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Massachusetts Comprehensive Assessment System

2012, Grade 8 Mathematics

  Question 21: Open-Response calculator allowed
The students at Smithfield Middle School are enrolled in Art, Music, both Art and Music, or neither Art nor Music.
  • A total of 88 students are enrolled in both Art and Music. 
  • A total of 194 students are enrolled in Art. 
  • A total of 143 students are enrolled in Music. 
  • There are a total of 351 students at the school. 
  1. What is the number of students who are enrolled in Music but not in Art? Show or explain how you got your answer.
In your Student Answer Booklet, copy the Venn diagram below.
Venn diagram with title Art and Music Enrollment. Two intersecting circles are shown, one labeled Art and the other labeled Music. Outside both circles, the label is Neither Art nor Music.
  1. Use the information given above to complete the Venn diagram you copied. 
  2. What is the number of students who are enrolled in neither Art nor Music? Show or explain how you got your answer.

Scoring Guide and Sample Student Work
Select a score point in the table below to view the sample student response.

ScoreDescription
4 The student response demonstrates an exemplary understanding of the Data Analysis, Statistics, and Probability concepts involved in selecting, creating, interpreting, and utilizing various tabular and graphical representations of data. The student uses given data to create and interpret a Venn diagram.
4
3 The student response demonstrates a good understanding of the Data Analysis, Statistics, and Probability concepts involved in selecting, creating, interpreting, and utilizing various tabular and graphical representations of data. 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 Data Analysis, Statistics, and Probability concepts involved in selecting, creating, interpreting, and utilizing various tabular and graphical representations of data. 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 Data Analysis, Statistics, and Probability concepts involved in selecting, creating, interpreting, and utilizing various tabular and graphical representations of data.
0 The student response contains insufficient evidence of an understanding of the Data Analysis, Statistics, and Probability concepts involved in selecting, creating, interpreting, and utilizing various tabular and graphical representations of data to merit any points.

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

Grade 8 Mathematics

Question 10: Number Sense and Operations
Question 21: Data Analysis, Statistics, and Probability

Return to the MCAS 2012 Student Work Directory



Last Updated: August 26, 2016
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