Select Program Area --Select Program Area-- DESE HOME Accountability, Partnership, & Assistance Adult & Community Learning Amazing Educators BESE Advisory Councils Board of Elementary & Secondary Education Career/Vocational Technical Education Charter Schools College and Career Readiness Compliance/Monitoring (PQA) Conferences, Workshops and Trainings Instructional Support Digital Learning District & School Turnaround District Review, Analysis, & Assistance Tools Educator Evaluation Educator Licensure Tests (MTEL) Educator Licensure Educational Proficiency Plan (EPP) Edwin ELAR Log In Employment Opportunities: DESE English Language Learners Every Student Succeeds Act (ESSA) Family Literacy Federal Grant Programs High School Equivalency (HSE) Testing Program Grants/Funding Opportunities Information Services Laws & Regulations Literacy LEAP Project MCAS MCAS Appeals METCO Office for Food and Nutrition Programs Performance Assessment for Leaders (PAL) Planning and Research Professional Development RETELL Safe and Supportive Schools School and District Profiles/Directory School Finance School Redesign Science, Technology Engineering, and Mathematics (STEM) Security Portal | MassEdu Gateway Special Education Special Education Appeals Special Education in Institutional Settings Statewide System of Support Student and Family Support Systems for Student Success (SfSS) Title I Part A
 Students & Families Educators & Administrators Teaching, Learning & Testing Data & Accountability Finance & Funding About the Department Education Board

# Massachusetts Comprehensive Assessment System

 Question 9: Open-Response Reporting Category: Operations and Algebraic ThinkingStandard: Mathematics.5.OA.1.01 - Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. 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.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. Write an expression using numbers and operations to represent Marisol’s age, in years.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.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 WorkSelect 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.