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 11: Open-Response Reporting Category: Operations and Algebraic ThinkingStandard: Mathematics.4.OA.3.05 - Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. Aaron shaded squares to make a pattern of T shapes, as shown below.Aaron shaded 5 squares to make the first T. Then he shaded 3 more squares each time he made the next T in his pattern. Aaron continued his pattern.On the grid in your Student Answer Booklet, shade squares to make the fourth T in Aaron’s pattern.How many squares in all does Aaron need to shade to make the sixth T in his pattern? Show or explain how you got your answer.Will there be any T in Aaron’s pattern that has exactly 30 shaded squares? 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 generating a shape pattern that follows a given rule and identifying apparent features of the pattern. Given a rule about a shape pattern, the student extends the pattern and justifies a given fact about a specific step in the pattern.
4
3 The student response demonstrates a good understanding of the Operations and Algebraic Thinking concepts involved in generating a shape pattern that follows a given rule and identifying apparent features of the pattern. 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 generating a shape pattern that follows a given rule and identifying apparent features of the pattern. 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 a minimal understanding of the Operations and Algebraic Thinking concepts involved in generating a shape pattern that follows a given rule and identifying apparent features of the pattern.
0 The student response contains insufficient evidence of an understanding of the Operations and Algebraic Thinking concepts involved in generating a shape pattern that follows a given rule and identifying apparent features of the pattern to merit any points.

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