




Massachusetts Comprehensive Assessment System
2015, Grade 10 Mathematics
Question 21: OpenResponse 

Reporting Category: Algebra and Functions Standard: 10.P.1  Describe, complete, extend, analyze, generalize, and create a wide variety of patterns, including iterative, recursive (e.g., Fibonacci Numbers), linear, quadratic, and exponential functional relationships. (AI.P.1)
Standard: Mathematics.F.BF.1.01  Write a function that describes a relationship between two quantities.*

The first five figures in a pattern are shown below. The pattern continues.  What is the number of pentagons in Figure 6? Show or explain how you got your answer.
 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.  What is the number of dots in Figure 6? Show or explain how you got your answer.
 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.
Score  Description 
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: October 9, 2018


