Massachusetts Curriculum Frameworks
MA.4.NF. Number and Operations—Fractions
4.NF.A. Extend understanding of fraction equivalence and ordering for fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
4.NF.A.1. Explain why a fraction a∕b is equivalent to a fraction (n x a)∕(n x b) by using visual fraction models, with attention to how the numbers and sizes of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions, including fractions greater than 1.
4.NF.A.2. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1∕2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
4.NF.B. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers for fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
4.NF.B.4. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
4.NF.B.4.a. Understand a fraction a∕b as a multiple of 1∕b. For example, use a visual fraction model to represent 5∕4 as the product 5 x (1∕4), recording the conclusion by the equation 5∕4 = 5 x (1∕4).