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NC.3.NF.4Comparing FractionsDomainNumber and Operations - FractionsClusterUnderstand fractions as numbers.Standard(s)NC.3.NF.4 Compare two fractions with the same numerator or the same denominator by reasoning about their size, using area and length models, and using the >, <, and = symbols. Recognize that comparisons are valid only when the two fractions refer to the same whole with denominators: halves, fourths and eighths; thirds and sixths.MaterialsNumber line, fraction models, paper, pencilsTaskPart I: Below are measurements of ribbon in feet. For each pair of ribbons, draw a picture to determine which is longer? Pair 1: 2/3 2/4Pair 2: 2/6 4/6 Part II: Determine which fraction in each set is larger. Explain your reasoning using only words and numbers (without using models or number lines).Pair 3: 1/3 2/3Pair 4: 3/6 3/4 RubricLevel INot YetLevel IIProgressingLevel IIIMeets ExpectationStudent does not achieve the correct answer and uses inappropriate solution strategy. Student determines which fractions are larger, but provides limited to no reasoning. ORStudent provides some sound reasoning, but is unable to determine which fractions are larger in each set.Student accurately determines which fraction in each set is larger: Set 1: 2/3Set 2: 4/6Set 3: 2/3Set 4: 3/4Student uses visual models or number lines to accurately explain which fractions in Sets 1-2 are larger.Student uses sound reasoning to explain how the larger fractions in Sets 3-4 were determined (i.e., When looking at the fractions in Set 4, the student recognizes that there are three pieces in each fraction. Since fourths are larger than sixths, three fourths would be larger than three sixths.)Standards for Mathematical Practice1. Makes sense and perseveres in solving problems.2. Reasons abstractly and quantitatively.3. Constructs viable arguments and critiques the reasoning of others.4. Models with mathematics.5. Uses appropriate tools strategically.6. Attends to precision.7. Looks for and makes use of structure.8. Looks for and expresses regularity in repeated paring FractionsPart I: Below are measurements of ribbon in feet. For each pair of ribbons, draw a picture to determine which is longer? Pair 1: 2/3 2/4Pair 2: 2/6 4/6 Part II: Determine which fraction in each set is larger. Explain your reasoning using only words and numbers (without using models or number lines).Pair 3: 1/3 2/3Pair 4: 3/6 3/4 Scoring ExamplesNot Yet: ?This student did not show evidence of understanding the idea of determining which fraction was larger. She drew pictures of a few of the fractions (correctly, but used an area model instead of a length model). Then she attempted to add the fractions, which does not show understanding of comparing fractions. On part 2, her explanation also did not show evidence of understanding what it means to compare fractions. She did not explain any of the fractions in part 2 or which one was bigger or smaller. For next steps, she needs to work on understanding what it means to compare fractions. This could be done through representing different fractional values with manipulatives.Not Yet: ?This student could not achieve the correct solution in either part of the task. ?His reasoning indicates that he does not understand the concept of greater fractions or lesser fractions because he repeatedly chooses the lesser fraction as greater, even when depicting the greater fraction in a picture or saying that a fraction is lesser because it has “more pieces.”Scoring ExamplesNot Yet: ?This student drew an accurate representation of the fractions in Part I, and indicates that 2/3 is greater than 2/4, but he does not compare the second pair of fractions. He did not make sense of the second part of the problem. He uses a strategy that does not involve number sense (“butterfly” method), and he did not consistently arrive at the correct solutions. ?For example, he stated that three sixths was greater than three fourths.Scoring ExamplesProgressing: ?This student showed partial understanding of comparing fractions. On part 1, he accurately drew each fraction, and he accurately compared 2/6 and 4/6. He did not accurately compare ? and 2/4. For part II, he did correctly state that ? is less than ?, but inaccurately stated that 3/6 is greater than ?. His explanation did not fully show understanding. For next steps, he may need to practice understanding the meaning of the < and > symbols because this could have been a reason for an incorrect answer in part 1. He also needs to practice with correct explanations. This could start by talking with the teacher about their explanations orally and then putting that explanation into writing.Part 1:Part II:Meets Expectations: ?This student showed full understanding of comparing the fractions in this task, even though he used an area model instead of a linear model to represent the ribbons. In part I, he accurately drew each fraction and showed which fraction was larger. In part II, he accurately explained in words how ? is less than ? because you can compare the numerator since the denominator is the same. He also explained how 3/6 is less than 4/6 because the bottom number being bigger leads to a smaller fractional part. For next steps, he could have some practice with switching from the area representation of fractions to linear representations. He could start to compare mixed numbers instead of fractions smaller than one.Part 1:Part II:Scoring ExamplesMeets Expectations: ?This student arrived at the correct solutions for every set of the task, and she used effective illustrations and written expression of reasoning. ?The pictures she made for the ribbon models in part I used equal sized wholes to compare shaded pieces. In part II, she expressed the rules for determining the larger fraction given the same numerators or denominators, respectively. ................
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