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Massachusetts Comprehensive Assessment System

2015, Grade 10 Mathematics

  Question 42: Open-Response calculator allowed
Parallel lines q and m are cut by transversal lines j and k. The lines, and the measures of some of the angles created by the intersections of the lines, are shown in the diagram below.
Four lines labeled q, m, j, and k are shown.  Lines q and m are parallel lines, and lines j and k are transversals that cut lines q and m.  , two, three, four, five, six, and seven. Lines j and k intersect to form the angles labeled one hundred ten degrees, and angle one. Angle two and angle three are corresponding angles formed by line k. Angle five and angle seven are corresponding angles formed by line j. Angle four is an exterior angle of line m, and angle six is an interior angle of line q. An exterior angle formed by line k and line q is labeled one hundred fifteen degrees.
  1. What is the measure, in degrees, of angle 1? Show or explain how you got your answer.
  1. What is the measure, in degrees, of angle 3? Show or explain how you got your answer.
  1. What is the measure, in degrees, of angle 5? Show or explain how you got your answer.
  1. What is the measure, in degrees, of angle 6? 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 Geometry concepts involved in using informal arguments to establish facts about the angles created when parallel lines are cut by a transversal. The student calculates angle measures in a diagram with parallel lines and transversals.
4
3 The student response demonstrates a good understanding of the Geometry concepts involved in using informal arguments to establish facts about the angles created when parallel lines are cut by a transversal. 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 Geometry concepts involved in using informal arguments to establish facts about the angles created when parallel lines are cut by a transversal. 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 Geometry concepts involved in using informal arguments to establish facts about the angles created when parallel lines are cut by a transversal.
0 The student response contains insufficient evidence of an understanding of the Geometry concepts involved in using informal arguments to establish facts about the angles created when parallel lines are cut by a transversal 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: October 19, 2017
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