Contributor: Marlene Vogel. Lesson ID: 10033
Equivalent fraction is a big term, but how this fraction looks helps us better measure, especially when we bake cookies or want to build something! Get ready to build 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! He can save the cookie recipe with his knowledge of equivalent fractions.
First, review some important concepts. Click on each question to reveal the answer.
Now, explore equivalent fractions and help Daniel solve his baking problem!
What you want to do is figure out which fractions are equal to each other.
One way to do this is to place the biggest building block, 2 x 4, on a table. (Blocks are named by the number of studs, or bumps, on the top.)
Make a table on paper for the next step. This table will help you see, remember, and 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? 
The 2 x 4 brick will be the whole and represented by the number 1 in your table.
Using 2 x 2 building blocks, cover the whole 2 x 4 brick with as many of them as possible. A 2 x 2 looks like this.
Once you have finished covering the 2 x 4 building block, go to the table 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 2 x 2 blocks it takes to cover the whole. That is your denominator. 1 represents one of those 4 x 4 building 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 covered 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 four 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 building blocks. 1 x 1 blocks look like this.
In your chart, write how many 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 figured out how many differentsized blocks it takes to cover the whole. 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 must put the number 2 in the denominator.





2 


You also know 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 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 will be your denominator. And you know you need to have all 4 of these blocks to cover the whole so that you will put a number 4 in your numerator.
Now, you can write a fraction equivalent to 1 (whole) for these blocks.



4 

4 
= 
1 

4 

4 

4 
Complete this activity by writing a fraction 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! 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 them ^{4}⁄_{4} or ^{2}⁄_{2!}
You can do this activity again if you like, but use a differentsized building block to represent the whole!
Continue to the Got It? section to learn how to CHECK your work!