3.NF.3

Support Videos & Extra Practice

In this standard, students will be expected to understand that equivalent fractions refer to fractions that cover the same amount of space/same area, or are located at the same point on a number line. Students will also have to draw models (circles, squares, number lines) to create equivalent fractions.

A common mistake: Fractions with the same numerator or same denominator are equivalent

      • 2/4 = 2/3 FALSE: I know that one-third is bigger than one-fourth, so two-thirds must be greater than two-fourths. In both fractions, there are two pieces, but two-thirds would have bigger pieces than two-fourths. 2/4 < 2/3
      • 1/4 = 3/4 FALSE: I know that these pieces are the same size; however, three-fourths has three pieces while one-fourth has only one piece. 1/4 < 3/4

In this standard, students must also understand that whole numbers can also be written as fractions.

      • 3 = 3/1
      • 1 = 3/3

A common mistake: Some students believe that 3/3 and 3/1 are equal, or they confuse the two answers. Drawing models can help them see the difference.

In this standard, students must also be able to compare fractions using <, >, or = symbols. Students should rely on their reasoning skills and models to make these comparisons.

Some examples of fractional reasoning:

      • 1/2 > 1/4 because these fractions both have one piece (unit fractions) and half pieces are greater than fourth pieces. One-half is also closer to one whole than one-fourth.
      • 2/3 > 1/3 because both of these fractions have the same size pieces, but two-thirds has two pieces while one-third only has one piece. Two-thirds is also closer to one whole than one-third.

Important note: Students must understand that comparisons are only true if the two fractions refer to the same size whole.

Example: If I eat 1/2 of a large pizza and my brother eats 1/4 of an XL pizza, then I cannot compare these fractions without more information. They are referring to different size wholes. If I eat 1/2 of large pizza and my brother eats 1/4 of a large pizza, then 1/2 > 1/4. I ate more pizza.