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Massachusetts Comprehensive Assessment System

2016, Grade 10 Mathematics

  Question 21: Open-Response no calculator allowed
Vivian and William are approximating the values of square roots and cube roots.
  1. Vivian approximated the value of square root of fifteen. What is the value of square root of fifteen to the nearest whole number? Show or explain how you got your answer.
  2. William approximated the value of cube root of thirty. What is the value of cube root of thirty to the nearest whole number? Show or explain how you got your answer.
Vivian approximated the value of square root of thirty five to be 5.8. William found a closer approximation to the value of square root of thirty five than Vivian did.
  1. What could be the approximation that William found? Show or explain how you got your answer.
Vivian approximated the value of cube root of one thousand and ten to be 10.0. William claimed that 10.1 is a closer approximation to the value of cube root of one thousand and ten than Vivian's approximation.
  1. Whose approximation, Vivian's or William's, is closer to the value of cube root of one thousand and ten? Explain your reasoning.

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. The student approximates an expression to a greater degree of accuracy than a given approximation of the expression.
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. 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. 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.
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 to merit any points.

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

Grade 10 Mathematics

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

Return to the MCAS 2016 Student Work Directory



Last Updated: October 17, 2017
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