




Massachusetts Comprehensive Assessment System
2017, Grade 10 Mathematics
Question 42: OpenResponse 

Reporting Category: Algebra and Functions Standard: 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: CCSS.Math.Content.HSAREI.B.3  Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 
Allen wants to add to his existing collection of 300 bottles. Starting today, he will collect 25 bottles each week.
 What will be the total number of bottles in Allen's collection after 4 weeks? Show or explain how you got your answer.
 Write an expression to represent the total number of bottles in Allen's collection after w weeks.
 After how many weeks will Allen have a total of exactly 1,000 bottles in his collection? Show or explain how you got your answer.
Allen's goal is to have between 1,500 and 1,600 bottles in his collection.
 Write and solve a compound inequality to determine the number of weeks it will take Allen to reach his goal. Show your work.

Scoring Guide and Sample Student Work Select a score point in the table below to view the sample student response.
Score  Description 
4 
The student response demonstrates an exemplary understanding of the Algebra and Functions concepts involved in creating inequalities in one variable and using them to solve problems. The student writes and solves an inequality to model a situation and applies the solution to the context of the problem. 
4 
3 
The student response demonstrates a good understanding of the Algebra and Functions concepts involved in creating inequalities in one variable and using them 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 Algebra and Functions concepts involved in creating inequalities in one variable and using them 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 Algebra and Functions concepts involved in creating inequalities in one variable and using them to solve problems. 
0 
The student response contains insufficient evidence of an understanding of the Algebra and Functions concepts involved in creating inequalities in one variable and using them to solve problems to merit any points. 
Note: There are 2 sample student responses for Score Point 4.
Grade 10 Mathematics
 Question 17: Geometry
 Question 20: Number and Quantity
 Question 21: Statistics and Probability
 Question 36: Algebra and Functions
 Question 41: Geometry
 Question 42: Algebra and Functions
Return to the MCAS 2017 Student Work Directory
Last Updated: June 27, 2018


