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Massachusetts Comprehensive Assessment System

2011, Grade 10 Mathematics

  Question 41: Open-Response calculator allowed
The numbers of games won and lost by six local baseball teams are shown in the double bar graph below.
A double bar graph titled
  1. How many more games did the Hawks win than the Wolves won? Show or explain how you got your answer.
  2. For the Panthers, what is the ratio of games won to games played? Show or explain how you got your answer.
  3. Which of the six teams has the greatest ratio of games won to games played? Show or explain how you got your answer.
The Scorpions later played additional games that were not included in the double bar graph. The additional games changed the Scorpions’ ratio of games won to games played to one half.
  1. What is the least number of additional games the Scorpions could have played? 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 interpreting an appropriate graphical representation for a set of data and using appropriate statistics to communicate information about the data. The student interprets a double-bar graph and determines the ratio of games won to total games played by different teams.
4
3 The student response demonstrates a good understanding of the Data Analysis, Statistics, and Probability concepts involved in interpreting an appropriate graphical representation for a set of data and using appropriate statistics to communicate information about 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 fair understanding of the Data Analysis, Statistics, and Probability concepts involved in interpreting an appropriate graphical representation for a set of data and using appropriate statistics to communicate information about 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 only minimal understanding of the Data Analysis, Statistics, and Probability concepts involved in interpreting an appropriate graphical representation for a set of data and using appropriate statistics to communicate information about the data.
0 The student response contains insufficient evidence of an understanding of the Data Analysis, Statistics, and Probability concepts involved in interpreting an appropriate graphical representation for a set of data and using appropriate statistics to communicate information about the data to merit any points.

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

Grade 10 Mathematics

Question 17: Number Sense and Operations
Question 20: Geometry
Question 21: Patterns, Relations, and Algebra
Question 31: Patterns, Relations, and Algebra
Question 41: Data Analysis, Statistics, and Probability
Question 42: Measurement

Return to the MCAS 2011 Student Work Directory



Last Updated: December 1, 2016
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