Math.Content.4.NF.A

Explain why a fraction 𝑎/𝑏 is equivalent to a fraction (𝑛 × 𝑎)/(𝑛 × 𝑏) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

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.

Develop understanding of fractions as numbers.

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

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.

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 and that the endpoint of the part based at 0 locates the number 1/𝑏 on the number line.

Understand a fraction 1/𝑏 as the quantity formed by 1 part when a whole is partitioned into 𝑏 equal parts; understand a fraction 𝑎/𝑏 as the quantity formed by 𝑎 parts of size 1/𝑏.

Extend understanding of fraction equivalence and ordering.

Extend understanding of fraction equivalence and ordering.

Extend understanding of fraction equivalence and ordering for fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.