Overview

In this performance assessment, students will expand and explain their understanding of how the meaning of division applies to dividing a whole number by a fraction. Specifically, students will be asked to describe how their understanding of division expands to include division of a whole number by a fraction as a result of modeling division using concrete and representational materials. 

Students will draw models of division to represent their concrete mathematical models and explain how their understanding of division has expanded to include the meaning of a quotient when a whole number is divided by a unit fraction.

This assessment may best be used as an introduction to division with fractions. This assessment should be used as an introduction to division of a whole number by a fraction, before any formal instruction takes place but after students have been taught the meaning of division (initially in third grade and expanded upon in fourth grade).

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Details

Big Ideas & Competencies

Big Ideas Competencies

B. Operations and Algebraic Thinking

Students can use mathematics to analyze and evaluate historical, political, economic, scientific, and social problems and make conjectures about possible solutions.

Solve Word Problems with Fractions 3

Students can represent and solve word problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions using models or equations.

NOTE ABOUT ASSESSMENT RUBRICS

Below are analytic teacher rubrics. The column on the left shows the dimension that is being measured in the student’s performance. The levels across the top row indicate the performance level in the dimensions. Occasionally all dimensions and performance levels are exemplified by multiple students in a single recording.

Teacher Rubric

Dimensions Not Yet Meeting Expectations Meeting Expectations Exceeding Expectations

Reasoning and Explaining
  • ​​The student attempts to explain their thinking but demonstrates an incomplete understanding or generalization. 
  • ​The student uses some, but limited, mathematical terminology and/or notation​.
  • ​​The student appropriately explains their thinking and justifies their understanding or generalization appropriately. 
  • ​The student uses accurate and appropriate mathematical terminology and/or notation​. 
No exemplars at this time.
  • ​​The student clearly and effectively explains their thinking and justifies their understanding and/or their generalization(s) demonstrate a deep understanding.
  • ​The student uses precise and sophisticated mathematical terminology and/or notation.​ 
No exemplars at this time.

Seeing Structure and Generalizing
  • Identifies some patterns, structure, and/or repeated calculation in math problems, but applies them incorrectly or in a limited way to solve the problem more efficiently.
No exemplars at this time.
  • Identifies patterns, structure, and/or repeated calculations in math problems and uses that information to solve part of the problem more efficiently. 
No exemplars at this time.
  • Identifies patterns, structure, and/or repeated calculations in math problems and uses that information to solve problems more efficiently or explain why a shortcut works.
No exemplars at this time.

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