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Massachusetts Comprehensive Assessment System

2015, Grade 5 Mathematics

  Question 9: Open-Response no calculator allowed
Carolina is twice as old as her brother Diego will be in 3 years. Diego is 4 years old now. The expression below shows how to find Carolina’s age, in years.
two times open parenthesis four plus three close parenthesis
  1. What is Carolina’s age, in years? Show or explain how you got your answer.
Carolina’s sister, Marisol, is three times as old as Diego was 2 years ago. 
  1. Write an expression using numbers and operations to represent Marisol’s age, in years.
  1. What is Marisol’s age, in years? Show or explain how you got your answer.
The expression below represents the difference, in years, between the ages of Carolina’s father and her mother.
open parenthesis fifteen times three close parenthesis minus open bracket open parenthesis ten times four close parenthesis minus two close bracket
  1. What is the difference, in years, between the ages of Carolina’s father and her mother? Show or explain how you got your answer.

Scoring Guide and Sample Student Work
Select a score point in the table below to view the sample student response.

ScoreDescription
4 The student response demonstrates an exemplary understanding of the Operations and Algebraic Thinking concepts involved in using parentheses, brackets, or braces in numerical expressions, and evaluating expressions with these symbols. The student writes and evaluates numerical expressions.
4
3 The student response demonstrates a good understanding of the Operations and Algebraic Thinking concepts involved in using parentheses, brackets, or braces in numerical expressions, and evaluating expressions with these symbols. Although there is significant evidence that the student was able to recognize and apply the concepts involved, some aspect of the response is flawed. As a result the response merits 3 points.
2 The student response demonstrates a fair understanding of the Operations and Algebraic Thinking concepts involved in using parentheses, brackets, or braces in numerical expressions, and evaluating expressions with these symbols. While some aspects of the task are completed correctly, others are not. The mixed evidence provided by the student merits 2 points.
1 The student response demonstrates only a minimal understanding of the Operations and Algebraic Thinking concepts involved in using parentheses, brackets, or braces in numerical expressions, and evaluating expressions with these symbols.
0 The student response contains insufficient evidence of an understanding of the Operations and Algebraic Thinking concepts involved in using parentheses, brackets, or braces in numerical expressions, and evaluating expressions with these symbols to merit any points.

Note: There are 2 sample student responses for Score Point 4.

Grade 5 Mathematics

Question 9: Operations and Algebraic Thinking
Question 12: Number and Operations-Fractions

Return to the MCAS 2015 Student Work Directory



Last Updated: May 16, 2017
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