Overview

In this performance assessment, students will apply their knowledge of the Pythagorean Theorem when working on a coordinate plane. Specifically, students will be asked to solve for unknown distances when provided with points plotted on a coordinate grid, right triangles drawn on a coordinate grid, and right triangles drawn on a coordinate plane in which leg length must be calculated using the Pythagorean Theorem. 

Students will explain their reasoning and mathematical processes for multi-step questions. Students will also identify their level of mathematical confidence and greatest challenges.

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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 2

Students can apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

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
  • Uses generic vocabulary to identify and explain the topic and/or supporting information.
  • Uses inconsistent grammar and conventions pertaining to a standard format for citation.
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. 
  • 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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