Massachusetts Comprehensive Assessment System

2018, Grade 6 Mathematics

Question 25: Constructed-Response

Reporting Category: The Number System
Standard: Mathematics.6.NS.B.04 - Use prime factorization to find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two relatively prime numbers. For example, express 36 + 8 as 4(9 + 2).
Item Description: Use understanding of greatest common factors and least common multiples to solve problems.

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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 Number System concepts involved in solving problems with common multiples and divisibility.
4
3	The student response demonstrates a good understanding of the Number System concepts involved in solving problems with common multiples and divisibility. 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 Number System concepts involved in solving problems with common multiples and divisibility. 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 Number System concepts involved in solving problems with common multiples and divisibility.
0	The student response contains insufficient evidence of an understanding of the Number System concepts involved in solving problems with common multiples and divisibility to merit any points.

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

Grade 6 Mathematics

Question 12: Statistics and Probability

Question 25: The Number System

Return to the MCAS 2018 Student Work Directory

Last Updated: March 11, 2024