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Massachusetts Comprehensive Assessment System

2015, Grade 10 Mathematics

  Question 21: Open-Response no calculator allowed
The first five figures in a pattern are shown below.
Five figures are shown. Figure one is a dot.  Figure two is a pentagon composed of five dots connected by five line segments. Figure three is a pentagon with each side showing three dots. Figure two is shown in the interior of Figure three and located in the lower right corner of Figure three. Figure four is a pentagon with each side showing four dots.  Figure two and Figure three pentagons are shown in the interior of Figure four and located in the lower right corner of Figure four. Figure five is a pentagon with each side showing five dots. Figure two, Figure three, and Figure four are shown in the interior of Figure five and located in the lower right corner of Figure five.
The pattern continues.
  1. What is the number of pentagons in Figure 6? Show or explain how you got your answer.
  1. Write an expression that represents the number of pentagons in Figure n.
Figure 1 is one dot. Figure 2 is composed of five dots connected by line segments.
  1. What is the number of dots in Figure 6? Show or explain how you got your answer.
  1. Explain how the number of dots in Figure 8 and the number of dots in Figure 9 can be used to determine the number of dots in Figure 10.

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 Algebra and Functions concepts involved in writing a function that describes a relationship between two quantities. The student analyzes a pattern and explains how to determine a number in the pattern in terms of its two preceding numbers.
4
3 The student response demonstrates a good understanding of the Algebra and Functions concepts involved in writing a function that describes a relationship between two quantities. 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 Algebra and Functions concepts involved in writing a function that describes a relationship between two quantities. 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 Algebra and Functions concepts involved in writing a function that describes a relationship between two quantities.
0 The student response contains insufficient evidence of an understanding of the Algebra and Functions concepts involved in writing a function that describes a relationship between two quantities 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: September 27, 2017
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