Select Program Area --Select Program Area-- ESE HOME Accountability, Partnership, & Assistance Adult & Community Learning Amazing Educators BOE Advisory Councils Board of Elementary & Secondary Education Career/Vocational Technical Education Charter Schools College and Career Readiness Compliance/Monitoring (PQA) Conferences, Workshops and Trainings Curriculum & Instruction Digital Learning District & School Assistance Centers (DSACs) 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: ESE English Language Learners Every Student Succeeds Act (ESSA) Family Literacy High School Equivalency (HSE) Testing Program Grants/Funding Opportunities Information Services Laws & Regulations Learning Supports and Early Learning (OLSEL) Literacy LEAP Project MCAS MCAS Appeals METCO Office for Food and Nutrition Programs Performance Assessment for Leaders (PAL) Planning and Research Professional Development Race to the Top (RTTT) 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 Support Title I/Federal Support Programs Systems for Student Success (SfSS)
 Students & Families Educators & Administrators Teaching, Learning & Testing Data & Accountability Finance & Funding About the Department Education Board

# Massachusetts Comprehensive Assessment System

## 2012, Grade 10 Mathematics

 Question 41: Open-Response Reporting Category: Patterns, Relations, and AlgebraStandard: 10.P.1 - Describe, complete, extend, analyze, generalize, and create a wide variety of patterns, including iterative, recursive (e.g., Fibonacci Numbers), linear, quadratic, and exponential functional relationships. (AI.P.1) The table below shows figures composed of circles. The number of circles in each figure and the diameter of each circle in each figure follow a pattern, as shown.What is the number of circles in figure 5? Show or explain how you got your answer.What is the diameter, in inches, of each circle in figure 5? Show or explain how you got your answer.What is the ratio of the number of circles in figure 6 to the number of circles in figure 7? Show or explain how you got your answer.Write an algebraic expression that could be used to determine the number of circles in figure n.Write an algebraic expression that could be used to determine the diameter, in inches, of each circle in figure n.

### 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 Patterns, Relations, and Algebra concepts involved in completing, extending, and generalizing a pattern. The student determines the number of circles in a figure and the diameter of each circle and creates algebraic expressions to represent each pattern.
4
3 The student response demonstrates a good understanding of the Patterns, Relations, and Algebra concepts involved in completing, extending, and generalizing a 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 fair understanding of the Patterns, Relations, and Algebra concepts involved in completing, extending, and generalizing a 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 only minimal understanding of the Patterns, Relations, and Algebra concepts involved in completing, extending, and generalizing a pattern.
0 The student response contains insufficient evidence of an understanding of the Patterns, Relations, and Algebra concepts involved in completing, extending, and generalizing a pattern to merit any points.

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

None found...

Return to the MCAS 2012 Student Work Directory

 E-mail this page| Print View| Print Pdf   .nav:before, .nav:after, .navbar:before, .navbar:after, .navbar-header:before, .navbar-header:after, .navbar-collapse:before, .navbar-collapse:after { display:inline; } .navbar { border-radius:0px; }