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1. I find students lack an understanding of fractional equivalency, and even if they "understand" it they abide by a rule because of what they learned in previous years.
2. This book keeps shattering my thought of what fractions are from a student perspective, and is showing my why we have so many misconceptions built.
3. In a classroom that doesn't have cuisenaire rods, I will complete Equivalent Expression MatchUp.

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1.  Classroom Scenario-I find that most students look at fractions still as numbers and not a a part of a whole.  Like the classroom scenario they see the digits and think that it must be bigger.

What's the Research-I did my own research in class and out of 42 fourth grade students only 4 disagreed with the statements.  Of the 4 only one could explain why they felt that way.
2.  I was surprised to see that in the research students sill felt this way in the 6th grade.  It make me wonder if it is conceptual problem that students of this age are having.
3.  I like the Equivalent Expression Matchup.  It gives the students an opportunity to express themselves and to be able to show their knowledge of of fractions.

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1. I have noticed that some of my students "know" what an equivalent fraction is (especially if it is equivalent to 1/2), but when it comes to more unfamiliar fractions they get confused by them. I try to use as many manipulatives as possible while teaching fractions because I find that helpful to my lower students. Then we typically move on to the procedures so that they have a solid foundation.  In my classroom, I have used both area models and number lines to find equivalent fractions.
2. The amount of 6th graders that could not answer the equivalent fraction questions was shocking! I almost want to try it out with my 4th graders so see what they would say....
3. I LOVED the 3.3 Equivalent Expression Matchup idea and would like to do that in my classroom.I have used cuisensaire rods and numbers line, but I have not thought about using cuisenaire rods to measure objects like they did in activity 3.1. I think that might be a good review activity for my students!

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1. Since this is my first year teaching fractions, everything about fractions has felt a little out of my element ;) But I'm learning! My students have been working on equivalent fractions and I feel like I'm learning so much just by watching them interact with the cuisenaire rods and fraction tiles.
2. I couldn't believe how many sixth graders were still under the impression that just because the denominator is larger, the fraction was too.
3. My goal for implementation would be to use the Connecting Cuisenaire Measurements to the number line. I think this would really help my students make a connection between the number line and equivalent fractions!

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1. I've noticed that students get confused really quickly on understanding equivalent fractions. I had to stop and take it back and have them understand that fractions are numbers. Using a number line to represent fractions really helped them to understand this, as we use number line all the time with addition, subtraction, multiplication and division. I also noticed when fractions are used in context they get confused easily. I think incorporating fractions into as many scenarios and real life context will help them see that fractions are numbers.
2. I was surprised to see how many upper grade students still struggle with understanding fractions and equivalent fractions.
3. I plan on using Activity 3.1: Measuring with Cuisenaire Rods followed by Activity 3:2: Connecting Cuisenaire Measurements to Number Lines so students can first understand through measurement that equivalencies and see that it is different ways to name the same quantity and take that understanding to the number line.

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1. My students did not understand the concept that fractions are numbers. We discussed this several times, but my students did not understand until I connected fractions with measurement on a ruler.
2. I was very surprised to learn that many students in the 6th grade still struggle with equivalent fractions.
3. I am using the "Equivalent Fraction Matchup" in my classroom this week. Students are using a variety of manipulatives to assist with this activity. (number lines, fractions strips, double decker rectangles)

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Susette McConnell, Long Mill Elementary, 5th Grade

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Susette McConnell, Long Mill Elementary, 5th Grade

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1. The scenario was familiar to me at the beginning of the year. As my students started to draw or use fraction strips they were able to see how two or more fractions could be equivalent. Allowing students to do this helps with understanding.
2. What was surprising and sad was even after 2 years of equivalent fractions , more than half of the 6th graders in the study still were unable to connect with equivalent fractions.
3. I am going to do the equivalent fraction match up. This will give me a good indication of who still needs help with this concept; although, we discuss equivalent fraction when we encounter them.

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1.  My students frequently use the terms value and the same interchangeably.  I stress value is very different from the same.    This shift in focus on the value of the number helps them equate value with money and they are beginning to make connections in the difference.  This has been huge because they will say 2/4 is not the same as 1/2 but both have the same value.
2.  I was kind of surprised when I asked my own daughter the same question and she gave the same response.
3.   I love all the activities and plan to do all of them in my room.  I need to see the how the one with the grid paper would work because I am having trouble envisioning the process but am hoping someone can help me tomorrow!
Cheers Friends
Wendy

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1. I have noticed that my students that have learned the "rules," still fail to think through those rules when problem solving. When I prompt them to think about their answer, they recognize the error. Whenever they see large numbers, they do not necessarily see them as playing a role in a fraction. They simply see the fraction as bigger.
2. I was surprised that most 6th graders were still struggling with this concept, even though they had been practicing it since 3rd grade.
3. I plan to use the Equivalent Expression Matchup with my third graders.

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1. While teaching fractions in fourth grade this year, I have noticed that my students were confused by the statement that fractions and numbers are the same thing.  This is something that we've had to have discussions about. My students also are convinced that when you multiply anything, the product is bigger.  This has helped by drawing a giant 1 around the 2/2 or whatever we are multiplying a fraction by to find an equivalent fraction.  They're in the habit now of saying "2/3 multiplied by 2/2 - which is a whole - is 4/6 and those fractions are equivalent."
2. I was surprised that SO MANY students were agreeing that 5/6 x 2/2 = 10/12 and that 10/12 was twice as large as 5/6.  I guess when you think of it as an 11 or 12 year old, it really can be confusing!
3. I want to do the "Equivalent Expression Matchup" with my students. I'll probably do it this week as a review for their post assessment. I think that it's extremely important for students to explain their thinking, using the correct vocabulary... this way, I know that they understand and can also fix any misconceptions.

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1. I can completely relate to the scenario when the student is explaining that "multiplication makes things bigger". I have said this phrase in my classroom before. Now I realize I need to choose my words more carefully. I think I say things sometimes because I want the student to "get it" then and don't really put in much thought about how this could affect them later on.
2. The part that was surprising to me was that so many students don't think of fractions as numbers. After I read this part, I asked my own students and they said fractions and numbers were completely different.
3. I like the last activity about matching equivalent fractions. This is something students struggle with in fourth grade; understanding that one fraction can be represented various ways. I want to spend more time on this in my own classroom as I think it will help students understand simplifying fractions.

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1. I definitely can relate to the scenario presented in the "classroom scenario."  I recently worked on a lesson with equivalent fractions where some of my students memorized the procedure of multiplying or dividing by n/n but when questioned about the fractions they could not expand on how they were related.  They do not understand how these fractions are equal they just know how to make equivalent fractions by multiplying or dividing by n/n.
2. It was surprising to see how many 5th and 6th graders would see the fraction 10/12 as larger than 5/6.  It really shows how many students lack the understanding of what the fractions represent and just see them as individual numbers.
3. I definitely want to implement the Connecting Cuisenaire Measurements to the Number Line activity. It is a weakness of mine to incorporate math concepts on a number line even though I know how beneficial it is. This activity would really allow students to see a visual of the equivalent fractions.

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1.  In Classroom Scenario, I understood the confusion from the students on reasoning about equivalent fractions.  My students know how to find equivalent fractions, but really didn't understand how or why they were equal.  Using manipulatives and number lines to compare have helped a lot.What's the Math also reconfirmed the necessary use of number lines and other representations and understanding fractions as numbers.
2.  The part that was new to me was different means to teach students to view fractions as numbers and how to relate to real life situations.
3. I really love the Agree/Disagree prompts. This allows students to research and respond in different ways and use different methods to support their opinion. I also liked the "Equivalent Expression Matchup". This will allow my students to explain/display multiple ways to show equivalent fractions.

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1. In the Classroom Scenario, it was quite familiar to see the teacher move right to procedures before working on concrete and abstract models. I was guilty of the same before I learned the strengths in taking the time to learn with manipulatives and drawings! In "What's the Math", I've done a lot with finding equivalent fractions on a number line.
2. The part that was new to me was how partition lines were used in "What's the Math". I've always determined equivalency by drawing 2 boxes stacked on top of each other. I've never considered simply adding another line!
3. I plan on implementing more "Agree/Disagree" statements and continuing to show fractions in multiple ways!