




Massachusetts Comprehensive Assessment System
2015, Grade 8 Mathematics
Question 21: OpenResponse 

Reporting Category: Geometry Standard: Mathematics.8.G.1.04  Understand that a twodimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar twodimensional figures, describe a sequence that exhibits the similarity between them. 
An art museum gift shop has rectangular posters that are similar to actual rectangular paintings. One poster that is 18 inches long is similar to a painting that is 45 inches long and 30 inches wide.  What is the scale factor used to reduce the size of the actual painting to the size of the poster? Express the scale factor as a fraction in simplest form. Show or explain how you got your answer.
 What is the width, in inches, of the poster that is 18 inches long? Show or explain how you got your answer.
 All the posters are sized using the same scale factor. A second poster is 16 inches long and 14 inches wide. What are the dimensions, in inches, of the actual painting? 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.
Score  Description 
4 
The student response demonstrates an exemplary understanding of the Geometry concepts involved in understanding that a twodimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations. The student uses their understanding of similarity to find a scale factor and the dimensions of a rectangle given a scale factor. 
4 
3 
The student response demonstrates a good understanding of the Geometry concepts involved in understanding that a twodimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations. 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 understanding that a twodimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations. 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 understanding that a twodimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations. 
0 
The student response contains insufficient evidence of an understanding of the Geometry concepts involved in understanding that a twodimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations to merit any points. 
Note: There are 2 sample student responses for Score Point 4.
Grade 8 Mathematics
 Question 10: Expressions and Equations
 Question 21: Geometry
Return to the MCAS 2015 Student Work Directory
Last Updated: June 26, 2017


