Massachusetts Curriculum Frameworks
MA.3.NF. Number and Operations—Fractions
3.NF.A. Develop understanding of fractions as numbers for fractions with denominators 2, 3, 4, 6, and 8.
3.NF.A.1. Understand a fraction 1∕b as the quantity formed by 1 part when a whole (a single unit) is partitioned into b equal parts; understand a fraction a∕b as the quantity formed by a parts of size 1∕b.
3.NF.A.3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
3.NF.A.3.c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. For example, express 3 in the form 3 = 3∕1; recognize that 6∕1 = 6; locate 4∕4 and 1 at the same point of a number line diagram.
3.NF.A.3.d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
3.G.A. Reason with shapes and their attributes.
3.G.A.2. Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into four parts with equal areas and describe the area of each part as 1/4 of the area of the shape.