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 21: Open-Response Reporting Category: Algebra and FunctionsStandard: 10.P.6 - Solve equations and inequalities including those involving absolute value of linear expressions (e.g., |x - 2| > 5) and apply to the solution of problems.  (AI.P.10) Standard: Mathematics.A.REI.2.03 - Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. A company packages barbeque sauce in two different-sized bottles, small and large. Although the label on each small bottle states that the bottle contains 18 ounces of sauce, the company allows a tolerance of plus or minus 0.25 ounce for the amount of sauce in each small bottle. In manufacturing, tolerance is the amount of error that is allowed in packaging a product. What is the maximum amount of sauce, in ounces, the company allows in each small bottle? Show or explain how you got your answer.In the absolute-value inequality below, x represents the amount of sauce, in ounces, the company allows in each small bottle.Solve the absolute-value inequality. Show or explain how you got your answer.The company also makes a large bottle of barbeque sauce.The label on the large bottle states that each bottle contains 24 ounces of sauce.The minimum amount of sauce allowed in each large bottle is 23.55 ounces.The maximum amount of sauce allowed in each large bottle is 24.45 ounces.What is the tolerance, in ounces, the company allows for the large bottle? Show or explain how you got your answer.Write an absolute-value inequality that represents y, the amount of sauce, in ounces, the company allows in the large bottle.

### 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 Algebra and Functions concepts involved in solving linear equations and inequalities in one variable involving absolute value. The student solves an absolute-value inequality and then writes a different absolute-value inequality in the context of manufacturing.
4
3 The student response demonstrates a good understanding of the Algebra and Functions concepts involved in solving linear equations and inequalities in one variable involving absolute value. 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 Algebra and Functions concepts involved in solving linear equations and inequalities in one variable involving absolute value. 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 Algebra and Functions concepts involved in solving linear equations and inequalities in one variable involving absolute value.
0 The student response contains insufficient evidence of an understanding of the Algebra and Functions concepts involved in solving linear equations and inequalities in one variable involving absolute value to merit any points.

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

Question 17:
Question 20:
Question 21:
Question 31:
Question 41:
Question 42: