




Massachusetts Comprehensive Assessment System
2013, Grade 10 Mathematics
Question 21: 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: 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 differentsized 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 absolutevalue inequality below, x represents the amount of sauce, in ounces, the company allows in each small bottle.  Solve the absolutevalue 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 absolutevalue inequality that represents y, the amount of sauce, in ounces, the company allows in the large bottle.

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 solving linear equations and inequalities in one variable involving absolute value. The student solves an absolutevalue inequality and then writes a different absolutevalue 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.
Grade 10 Mathematics
 Question 17: Statistics and Probability
 Question 20: Number and Quantity
 Question 21: Algebra and Functions
 Question 31: Algebra and Functions
 Question 41: Geometry
 Question 42: Geometry
Return to the MCAS 2013 Student Work Directory
Last Updated: February 22, 2017


