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# Massachusetts Comprehensive Assessment System

Question 5: Constructed-Response
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 A

What is the total number of crayons that Carmen put into the cups? Explain your reasoning.

#### Part C

This 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.

### Scoring Guide and Sample Student WorkSelect 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 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 one-digit number, and determining whether a given whole number in the range 1–100 is prime or composite. The student solves a real-world 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 one-digit 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 one-digit 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 one-digit 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 one-digit 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.