Reflection: Comparing & Ordering Fractions
Global Concept 1: Models and Benchmarks to Compare fractions
This week, we started a new unit. This unit requires a lot of prior knowledge from the last unit. Students have to take what they have learned about what a fraction is and what each part stands for and apply it so they can compare and order multiple fractions from least to greatest. It was crucial to keep referring back to the meaning of a denominator and numerator.
An important concept that kiddos need to pay attention to when comparing fractions is the size of the parts and the number of parts. For example, 1/8 is smaller than 1/3 because when one whole is cut into eight pieces, the pieces are smaller than when you cut one whole into three pieces. This was very challenging for my kids to understand.
My CT and I began with an engaging question to our class. We explained to them that we had a serious dilemma. I told them that I had baked two cakes over the weekend and I wanted 1/4 of a piece and my CT wanted 1/8 of a piece - and we both thought that we had the larger piece. We asked for our classes help to put out argument to rest. Of course, initially, almost everyone agreed that my CT would get the larger piece because 8 is greater than 4. However, because the class did not come to a consensus, we pulled out the fraction tiles so we could explore the problem further. The fraction tiles give the kids a visual understanding of fractions and their size compared to 1 whole. It allows them to see that it takes four 1/4 pieces to make up a whole and eight smaller 1/8 pieces to make up a whole. Pretty quickly, a group of students noticed that two 1/8 pieces fit into one 1/4 piece so 1/4 has to be larger. Additionally, after giving them time to "play" with the tiles another group noticed and explained to the class that the larger the denominator, the smaller the fraction piece. I was thrilled that someone noticed that because that concept helped us out a ton the rest of the week.
Another big part of this lesson was to encourage use of the number line. My class could draw a picture to represent the two fractions and they could write the greater than or less than EQUATION, but my kiddos struggled taking that information and putting number line. They have the benchmark fractions (0, 1/2 and 1) memorized and they can easily black those benchmarks on a number line, but they don't know how to use those benchmarks to compare two fractions. For example, by using the benchmarks, they would be able to say that 5/6 is only one away from 1 whole, so it would be placed right before 1; and, 3/6 is the same as 1/2 so it would be in the middle. After reading their journal entries and looking at their work, I think they lack the central understanding of how a number line works. They can tell me that 5/6 is greater, but they do not know it's because it's closer to 1 whole, which is extremely important. I don't think we explicitly taught the meaning of a number line in the first unit.
So, next week, I will start Global Concept 2: Models and Strategies to Compare Fractions. We will definitely be spending time on using the linear model and a reliable and efficient strategy when comparing and ordering fractions.
Global Concept 1: Models and Benchmarks to Compare fractions
This week, we started a new unit. This unit requires a lot of prior knowledge from the last unit. Students have to take what they have learned about what a fraction is and what each part stands for and apply it so they can compare and order multiple fractions from least to greatest. It was crucial to keep referring back to the meaning of a denominator and numerator.
An important concept that kiddos need to pay attention to when comparing fractions is the size of the parts and the number of parts. For example, 1/8 is smaller than 1/3 because when one whole is cut into eight pieces, the pieces are smaller than when you cut one whole into three pieces. This was very challenging for my kids to understand.
My CT and I began with an engaging question to our class. We explained to them that we had a serious dilemma. I told them that I had baked two cakes over the weekend and I wanted 1/4 of a piece and my CT wanted 1/8 of a piece - and we both thought that we had the larger piece. We asked for our classes help to put out argument to rest. Of course, initially, almost everyone agreed that my CT would get the larger piece because 8 is greater than 4. However, because the class did not come to a consensus, we pulled out the fraction tiles so we could explore the problem further. The fraction tiles give the kids a visual understanding of fractions and their size compared to 1 whole. It allows them to see that it takes four 1/4 pieces to make up a whole and eight smaller 1/8 pieces to make up a whole. Pretty quickly, a group of students noticed that two 1/8 pieces fit into one 1/4 piece so 1/4 has to be larger. Additionally, after giving them time to "play" with the tiles another group noticed and explained to the class that the larger the denominator, the smaller the fraction piece. I was thrilled that someone noticed that because that concept helped us out a ton the rest of the week.
Another big part of this lesson was to encourage use of the number line. My class could draw a picture to represent the two fractions and they could write the greater than or less than EQUATION, but my kiddos struggled taking that information and putting number line. They have the benchmark fractions (0, 1/2 and 1) memorized and they can easily black those benchmarks on a number line, but they don't know how to use those benchmarks to compare two fractions. For example, by using the benchmarks, they would be able to say that 5/6 is only one away from 1 whole, so it would be placed right before 1; and, 3/6 is the same as 1/2 so it would be in the middle. After reading their journal entries and looking at their work, I think they lack the central understanding of how a number line works. They can tell me that 5/6 is greater, but they do not know it's because it's closer to 1 whole, which is extremely important. I don't think we explicitly taught the meaning of a number line in the first unit.
So, next week, I will start Global Concept 2: Models and Strategies to Compare Fractions. We will definitely be spending time on using the linear model and a reliable and efficient strategy when comparing and ordering fractions.