




Massachusetts Comprehensive Assessment System
2017, Grade 4 Mathematics
Question 5: ConstructedResponse 

Reporting Category: Operations and Algebraic Thinking Standard: CCSS.Math.Content.4.OA.B.4  Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given onedigit number. Determine whether a given whole number in the range 1–100 is prime or composite. Item Description: Determine multiples, factors, and whether numbers are prime or composite and justify the reasoning used to determine the answers. 
During art class last week, Carmen put crayons into cups for her art teacher. She put exactly 9 crayons into each cup.
Altogether, Carmen put more than 20 crayons, but fewer than 30 crayons, into the cups.
Part AWhat is the total number of crayons that Carmen put into the cups? Explain your reasoning.
Enter your answer and your explanation in the space provided.
Part BIs your answer to Part A a prime number or a composite number? Explain your reasoning.
Enter your answer and your explanation in the space provided.
Part CThis week, Carmen's art teacher has a total of 28 crayons to put into cups. She wants Carmen to put the same number of crayons into each cup.
Write all the factor pairs of 28 that show possible ways Carmen can divide 28 crayons equally to put into cups.
Enter your answer in the space provided.

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 Operations and Algebraic Thinking concepts involved in finding all factor pairs for a whole number in the range 1–100, recognizing that a whole number is a multiple of each of its factors, determining whether a given whole number in the range 1–100 is a multiple of a given onedigit number, and determining whether a given whole number in the range 1–100 is prime or composite. The student solves a realworld problem by identifying a multiple, justifies whether the number is prime or composite, and determines all the factor pairs of a number. 
4 
3 
The student response demonstrates a good understanding of the Operations and Algebraic Thinking concepts involved in finding all factor pairs for a whole number in the range 1–100, recognizing that a whole number is a multiple of each of its factors, determining whether a given whole number in the range 1–100 is a multiple of a given onedigit number, and determining whether a given whole number in the range 1–100 is prime or composite. 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 finding all factor pairs for a whole number in the range 1–100, recognizing that a whole number is a multiple of each of its factors, determining whether a given whole number in the range 1–100 is a multiple of a given onedigit number, and determining whether a given whole number in the range 1–100 is prime or composite. 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 finding all factor pairs for a whole number in the range 1–100, recognizing that a whole number is a multiple of each of its factors, determining whether a given whole number in the range 1–100 is a multiple of a given onedigit number, and determining whether a given whole number in the range 1–100 is prime or composite. 
0 
The student response contains insufficient evidence of understanding of the Operations and Algebraic Thinking concepts involved in finding all factor pairs for a whole number in the range 1–100, recognizing that a whole number is a multiple of each of its factors, determining whether a given whole number in the range 1–100 is a multiple of a given onedigit number, and determining whether a given whole number in the range 1–100 is prime or composite to merit any points. 
Note: There are 2 sample student responses for Score Point 4.
Grade 4 Mathematics
 Question 5: Operations and Algebraic Thinking
Return to the MCAS 2017 Student Work Directory
Last Updated: November 6, 2014


