Module 5

Develop understanding of fractions as numbers.

MGSE3.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 _.

MGSE3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram.

MGSE3.NF.3 Explain equivalence of fractions through reasoning with visual fraction models. Compare fractions by reasoning about their size.

a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

b. Recognize and generate simple equivalent fractions with denominators of 2, 3, 4, 6, and 8 (1/2, 2/3, 3/4, 1/6, 4/8). Explain why the fractions are equivalent, e.g., by using a visual fraction model.

c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

• 4/4= 1 whole
• 3/1= 3 wholes

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 (visual fraction model, number line, cross multiplication).