Vertical Progression of Fractions

27.G.6 compose simple shapes to form larger shapes (e.g., "Can you join these two triangles with full sides touching to make a rectangle?")

• Kindergarten

• First Grade

• Second Grade

• Third Grade

25. G.3 partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares

• Kindergarten

• First Grade

• Second Grade

• Third Grade

28.G.3 partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape

• Kindergarten

• First Grade

• Second Grade

• Third Grade

13.NF.1 understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts (unit fraction); understand a fraction a/b as the quantity formed by a parts of size 1/b. For example, 3/4 means there are three 1/4 parts, so 3/4 = 1/4+1/4+1/4

• Second Grade

• Third Grade

• Fourth Grade

• Fifth Grade

14.NF.2 recognize a fraction as a number on the number line; represent fractions on a number line diagram

• Second Grade

• Third Grade

• Fourth Grade

• Fifth Grade

15.NF.2_a represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into "b" equal parts; recognize that each part has size 1/b. Recognize that a unit fraction 1/b is located 1/b whole unit from 0 on the number line

• Second Grade

• Third Grade

• Fourth Grade

• Fifth Grade

16.NF.2_b represent a non-unit fraction a/b on a number line diagram by marking off “a” lengths 1/b (unit fractions) from 0 and recognize that the resulting interval has size a/b and that its endpoint locates the non-unit fraction a/b on the number line

• Second Grade

• Third Grade

• Fourth Grade

• Fifth Grade

17.NF.3 explain equivalence of fractions through reasoning with visual fraction models. Compare fractions by reasoning about their size

• Second Grade

• Third Grade

• Fourth Grade

• Fifth Grade

18.NF.3_a recognize two fractions as equivalent (equal) if they are the same size or the same point on a number line

• Second Grade

• Third Grade

• Fourth Grade

• Fifth Grade

19.NF.3_b recognize and generate simple equivalent fractions with denominators of 2, 3, 4, 6, and 8. (e.g., 1/2 = 2/4, 4/6 = 2/3); explain why the fractions are equivalent by using a visual fraction model

• Second Grade

• Third Grade

• Fourth Grade

• Fifth Grade