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

## 2016, Grade 10 Mathematics

 Question 42: Open-Response Reporting Category: GeometryStandard: 10.M.2 - Given the formula, find the lateral area, surface area, and volume of prisms, pyramids, spheres, cylinders, and cones, e.g., find the volume of a sphere with a specified surface area.Standard: Mathematics.G.GMD.1.03 - Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.* A wooden cube with an edge length of 3 inches is composed of six congruent right square pyramids. The cube and one of the pyramids is shown in the diagram below.What is the volume, in cubic inches, of the entire cube? Show or explain how you got your answer.What is the volume, in cubic inches, of one of the six pyramids? Show or explain how you got your answer.What is the total surface area, in square inches, of the cube? Show or explain how you got your answer.What is the total surface area, to the nearest square inch, of one of the six pyramids? 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 Geometry concepts involved in using volume formulas for pyramids to solve problems. The student finds the surface area and volume of a right square pyramid which is a part of the composition of a cube.
4
3 The student response demonstrates a good understanding of the Geometry concepts involved in using volume formulas for pyramids to solve problems. 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 Geometry concepts involved in using volume formulas for pyramids to solve problems. 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 Geometry concepts involved in using volume formulas for pyramids to solve problems.
0 The student response contains insufficient evidence of an understanding of the Geometry concepts involved in using volume formulas for pyramids to solve problems to merit any points.

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

### Grade 10 Mathematics

Question 17:
Question 20:
Question 21:
Question 36:
Question 41:
Question 42:

Return to the MCAS 2016 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; }