3rd Grade Math: Equivalent Fractions Games

Look at the words:

Thank You! , Gracias! , Je vous remercie! , Danke! , Grazie!

Is there anything common in these words? They all mean thank you in different languages! That is, they all are the same thing but expressed differently.

Equivalent fractions have the similar property. They have exactly the same value but expressed using different fractions.

Consider a watermelon cut into 8 slices and another one cut into 4. Eating two slices from the first watermelon is equivalent to eating one slice from the second. That is, the watermelon fractions calculated either way is the same.

That is, the unit fraction  is equivalent to . Another fraction equivalent to these two is .

Equivalent fractions have the exact same area covered. Also, equivalent fractions occupy the exact same place on a number line.

Simple equivalents of fractions can be generated by doubling or tripling the given fraction. Equivalent fractions calculator multiplies the numerator (the number above the fraction bar) and the denominator (the number below the fraction bar) by the same number to generate equivalent fractions. Similarly, dividing the numerator and denominator of a fraction by the same number also give an equivalent fraction.

 

Manipulatives for teaching equivalent fractions

The below discussed math manipulatives would help to understand the concept of equivalent fractions.

1. Play dough: Children can use play dough to divide a whole into equivalent fractions.

 

 

Further, they can use parts of these whole to identify more equivalent fractions.

 

2. Fraction Charts / Fraction strips: This is one of the most commonly used manipulative for learning fractions.

 

 

 

The definition, as well as the equivalence of fractions, can be explained using fractional strips. Children can make such equivalent fractions chart using multicolored chart papers. As they do the activity by themselves, they enjoy independent learning as well as the concept gets reinforced.

 

3. Pattern blocks: These are another similar math manipulative for teaching fractions.

 

 

 

All the above pattern blocks represent equivalent fractions of a whole.

Further, parts of these patterns also can be used to illustrate the same. For example, one red trapezoid is equivalent to three green triangles. Also, one blue parallelogram is equivalent to 2 green triangles.

 

Math Activities/Games for teaching equivalent fractions

Once the concept of fractions is clear, the equivalence of fractions should be introduced using activities and fraction games for kids. A mere robotic repetitional practice can give children computational fluency. But for a better understanding of the topic, it should be demonstrated using real-life activities and math games.

 

1. Real World Connected Activities: Children can learn very quickly if the concept is connected to real-world activities or characters they are fond of. A cartoon character, say Hulk with a fraction board hung on his neck standing on one side of a weighing scale and the kids are expected to choose an equivalent fraction to put on the other side to balance. This real-life activity can really be a matter of interest for an Avenger loving kid.
2. Equivalent Fractions Memory Game: A four by four square can be made using 16 cards as shown.  

 

Each card will have a fraction written on it. The cards can have six different fractions with their equivalent fractions written. For example, a card can have a fraction  , another card can have its equivalent fraction like  . The cards can be kept in random order upside down. Each child can open two cards in a chance. The child has to open the equivalent fractions each time and the one who gets maximum pairs of equivalent fractions wins the game.

 

3. Writing Equivalent Fractions with Timer: This is a very easy game to play and can be played with any number of kids. All the kids are made to sit in a circle with a timer at the center. At a given time interval, the one who writes a maximum number of equivalent fractions wins the game. The difficulty level can be adjusted by giving a fraction to start with. The more complex fractions you give, the more difficult the game is.

 

 

 

Teaching methodologies for equivalent fractions

The Equivalence

 

Two fractions are equivalent if they have the exact same size.

Consider the fractional area models below:

 

In the first strip, one part out of two is colored in red. In the second strip, two parts out of 4 are colored in blue and in the third 4 out of 8 is colored in green. When the number of portions colored is considered, it varies from 1 to 4. But the total area colored in each color as a part of the whole is half. That is, in all the three strips, half of the total area is colored. So, the fractions represented are equivalent.

Thus,  =  =   .

Plot these fractions on a number line.

To mark the ½ on a number line, the whole part from 0 to 1 can be divided into two equal parts and the midpoint can be marked as ½.

Similarly, to mark  , the whole part between 0 and 1 can be divided into four equal parts and the second mark from 0 denotes . The fraction  is the fourth mark from 0 when the whole from 0 to 1 is divided into 8 equal parts.

Thus, the fractions on number lines show that equivalent fractions are plotted at the exact same place.

Further, fractional strips are used to recognize equivalent fractions.

For example, by comparing fractional strips children can identify the missing number in a fraction equation, thus solving fractions.

Here in the first strip, one out of 4 parts of the whole is shaded and in the second strip, 3 out of 12 are shaded. Since the areas of the whole and the shaded parts of both the strips are the same, they represent equivalent fractions.

That is, . Thus, the missing number is 3.

Another way of understanding the equivalence is to simplify fractions or to reduce fractions.

 

The area of 6 parts out of 8 parts is same as that of 3 parts out of 4. So, the given fraction   can be simplified to .  In the image at the bottom left corner, three parts out of four have been shaded. So, it represents the fraction equivalent to .

A child can practice solving fraction equations using models . The child also gets good practice for writing a fraction in simplest form by doing the above worksheet.

 

Generating Equivalent Fractions

The 3rd grade fractions skills include generating equivalents for common fractions like    and . Children can generate equivalent fractions without using any fractional models.

Consider the fraction equation,   =    .

For solving equations with fractions, the child needs to find the missing number in the second fraction.

Comparing the numerators of the two fractions, the numerator of the first fraction is doubled to get that of the second fraction. That is, 4 = 2. Since the two fractions are equivalent the denominator is also multiplied correspondingly. That is, the denominator of the first fraction has to be doubled to get that of the second fraction.

Thus, the denominator of the second fraction is 2 .

Using the same technique, children can identify a pair of equivalent fractions among others.

 

Equivalent Fractions in Comparing Fractions

The result of comparing two fractions can be written using either .

How to compare fractions?

If two fractions have the same denominator, then the two can be compared by simply comparing the numerators.

 For example:

Here, both the pizzas are cut into 4. To compare fractions of pizzas left, the child just needs to compare the number of pieces left. That is, in the first pizza there is only one piece left and in the second there are 3. It is obvious that the second pizza has more pieces left and hence the fraction representing the second pizza is bigger than the first one.

That is,   or  .

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

So, when the fractions to be compared do not have the same denominator, then the child can use equivalent fractions to generate fractions with the same denominator.

Suppose   has to be compared with  . Since the two fractions do not have the same denominator, it cannot be compared directly.

If the numerator and denominator of the first fraction are doubled, you get an equivalent fraction as . Similarly, when if the numerator and denominator of the second fraction are tripled, you get an equivalent fraction as . Now, the two fractions to be compared are like fractions and can be done so by comparing the numerators.

That is,  as .

Thus, .

Comparing fractions worksheets available in SplashLearn deals with the fractions with same denominators as well as the ones with same numerators. A good amount of practice and a clear understanding of this topic will help in ordering fractions in later stages.

Whole Numbers as fractions:

Each of the circle below represents a whole.

 

The first circle is divided into 1 and 1 part is shaded in red. So, the fraction represented is   or 1.

The second circle is divided into 2 and both the parts are shaded in blue. So, the fraction represented is  or 1.

The third circle is divided into 3 and all the three parts are shaded in green. So, the fraction represented is  or 1.

The fourth circle is divided into 4 and all the four parts are shaded in purple. So, the fraction represented is  or 1.

The area covered by the shaded part in each of the circle is the same. Therefore, they are equivalent fractions. That is, .

Now, consider 4 whole which is divided into 1 each.

Each of the circles is represented as    and there is 4 such whole. Thus, the fraction represented here is   .

This can also be represented using a number line.

Like normal addition, 4 wholes are added one by one by taking leaps to the right on a number line.

Since the skip counting is by 1, each addition takes a leap of one whole to the right and the denominator of the fractional representation is 1. Thus, the whole number 4 represented in fractional form is  .

Now, the same representation can be done with skip counting by .

 

Since the skip counting is by ½, each addition takes a leap of one-half to the right and the denominator of the fractional representation is 2. Thus, the whole number 4 represented in fractional form is  .

In a similar way, by skip counting by ¼ one can re-write the whole number 4 into  , as a fraction. Since all these fractions represent the same number on the number line, they are equivalent fractions.

Thus, 4 ==.

Note that any whole number can be written as a fraction with a denominator 1. Thus, to write the whole number 75 as a fraction, the numerator is 75 and the denominator is 1. That is, .

Solving fraction word problems worksheets can improve the overall understanding of the topic.

 

Evaluation:

To evaluate the equivalent fraction skills for 3rd graders one can use the below assessment questions:

1. Find the missing number in the fraction equation,  . Ans: 6
2. Compare the fractions and fill up the blanks using either .

  

  Ans: =

1. Identify the equivalent fraction pairs.

1.  
2.  
3.  

Ans: b