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Massachusetts Comprehensive Assessment System

2014, Grade 4 Mathematics

  Question 11: Open-Response no calculator allowed
Aaron shaded squares to make a pattern of T shapes, as shown below.
A grid with ten rows and twenty-three columns. A pattern of three T's are shown. The first T has five squares shaded; the second T has three more squares shaded than the first T; the third T has three more squares than the second T.
Aaron shaded 5 squares to make the first T. Then he shaded 3 more squares each time he made the next T in his pattern. Aaron continued his pattern.
  1. On the grid in your Student Answer Booklet, shade squares to make the fourth T in Aaron’s pattern.
  2. How many squares in all does Aaron need to shade to make the sixth T in his pattern? Show or explain how you got your answer.
  3. Will there be any T in Aaron’s pattern that has exactly 30 shaded squares? 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 Operations and Algebraic Thinking concepts involved in generating a shape pattern that follows a given rule and identifying apparent features of the pattern. Given a rule about a shape pattern, the student extends the pattern and justifies a given fact about a specific step in the pattern.
4
3 The student response demonstrates a good understanding of the Operations and Algebraic Thinking concepts involved in generating a shape pattern that follows a given rule and identifying apparent features of the pattern. 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 Operations and Algebraic Thinking concepts involved in generating a shape pattern that follows a given rule and identifying apparent features of the pattern. 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 Operations and Algebraic Thinking concepts involved in generating a shape pattern that follows a given rule and identifying apparent features of the pattern.
0 The student response contains insufficient evidence of an understanding of the Operations and Algebraic Thinking concepts involved in generating a shape pattern that follows a given rule and identifying apparent features of the pattern to merit any points.

Note: There are 2 sample student responses for Score Point 4.

Grade 4 Mathematics

Question 5: Number and Operations-Fractions
Question 11: Operations and Algebraic Thinking

Return to the MCAS 2014 Student Work Directory



Last Updated: October 6, 2017
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