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Massachusetts Comprehensive Assessment System

2016, Grade 10 Mathematics

  Question 41: Open-Response calculator allowed
The table below shows the distribution of eye color and hair color for the 60 students in a chorus.
A table has four columns of hair colors. The first column title is Black, the second column title is Blond, the third column title is Brown, and the fourth column title is Red, the table has four rows of eye colors, the first row title is Brown and has values of seven three ten and two, the second row title is Blue and has values of five sis six and two, the third row title is Green and has values of four three three and three, the fourth row title is Hazel and has values of one two one and two
  1. How many students in the chorus have brown hair? Show or explain how you got your answer.
  2. What fraction of the students with blond hair have hazel eyes? Show or explain how you got your answer.
  3. What percentage of all the students have both green eyes and red hair? Show or explain how you got your answer.
  4. What percentage of all the students have green eyes or red hair? 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 Statistics and Probability concepts involved in summarizing categorical data for two categories in two-way frequency tables and interpreting relative frequencies in the context of the data. The student interprets data from a table and calculates percentages based on the data.
4
3 The student response demonstrates a good understanding of the Statistics and Probability concepts involved in summarizing categorical data for two categories in two-way frequency tables and interpreting relative frequencies in the context of the 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 a fair understanding of the Statistics and Probability concepts involved in summarizing categorical data for two categories in two-way frequency tables and interpreting relative frequencies in the context of the 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 a minimal understanding of the Statistics and Probability concepts involved in summarizing categorical data for two categories in two-way frequency tables and interpreting relative frequencies in the context of the data.
0 The student response contains insufficient evidence of an understanding of the Statistics and Probability concepts involved in summarizing categorical data for two categories in two-way frequency tables and interpreting relative frequencies in the context of the data to merit any points.

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

Grade 10 Mathematics

Question 17: Algebra and Functions
Question 20: Geometry
Question 21: Number and Quantity
Question 36: Algebra and Functions
Question 41: Statistics and Probability
Question 42: Geometry

Return to the MCAS 2016 Student Work Directory



Last Updated: June 7, 2017
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