




Massachusetts Comprehensive Assessment System
2015, Grade 10 Mathematics
Question 36: OpenResponse 

Reporting Category: Statistics and Probability Standard: 10.D.1  Select, create, and interpret an appropriate graphical representation (e.g., scatterplot, table, stemandleaf plots, boxandwhisker plots, circle graph, line graph, and line plot) for a set of data and use appropriate statistics (e.g., mean, median, range, and mode) to communicate information about the data. Use these notions to compare different sets of data. Standard: Mathematics.6.SP.2.04  Display numerical data in plots on a number line, including dot plots, histograms, and box plots. 
The table below shows the numbers of students enrolled in different science classes at a high school. Number of Students Enrolled in Science Classes Science Class  Number of Students  biology  240  environmental science  285  earth science  300  physics  195  chemistry   There are a total of 1200 students enrolled in science classes at the high school. Each student is enrolled in only one science class.  What is the total number of students enrolled in chemistry class? Show or explain how you got your answer.
 What percent of the total number of students enrolled in science classes are enrolled in chemistry class? Show or explain how you got your answer.
A guidance counselor at the high school made a circle graph based on the information in the table. The central angle of one sector of the circle graph measures 90°.  Which science class is represented by the sector of the circle graph that has a central angle that measures 90°? Show or explain how you got your answer.
 What is the degree measure of the central angle of the sector of the circle graph that represents the number of students in biology class? 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.
Score  Description 
4 
The student response demonstrates an exemplary understanding of the Statistics and Probability concepts involved in reading and interpreting circle graphs. The student uses a table of information to determine the angle measurements of different sectors of a circle graph. 
4 
3 
The student response demonstrates a good understanding of the Statistics and Probability concepts involved in reading and interpreting circle graphs. 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 Statistics and Probability concepts involved in reading and interpreting circle graphs. 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 Statistics and Probability concepts involved in reading and interpreting circle graphs. 
0 
The student response contains insufficient evidence of an understanding of the Statistics and Probability concepts involved in reading and interpreting circle graphs to merit any points. 
Note: There are 2 sample student responses for Score Point 4.
Grade 10 Mathematics
 Question 17: Number and Quantity
 Question 20: Geometry
 Question 21: Algebra and Functions
 Question 36: Statistics and Probability
 Question 41: Algebra and Functions
 Question 42: Geometry
Return to the MCAS 2015 Student Work Directory
Last Updated: February 8, 2018


