Overview

In this performance assessment, students will create a story problem requiring the addition of fractions with uncommon denominators. Students will demonstrate their competency at adding fractions with unlike denominators by choosing which of three problems to solve. Each problem has a different level of difficulty.

Regardless of the difficulty level chosen, students will be given two different fractions and asked to create a story problem that requires the fractions to be added. Then, they will solve their story problem by adding the fractions together by creating common denominators. Finally, they will write an equation to represent the problem. Students will demonstrate their thinking through showing their work and answering three reflection questions.

This assessment should be used after instruction in adding fractions with unlike denominators.

Students should create the final presentation by using paper and pencil and/or colored pens/pencils/ markers. Final student work should be saved as an Acrobat PDF for uploading to the virtual scoring software.

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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 1

Students can represent and solve word problems involving addition and subtraction of fractions, including cases of unlike denominators, 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

Concepts and Procedures
  • Applies some appropriate mathematical processes and/or strategies demonstrating partial understanding of the required concepts and procedures.
  • A basic or partially correct approach is used to solve the problem, but provides insufficient evidence of the ability to carry out the necessary procedures.
  • Calculation errors are present.
  • Solutions may be incomplete, failing to address some of the mathematical components presented in the task. 
  • Applies appropriate mathematical processes and strategies demonstrating complete understanding of the required concepts and procedures.
  • Uses a logical approach to solve the problem.
  • Few and minor calculation errors, if any.
  • Solutions are complete and address all mathematical components presented in the task. 
  • Applies appropriate mathematical processes and strategies demonstrating sophisticated understanding of the required concepts and procedures. 
  • Uses the most efficient approach to solve the problem.
  • No calculation errors.
  • Solutions completely address all mathematical components presented in the task and demonstrate advanced mathematical fluency, if applicable.  

Reasoning and Explaining
  • Attempts to explain the solution(s) to the task and may provide an incomplete justification for the conclusion(s). 
  • Uses some, but limited, mathematical terminology and/or notation. 
No exemplars at this time.
  • Appropriately explains the solution(s) so that the reader does not have to infer how the task was completed.
  • Justifies the conclusion(s) appropriately at multiple decision points.
  • Uses accurate and appropriate mathematical terminology and notation.
No exemplars at this time.
  • Clearly and effectively communicates the solution(s) to convey advanced conceptual understanding of the mathematical content. 
  • Justifies the conclusion(s) effectively at multiple decision points and may evaluate the efficiency or adequacy of differing approaches.
  • Uses precise and sophisticated mathematical terminology and notation.
No exemplars at this time.

Modeling and Using Tools
  • Attempts to use an appropriate representation to model the mathematical concepts or relationships, but the model contains inaccuracies or is incomplete, and/or analyzes and interprets a math model in a limited way. 
  • Selects tools and applies with partial accuracy. 
  • Uses accurate representations to correctly model the mathematical concepts or relationships, and/or accurately analyzes and interprets a math model.
  • Uses an appropriate tool to solve a problem. 
  • Uses an accurate and effective representation to clearly model the mathematical concepts or relationships, and/or accurately analyzes and interprets a math model.
  • Uses an appropriate tool to solve a problem and is able to justify the tool selection. Uses an appropriate tool to solve a problem and is able to justify the tool selection. 

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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