Massachusetts Comprehensive Assessment System

2019, Grade 3 Mathematics

Question 15: Constructed-Response

Reporting Category: Operations and Algebraic Thinking
Standard: Mathematics.3.OA.B.05 - Apply properties of operations to multiply. For example: When multiplying numbers order does not matter. If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known (Commutative property of multiplication); The product 3 x 5 x 2 can be found by 3 x 5 = 15 then 15 x 2 = 30, or by 5 x 2 = 10 then 3 x 10 = 30 (Associative property of multiplication); When multiplying two numbers either number can be decomposed and multiplied; one can find 8 x 7 by knowing that 7 = 5 + 2 and that 8 x 5 = 40 and 8 x 2 = 16, resulting in 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56 (Distributive property); When a number is multiplied by 1 the result is the same number (Identity property of 1 for multiplication). [Note: Students need not use formal terms for these properties. Students are not expected to use distributive notation]
Item Description: Show how to use the distributive property to solve a multiplication problem and critique the reasoning of another student who wants to use a different method.

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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
3	The student response demonstrates an exemplary understanding of the Operations and Algebraic Thinking concepts involved in applying properties of operations as strategies to multiply and divide. The student correctly shows how to use the distributive property to solve a multiplication problem and critiques the reasoning of another student who wants to use a different method.
3
2	The student response demonstrates a good understanding of the Operations and Algebraic Thinking concepts involved in applying properties of operations as strategies to multiply and divide. 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 2 points.
1	The student response demonstrates a minimal understanding of the Operations and Algebraic Thinking concepts involved in applying properties of operations as strategies to multiply and divide. While some aspects of the task are completed correctly, others are not. The mixed evidence provided by the student merits 1 point.
0	The student response contains insufficient evidence of an understanding of the Operations and Algebraic Thinking concepts involved in applying properties of operations as strategies to multiply and divide to merit any points.

Note: There are 2 sample student responses for Score Point 3.

Grade 4 Mathematics

Question 3: Number and Operations-Fractions

Question 4: Ratios and Proportional Relationships

Question 4: Measurement and Data

Question 4: Technology/Engineering

Question 5: Earth and Space Science

Question 5: Functions

Question 6: Operations and Algebraic Thinking

Question 6: Technology/Engineering

Question 6: Measurement and Data

Question 8: Expressions and Equations

Question 8: Language and Writing

Question 8: Reading

Question 8: Language and Writing

Question 9: Language and Writing

Question 9: Number and Quantity

Question 12: Ecology

Question 12: Waves and Radiation

Question 12: Expressions and Equations

Question 13: Number and Operations in Base Ten

Question 14: Statistics and Probability

Question 15: Operations and Algebraic Thinking

Question 15: Statistics and Probability

Question 16: Language and Writing

Question 16: Life Science

Question 17: Physical Science

Question 17: Language and Writing

Question 18: Earth and Space Science

Question 18: Language and Writing

Question 23: Motion and Forces

Question 23: Anatomy and Physiology

Question 30: Geometry

Question 32: Biochemistry and Cell Biology

Question 32: Motion and Forces

Question 35: Algebra and Functions

Question 44: Heat and Heat Transfer

Question 44: Evolution and Biodiversity

Question 45: Electromagnetism

Question 45: Genetics

Return to the MCAS 2019 Student Work Directory

Last Updated: May 5, 2020