Massachusetts Comprehensive Assessment System

2018, Grade 8 Mathematics

Question 12: Constructed-Response

Reporting Category: Expressions and Equations
Standard: Mathematics.8.EE.A.02 - Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
Item Description: Find the value of the unknown variable in a given equation for different situations.

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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 Expressions and Equations concepts involved in using square root and cube root symbols to represent solutions to equations of the form $x^{2} = p$ and $x^{3} = p$ , where p is a positive rational number; evaluating square roots of small perfect squares and cube roots of small perfect cubes, and knowing that $\sqrt{2}$ is irrational.
4
3	The student response demonstrates a good understanding of the Expressions and Equations concepts involved in using square root and cube root symbols to represent solutions to equations of the form $x^{2} = p$ and $x^{3} = p$ , where p is a positive rational number; evaluating square roots of small perfect squares and cube roots of small perfect cubes, and knowing that $\sqrt{2}$ is irrational. 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 Expressions and Equations concepts involved in using square root and cube root symbols to represent solutions to equations of the form $x^{2} = p$ and $x^{3} = p$ , where p is a positive rational number; evaluating square roots of small perfect squares and cube roots of small perfect cubes, and knowing that $\sqrt{2}$ is irrational. 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 Expressions and Equations concepts involved in using square root and cube root symbols to represent solutions to equations of the form $x^{2} = p$ and $x^{3} = p$ , where p is a positive rational number; evaluating square roots of small perfect squares and cube roots of small perfect cubes, and knowing that $\sqrt{2}$ is irrational.
0	The student response contains insufficient evidence of an understanding of the Expressions and Equations concepts involved in using square root and cube root symbols to represent solutions to equations of the form $x^{2} = p$ and $x^{3} = p$ , where p is a positive rational number; evaluating square roots of small perfect squares and cube roots of small perfect cubes, and knowing that $\sqrt{2}$ is irrational to merit any points.

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

Grade 8 Mathematics

Question 12: Expressions and Equations

Question 32: Statistics and Probability

Return to the MCAS 2018 Student Work Directory

Last Updated: July 18, 2018