Contributor: Marlene Vogel. Lesson ID: 10033
"Equivalent fraction" is a big term but what this type of fraction looks like helps us be better at measuring, especially when we bake cookies or want to build something! Get out your LEGOs and learn!
Daniel loves to bake! However, sometimes he cannot find the correct size measuring cup to use. He can find other measuring cups of different sizes, but he is not sure which one to use.
For example, the cookie recipe calls for ^{1}/_{2} cup sugar, but Daniel is missing that measuring cup. He finds a ^{1}/_{8} measuring cup and a ^{1}/_{4} measuring cup.
Can you help Daniel measure an equal amount of sugar for the cookie recipe?
Can Daniel use either the ^{1}/_{8} cup or the ^{1}/_{4} cup to make an equivalent amount to ^{1}/_{2} cup?
Daniel is in luck! All he has to do is use his knowledge of equivalent fractions to save the cookie recipe.
First, let’s review some important concepts. Click on each question to reveal the answer.
Now, let’s explore equivalent fractions and help Daniel solve his baking problem!
What we want to do is figure out what fractions are equal to each other.
One way we can do this is take the biggest LEGO^{®} we have in the bag, 2 x 4, and place it on the table (Blocks are named by the number of studs, or bumps, on the top).
The 2 x 4 brick is called the "whole" and will be represented by the number 1 in your table (see below):
For the next step, make a table on a piece of paper. This table will help you see, remember, and maybe predict, equivalent fractions. It should look like the one below:
Brick size  # of bricks to cover whole  What fraction of the whole is one of these bricks? 
For this activity, "whole" refers to the 2 x 4 LEGO^{®} that is lying on the table in front of you.
Using 2 x 2 LEGO^{®} blocks, cover the whole 2 x 4 brick with as many of them as you can. A 2 x 2 looks like this:
Once you have finished covering the 2 x 4 LEGO^{®} block, go to the table that you made on the sheet of paper. Fill out the first row. It should look like this:
Brick size  # of bricks to cover whole  What fraction of the whole is one of these bricks? 
2 x 2  2  ^{1}/_{2} 
Look at the last column of the table, "What fraction of the whole is one of these bricks?"
Remember, fractions are a part of something. If it takes 2 of the 2 x 2 blocks to cover, then you can write a fraction showing what one of those blocks is called. That fraction would be ½.
The number 2 represents how many of the 2 x 2 blocks it takes to cover the whole. That is your denominator. The number 1 represents one of those 4 x 4 LEGO^{®} blocks. That is your numerator.
Try this activity again using 1 x 2 blocks. A 1 x 2 block looks like this:
Cover the 2 x 4 block (the "whole") with 1 x 2 blocks. Once you have completed covering the whole, fill out row 2 in your table. It should look like this:
Brick size  # of bricks to cover whole  What fraction of the whole is one of these bricks? 
2 x 2  2  ^{1}/_{2} 
1 x 2  4  ^{1}/_{4} 
Again, look at the last column in your table. If it takes 4 blocks to cover the whole, then one of those blocks would be ¼ of the whole.
Complete the activity one last time. This time, use 1 x 1 LEGO^{®} blocks. 1 x 1 blocks look like this:
In your chart, write how many of the 1 x 1 bricks you needed to cover the “whole.” See the table below:
Brick size  # of bricks to cover whole  What fraction of the whole is one of these bricks? 
2 x 2  2  ^{1}/_{2} 
1 x 2  4  ^{1}/_{4} 
1 x 1  8  ^{1}/_{8} 
Again, look at the last column in your table. If it takes 8 of the 1 x 1 blocks to cover the whole, then one of those blocks is ^{1}⁄_{8} of the whole.
You have just finished figuring out how many differentsized blocks it takes to cover the whole. Now, it is time to write fractions to represent the whole.
In the first row, you used 2 of the 2 x 2 blocks to cover the whole. When writing your fraction, you need to put the number 2 in the denominator:





2 


You also know that you need BOTH of these pieces to make a whole. Put a number 2 in the numerator so your fraction looks like this:

2 



2 


You have just written a fraction that is equivalent to 1 (whole). See below:

2 
= 
1 

2 
Try this again with the second column. Remember, it took four of the 1 x 2 blocks to cover the whole, so the number 4 is going to be your denominator. And you know you need to have all 4 of these blocks to cover the whole, so you will put a number 4 in your numerator.
Now you can write a fraction for these blocks that is equivalent to 1 (whole).



4 

4 
= 
1 

4 

4 

4 
Complete this activity by writing a fraction that is equivalent to 1 with the information from the third row of the table. Your fraction should look like this:



8 

8 
= 
1 

8 

8 

8 
Congratulations! You have written three fractions that are equivalent to 1!
However, you wrote three fractions that are equivalent to each other, too! You just did not realize it! Think about this for a few minutes. Each of the fractions you wrote is the equivalent of 1.
Look at the example below:

2 


= 
1 

2 





4 


4 





8 


8 
Yes, they are! If someone asks you to name a fraction that is equivalent to ^{8}⁄_{8}, you can now tell him or her ^{4}⁄_{4} or ^{2}⁄_{2!}
You can do this activity again if you would like, but use a differentsized LEGO^{®} block to represent the "whole"!
Continue on to the Got It? section to learn how to CHECK your work!
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