Massachusetts Comprehensive Assessment System

2019, Grade 8 Mathematics

Question 15: Constructed-Response

Reporting Category: Statistics and Probability
Standard: Mathematics.8.SP.A.04 - Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?
Item Description: Interpret a two-way table to answer statistical questions about categorical data collected from the same subjects.

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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 interpreting a two-way table summarizing data on two categorical variables collected from the same subjects. The student determines the number of students in a category, calculates relative frequencies, and uses relative frequencies to analyze the validity of a possible association between the two variables.
4
3	The student response demonstrates a good understanding of the Statistics and Probability concepts involved in 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 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 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 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 4 Mathematics

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Question 4: Measurement and Data

Question 4: Technology/Engineering

Question 5: Earth and Space Science

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Question 6: Operations and Algebraic Thinking

Question 6: Technology/Engineering

Question 6: Measurement and Data

Question 8: Expressions and Equations

Question 8: Language and Writing

Question 8: Reading

Question 8: Language and Writing

Question 9: Language and Writing

Question 9: Number and Quantity

Question 12: Ecology

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Question 13: Number and Operations in Base Ten

Question 14: Statistics and Probability

Question 15: Operations and Algebraic Thinking

Question 15: Statistics and Probability

Question 16: Language and Writing

Question 16: Life Science

Question 17: Physical Science

Question 17: Language and Writing

Question 18: Earth and Space Science

Question 18: Language and Writing

Question 23: Motion and Forces

Question 23: Anatomy and Physiology

Question 30: Geometry

Question 32: Biochemistry and Cell Biology

Question 32: Motion and Forces

Question 35: Algebra and Functions

Question 44: Heat and Heat Transfer

Question 44: Evolution and Biodiversity

Question 45: Electromagnetism

Question 45: Genetics

Return to the MCAS 2019 Student Work Directory

Last Updated: May 5, 2020