Equivalent Fractions

NF3.a. Understand two fractions are equivalent if they are the same size or the same point on a number line. 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 number and size of the parts differ even though the two fractions themselves are the same size

NF3.b. Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers. Recognize that comparisons are only valid when the two fractions refer to the same whole.

Students need to be able to flexibly compare fractions and rename fractions using multiple representations. Area models, number lines, manipulatives such as pattern blocks, paper folding, and virtual manipulatives support students to make sense of equivalence before using procedures.

Students need opportunities to develop understanding about how comparing whole numbers is different than comparing fractions and cannot be uniformly applied to fraction comparisons. For example, students who apply whole number reasoning to fractions might say, "1/4 is bigger than 1/3 because 4 is greater than 3."