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1. I find that I look at fractions in relation to common denominators and when looking at fractions I have seen that I have to find some sort of way to compare my fractions whether through circle models, etc., as in the "Classroom Scenario" I would have been able to have known how to divide my pizza, but I'm not sure I could have easily figured out which was larger on questions 1/4 or 1/8
2. I found it surprising that finding a common denominator or cross multiplication do not require consideration of the size of the fraction and allowing a comparison to the whole. I was knocked down a couple of rungs knowing that the method I had used for years doesn't teach conceptual understanding of fractions.

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1.   The larger the smaller the denominator the larger the larger the fraction is something I have used in my room.  I was not surprised by the research because I think my understanding of fractions is growing and developing every day.
2. I have not used the rods and ordered them for my room.

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1. Familiar: if the denominator is smaller, the piece is bigger; the scenario was familiar as well with sharing pizza/brownies/etc. Also familiar were misconceptions of a bigger number meaning a bigger piece!

2. Before this cohort, I have never thought of using rods to compare fractions!

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1. It has been awhile since I have taught Math so I can't
2.

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Susette McConnell- Long Mill Elementary- 5th

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Susette McConnell- Long Mill Elementary- 5th

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1.  In the "Classroom Scenario" the math presented was a group discussion of whether or not they wanted to share their favorite pizza with 3 other people or 7 other people with a visual explaining.
The research section was familiar to me because I find myself thinking the same way as the students when comparing unless I use a visual like  fraction strips.
2.The information presented that was surprising to me was the different ways you can compare fractions. :)

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1. Even though a student understand that sharing with more people means that they get smaller pieces, they can't transfer that understanding to the broader concept.
2. Comparing the importance of looking at both parts of the fraction to place value.

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1. I have had the issue with students looking at denominators and thinking that they are whole numbers.  "Well, 8 is greater than 6 so that must be bigger".  While in the case in the book, it would get the correct answer, that's not always true.  My students were also like Ms. Alvarez's students.
2. I was totally blown away that 6th graders were missing that problem as well! Wow. I loved the example about the pizzas!

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Although we haven't started fractions, I can visualize my students focusing on the sharing idea and basing decisions on that method alone. The different methods will allow students to understand based on their learning style.

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1. Students can understand it when you talk about them getting food with unit fractions. They understand that 1/4 is larger than 1/8 but when you talk about it in other terms (not them getting food) they seem to have no idea.

2. It is odd to me that they know that 1/4 is larger than 1/8 but can't seem to reverse that and know that 7/8 is more of a pizza than 3/4.

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1. In second grade, some of my students used to really have trouble with the relationships between numbers when we would be working on place value. They struggled seeing the relationship between the numbers (such as 23 tens = 230) so I can definitely see where the relationships between the numerator and the denominator in fractions might cause some misunderstandings.

2. I didn't realize there were so many different ways to compare fractions! When I was in school, we were taught the "cross-multiplication/butterfly method and that is what we were expected to use on classwork and especially on assessments. I hadn't realized how much this hindered my conceptual understanding of the fractions as numbers. I remember struggling a lot with this concept and fractions as a whole as a student and I definitely think I would have had a different experience if I had been aware of the other strategies

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1. In my experience I have seen my students focus solely on the denominator as a whole number and compare the fractions only using that information.  They are not able to see the full picture and do not make note of the numerator that goes along with that fraction.
2. It was surprising to see some of the reasoning that the students gave for which fraction was greater. It was also shocking to see how much the one generalization can impact the thinking of the students in your c lass. I also learned a new strategy to help students compare fractions which would hopefully give the students a better visual and understanding of which fraction is greater than the other.

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1. I notice that some of my students use their "whole" number sense when it comes to fractions and they have a hard time realizing/recognizing that there are numbers between whole numbers.
2. I was surprised at the amount of 6th graders that still did not understand the concept of comparing numbers. There was not a huge difference in mistakes from 4th to 6th grade. Also, I was surprised by some of the explanations even when the answer is correct. This reminds me to always ask why and how valuable it is to have students explain their thinking.

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1. The information presented in that is similar to my experience with students is that students have trouble looking at the whole picture and the relationship between numbers. As previously in second grade, students struggled with this a lot with place value understanding. I can see how this can impact their understanding of fractions.
2. Information presented that was new to me was all the various ways fractions can be compared. Being new to 3rd grade, I am used to the way I learned of finding the common denominator. I love learning all the different ways students can compare fractions that explicitly require them to consider the size of the fraction.

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1. Just like the teacher in the classroom scenario I have told my students that "the smaller the denominator, the larger the fraction". I did not realize that this was really hindering their perception of fractions. I have had students use that as their reasoning when working with fractions. The students are not really understanding the relationship between the numerator and denominator.

2. I think it was surprising that there is a large percentage of students who are successful in working with fractions because they don't have a clear understanding of the relationship between the numerator and the denominator. I agree with Nancy Mack that "students rely more on whole number strategies when solving fraction problems". I will keep this in consideration when teaching the fraction unit this year.