Letters about fractions

Our assignment on Friday was for students to write a letter to a second grader explaining if they think 1 and 1/3 is bigger than 1 and 1/4 or if 1 and 1/4 is bigger than 1 and 1/3. Look for key words that students included like numerator, denominator, and equivalent.
Here are 6 students letters that we found exceptional. Some required pictures of their letters to see their diagrams.

The first letter is Maxine's.
Dear 2nd grader,
Did you know that 1 and 1/3 ( 1 and 1 third) is bigger than 1 and 1/4 (1 and 1 fourth)? Well, it is. I don't know if you knwoo this, but it takes 4/4(four fourths) to make 1 whole and only 3 thirds to make 1 whole. Then, you add 1 whole to each. 2 whole is equivalent (e-qui-vol-int) to 1 whole. But 1/3 is still a little bit more than 1/4. That's why 1 and 1/3 is bigger than 1 and 1/4.
3rd grader,
Maxine

The second letter is Gabrielle's. You can see most of her letter, including her diagrams, in the photo below.

Dear second grader,
What is larger? 1 and 1/4 or 1 and 1/3. 1 and 1/3 is larger. You probly thought 1 and 1/4 was bigger because 4 is bigger than 3.This is why you are wrong. Look at 1/4. (See picture) Look at 1/3. (See picture) Now that you see it, 1/3 is obeously bigger. Now you know that the littler number on the bottom is bigger. You will never be fooled again!
Sincerly,
Gabrielle
The third letter is Jack K's. You can see the diagram that he refers to in his letter pictured below.

Dear second grader,
Do you think that 1 and 1/4 is bigger than 1 and 1/3? If so, I will explain why that is wrong. First, you need to know that the denominator (de-noin-a-tor) is the number on the bottom of the fraction. The numerator (num-er-a-tor) is the number at the top of the fraction. I will give you an example 1/4- 1 is the numerator, 4 is the denominator. Now I will explain how 1 and 1/3 is bigger than 1 and 1/4. Do you know how 1/2 is the biggest fraction? That means the lower the number the bigger the piece. Like this (See picture) Do you see the 1/3 part colored in was bigger than the 1/4 shaded in? That is how 1 and /3 is bigger than 1 and 1/4.
Sincerely,
Jack K.


The next letter is Serena's. You can see the diagram she refers to is pictured below.

Dear Second grader,
1 and 1/3 is bigger than 1 and 1/4. It is bigger because, well, it might sound weird but if you had 2 brownies and got 1 whole and cut the other into thirds, the 1/3 would look bigger than 1/4. (See example below.) See how thirds are bigger? Hope you learned alot.
Serena


The letter below belongs to Analiese. Please look at her diagrams that went along with her letter.
Dear Second grader,
1 and 1/3 is bigger than 1 and 1/4. I will show you. See would you like to have 1 and 1/3 or 1 and 1/4? I would like to have 1 and 1/3. Wouldn't you if they were brownies. Even though the bottom number for 1/4is bigger, that does not mean it is more. So if your brother or sister says I am getting 1/2 of a brownie and you are getting a 1/4, say no! Cause you get this much 1/4 and your brother or sister would get this much 1/2. OK
Sincerely,
Analiese



Here is Ian's letter.
Dear Second grader,
To tell you 1/3 is a bigger fraction because if you put a sideways line though 1/3 it is 2/6. If you put two lines down the squre it makes 2/8 = 1/4. The smaller the bottom number the bigger the fraction. So second graders 1/3 is indeed the bigger fraction.
Sincerely,
Ian