Overview

In this performance assessment, students will apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world problems. Specifically, students will be asked to find the length of a side of a right triangle that is seen in the real world. Students will explain their process of finding the different lengths.  

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Details

Big Ideas & Competencies

Big Ideas Competencies

D. Geometric Reasoning

Students can collect and organize data to interpret, model, and investigate issues connected to their communities, lived experiences, and cultural identities.

Distance Between Two Points 1

Students can apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

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.  
No exemplars at this time.
  • 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.
No exemplars at this time.
  • 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.
No exemplars at this time.

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. 
No exemplars at this time.
  • 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. 
No exemplars at this time.
  • Uses and 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.
No exemplars at this time.

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