the denominator by the same number.

Let’s say that we want to determine whether ^{6}⁄_{8} = ^{3}⁄_{4}.

Point out to students that we can look at the denominators of both fractions first. The fraction ^{6}⁄_{8} contains a bigger denominator, that is, 8. The denominator of the other fraction is 4. Then we ask ourselves, how can we get to 4 from 8 by dividing?

To get to 4 from 8, we need to divide 8 by 2, and since with equivalent fractions we need to do the same to the numerator so that the value of the fraction remains unchanged, we’ll also divide the numerator 6 by 2. In other words:

^{6}⁄_{8} ÷ ^{2}⁄_{2} = ^{3}⁄_{4}

By diving ^{6}⁄_{8} by ^{2}⁄_{2}, we’ve demonstrated that the fractions ^{6}⁄_{8} and ^{3}⁄_{4} are equivalent.

## Activities to Practice Fraction Equivalence

### Equivalent Fractions Game

In this online game, children can practice identifying whether two fractions are equivalent. The only thing you’ll need for this game is a sufficient amount of devices so that children can play. The game is played in pairs, but children can also play it individually.

Explain the rules of the game. The game contains twenty questions. In each question, children are presented with one fraction and they have to choose an equivalent to the initial fraction from four other fractions. To do so, they must target this equivalent fraction.

If children target the correct fraction, they score one point. If they target a fraction that’s not equivalent, they lose one point. At the end of the game, students compare their final scores. The student with the most points wins the game.

## Before You Leave…

If you liked these tips and activities, you’ll want to check out our lesson that goes in-depth into teaching fraction equivalence! So if you need additional guidance for your math lessons, sign up for our emails to receive loads of free content!

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This article is based on:

**Unit 5 – Fractions**