3.NF.A.1

Develop understanding of fractions as numbers.

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.


 

Summary:

The key point of this standard is the concept of a pre-defined "whole" (which one must pay attention to when solving problems) and the idea of equal parts (not just parts of any size). The standard asks students to understand a/b as the quantity formed by a/b parts of a whole. Note that a can be greater than b; the standards do not make any distinction between proper and improper fractions.

Integration Ideas:

  • Students need practice identifying fractions with their appropriate word names and picture representations.
  • To help with conceptualizing fractions as parts of a whole, students will use fraction manipulatives (such as pattern blocks or fraction bars) to compare portions of a circle or rectangle and its whole counterparts. In this manner, students can better understand that fractions are pieces of a whole.

Questions to Focus Learning:

  • Can students match a fraction with its word name and picture representation?
  • Are students able to create a fraction that was given in words using pictures or manipulatives and then write it in the form a/b?
  • Can students use appropriate vocabulary to name the specific parts of a fractional number (denominator and numerator)?
  • Can students construct a visual representation of a fraction a/b, where a > b? (shows whether students understand improper fractions in the same way they understand proper fractions)

Skills

Prior to: Students have had previous experience dividing circles and rectangles into a specific number of equal pieces (two, three, or four) and then shading in a portion of those pieces. Further, they are able to write such a pictorial representation using a fractional word such as halves, thirds, and fourths.

At Grade Level:
Students can use appropriate language when identifying parts of a fraction. Students can accurately depict a fraction using a picture representation and a symbolic representation of the form a/b.