Measured Progress - Newsletter - Open Response

Permission to use this item was granted by the Massachusetts Department of Education. For more information, visit the Massachusetts Department of Education on the Web.

(Note: Just as there are many approaches to asking questions, so too are there different approaches to devising scoring guides. In this case, a more holistic approach was used. However, it should be recognized that the descriptors in the scoring guide above were elaborated on considerably in scorer training through additional explanation and sample responses to more fully convey the meanings of “comprehensive,” “general,” “basic,” and “minimal understanding” of patterns.)

Released Item

A worker placed white tiles around black tiles in the pattern shown in the three figures below.

a. Based on this pattern, how many white tiles would be needed for 4 black tiles?
b. Based on this pattern, how many white tiles would be needed for 50 black tiles?
c. Make a scatterplot of the first five figures in this pattern showing the relationship between the number of white tiles and the number of black tiles. Be sure to label the axes.
d. Based on this pattern, explain how you could find the number of white tiles needed for any number, n, of black tiles. Show or explain your work.

Scoring Guide

Score	Description
4	The response shows a comprehensive understanding of how to extend, represent and generalize a pattern with graphs and symbolic expressions.
3	The response shows a general understanding of how to extend, represent and generalize a pattern with graphs and symbolic expressions.
2	The response shows a basic understanding of patterns.
1	The response shows a minimal understanding of patterns.
0	The response is incorrect or contains some correct work that is irrelevant to the skill or concept being measured.
Blank	No response

Sample Responses

The sample responses provided here are selections of actual student work from the MCAS administered in spring 2002. To protect individual students’ privacy, all names and references of a personal nature have been altered or removed. The responses have been recopied exactly as the student wrote them.