Understanding a Fraction as a Number

Author: Student Achievement Partners

  • Description
  • Files

This mini-assessment is designed to illustrate how the work of  3.NF.A expands students’ understanding of the number system by introducing fractions as an extension of earlier work with whole numbers and as a subset of the rational number system, which is more fully introduced in grade 6. This mini-assessment is designed for teachers to use either in the classroom, for self-learning, or in professional development settings to:

  • Evaluate students’ understanding of aspects of 3.NF.A. before or after teaching this material;
  • Gain knowledge about assessing conceptual understanding of fractions;
  • Illustrate CCR-aligned assessment problems;
  • Illustrate best practices for writing tasks that allow access for all learners; and
  • Support mathematical language acquisition by offering specific guidance.

  • Making the Shifts

    How does this mini-assessment exemplify the instructional Shifts required by CCSSM?

    Focus Belongs to the major work of third grade

    Sets the foundation for understanding fractions that will be needed in Grade 4 and beyond


    Conceptual Understanding: primary in this mini-assessment

    Procedural Skill and Fluency: secondary in this mini-assessment

    Application: not targeted  in this mini-assessment

  • Noteworthy features of this resource


    • Addresses all standards within the Grade 3 Number and Operations – Fractions domain
    • Includes fractions greater than one to attend to the full meaning of the standards in 3.NF
    • Provides opportunity for students to construct viable arguments as they develop their understanding of fractions as numbers (MP.3)
    • Does not contain any problems with real-world context to ensure that the evidence elicited by the items clearly reflects the intended focus on conceptual understanding consistent with the standards
    • Places more emphasis on representing fractions on a number line than on representing fractions with area models, consistent with the cluster level heading for Grade 3: "Develop understanding of fractions as numbers"

    As a mini-assessment:

    • Assesses important concepts directly, like knowing that a fraction a/b is located in a position defined by marking off a lengths of 1/b equal parts
    • Mixes short conceptual problems with problems that require longer chains of reasoning
    • Offers sample solution methods and item-level analyses in the answer key to support teachers in using student data from the assessment
    • Provides detailed alignment to Achieve’s cognitive complexity framework

Supplemental Resources