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Massachusetts Comprehensive Assessment System

2015, Grade 10 Mathematics

  Question 17: Open-Response no calculator allowed
A student is approximating the locations of square roots and cube roots of integers on a number line.
  1. Between which two consecutive integers on the number line is square root of fifty-five located? Show or explain how you got your answer.
  1. What is the value of square root of fifty-five to the nearest tenth? Show or explain how you got your answer.
The value of square root of m where m is an integer, is located between 11 and 12 on the number line.
  1. What could be the value of m? Show or explain how you got your answer.
The value of cube root of n where n is an integer, is also located between 11 and 12 on the number line.
  1. What could be the value of n? 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 Number and Quantity concepts involved in using rational approximations of irrational numbers to compare the size of irrational numbers, locating them approximately on a number line diagram, and estimating the value of expressions.
4
3 The student response demonstrates a good understanding of the Number and Quantity concepts involved in using rational approximations of irrational numbers to compare the size of irrational numbers, locating them approximately on a number line diagram, and estimating the value of expressions. 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 Number and Quantity concepts involved in using rational approximations of irrational numbers to compare the size of irrational numbers, locating them approximately on a number line diagram, and estimating the value of expressions. 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 Number and Quantity concepts involved in using rational approximations of irrational numbers to compare the size of irrational numbers, locating them approximately on a number line diagram, and estimating the value of expressions.
0 The student response contains insufficient evidence of an understanding of the Number and Quantity concepts involved in using rational approximations of irrational numbers to compare the size of irrational numbers, locating them approximately on a number line diagram, and estimating the value of expressions to merit any points.

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

Grade 10 Mathematics

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

Return to the MCAS 2015 Student Work Directory



Last Updated: November 3, 2011
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