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Massachusetts Comprehensive Assessment System

2016, Grade 8 Mathematics

  Question 21: Open-Response calculator allowed
An athletic director wants to add either tennis or gymnastics to the physical education program at her school. She surveyed the seventh-grade students and eighth-grade students to determine whether they preferred tennis or gymnastics. Some of the data from the survey is listed below.
  • A total of 255 students were surveyed.
  • 120 of the students surveyed are seventh-graders.
  • 72 of the seventh-graders surveyed chose tennis.
  • 62 of the eighth-graders surveyed chose gymnastics.
In your Student Answer Booklet, copy the table exactly as shown below.
 
a blank table is shown, the table is titled Student Preference by Grade, the column labels are Tennis and Gymnastics, the row labels are Seventh Grade and Eighth Grade
  1. Use the data from the survey to complete your table. Show or explain how you got your answers.
  2. Based on your table, what percentage of the eighth-graders chose tennis? Show or explain how you got your answer.
  3. Among those students who chose gymnastics, what is the relative frequency of seventh-graders? Show or explain how you got your answer.
  4. In which grade did a higher percentage of students choose tennis? 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 understanding that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table, and constructing and interpreting a two-way table summarizing data on two categorical variables collected from the same subjects.
4
3 The student response demonstrates a good understanding the Statistics and Probability concepts involved in understanding that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table, and constructing and interpreting a two-way table summarizing data on two categorical variables collected from the same subjects. 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 understanding that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table, and constructing and interpreting a two-way table summarizing data on two categorical variables collected from the same subjects. 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 understanding that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table, and constructing and interpreting a two-way table summarizing data on two categorical variables collected from the same subjects.
0 The student response contains insufficient evidence of an understanding of the Statistics and Probability concepts involved in understanding that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table, and constructing and interpreting a two-way table summarizing data on two categorical variables collected from the same subjects to merit any points.

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

Grade 8 Mathematics

Question 11: Functions
Question 21: Statistics and Probability

Return to the MCAS 2016 Student Work Directory



Last Updated: June 27, 2016
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