Clip 10/16: Adding and Subtracting Fractions Using a Line Plot Lesson Part 2B
Continuing their work in groups, Mallory circulates around groups, asking about their progress and their process. “Is that the strategy you want to use, or do you want to use a different strategy?” She also encourages students to convey clarity with their models: “How would they know it would be equal to 3 3/8 if we took off that label? ... How can we model 3 3/8?” She recommends to students that when they’re doing their models, they make sure they are “as neat and organized as possible.”
Another misconception or something that I saw that was a great discussion piece was in one of the problems, in the first problem, it asked you to repeatedly add three-fourths four times or three-fourths and multiply by that by four. So, a lot of the students, when they ask you or you asked them, do you know how to model three-fourths, they can easily show you that representation. But then to repeatedly add it, you have to keep drawing. One group shaded in what the answer would be, twelve-fourths, and could show you how and explain how they labeled each part.
And one group actually drew an array model four times and shaded in three parts out of the four, four different times. So, making that connection is really hard for them. If you are going to shade in repeatedly, you don't want to draw all of those arrays. We recommend, like, using different colors to kind of understand that concept and how repeated addition is used to find that solution, but when you're using all the same color, like a pencil, it's hard to see where you're repeatedly adding three-fourths over and over again. So, some groups decided to use that particular model, three-fourths, as that array over and over again, and other groups decided to draw the solution and label how they were able to connect the dots from three-fourths to the twelve-fourths, which is equal to three.
I think for lower-level learners, the advantage for separating your array is where you can easily see the connection. This three-fourths is modeled this way, and so they're able to see if I write out three-fourths four times, I can easily see four different groups of three-fourths. When you shade all of them in at once, whether using different colors or labeling them, I think someone who is quick with their fluency is able to understand each group. This is one group of three-fourths, three-fourths, six-fourths, nine-fourths, twelve-fourths. So sometimes I ask them to explain or label a little bit more in detail so they actually understand what is taking place, the concept that's happening, because in their mind they're counting by groups of three, so three, six, nine, twelve.
But we're also dealing with fourths. So, I think for someone who wants a very detailed, basic understanding, it's easier to separate those arrays. But for someone who just wants to understand the concept of quickly multiplying or quickly, efficiently going by those groups, they're going to count by groups of three and clump them together. So, you understand the relationship of what's being asked and how to find the solution.
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