These patterns support students in making conjectures, supporting their reasoning, and proving mathematical claims. When comparing fractions, use benchmark fractions to make estimations. When doing mathematics, patterns emerge.When the numerator is a bigger number than the denominator, the fraction is greater than one whole.Â.Fractions equivalent to 1 whole have the same numerator and denominator. The only benchmark fractions addressed in this task are $\frac$ have a numerator that is half of the denominator. This can also be shown with a model so that students can see the difference in sizes of pieces when related to the whole.The goal of this task is to determine appropriate benchmarks for fractions with a focus on providing explanations that demonstrate deep conceptual understanding.Recognizing that 1 (in the numerator) is less than half of 4 (the denominator) so they can reason that 1 4< 1 2. For example, students think about the fraction by reasoning about the size of the parts related to the numerator or denominator.Instruction includes models that represent different numerators and denominators.The student incorrectly judges that a mixed number like 1 3 4 is always greater than an improper fraction like 17 4 because of the whole number in front.The student may not pay attention to the relationship between numerator and denominator when estimating. (F) valuate the reasonableness of sums and differences of fractions using benchmark fractions 0, 1/4, 1/2, 3/4, and 1, referring to the same whole. The student may mistake the fraction with the larger numerator and denominator as the larger fraction. The student applies mathematical process standards to represent and generate fractions to solve problems.Instruction includes fractions equal to and greater than one.Students can revisit this activity multiple times to learn these common equivalencies by heart. Students can compare 3 5 to 1 2 by recognizing that 3 (in the numerator) is more than half of 5 (the denominator) so they can reason that 3 5 > 1 2. This activity visually connects the familiar rainbow fraction tiles to the number line to help bridge understanding.Easy to prep, this activity has two sets of fractions: Set 1 is Halves, Fourths, and Eighths. Instruction may include using benchmark fractions and estimates to reason about the size.To measure to the nearest 1 6 of one inch. Instruction may include number lines, which will make a connection to using inch rulers.Instruction may include helping students extend understanding by generating equivalent fractions with common numerators or common denominators to compare and order.Work builds on conceptual understanding of the size of fractions from grade 3 ( MA.3.FR.2.1) where students learned to compare fractions with common numerators or common denominators. Therefore, the most common benchmark fraction example is (one-half). We can easily divide any object to be measured or compared into two equal parts. Students will plot fractions on the appropriate scaled number line, compare fractions using relational symbols, and order fractions from greatest to least or least to greatest. Using benchmark fractions for estimations helps students develop fraction number sense and advance their mental math skills. The purpose of this benchmark is to understand the relative size of fractions. Connecting Benchmarks/Horizontal Alignment
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