MAFS.3.OA.2.5

Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
General Information
Subject Area: Mathematics
Grade: 3
Domain-Subdomain: Operations and Algebraic Thinking
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Understand properties of multiplication and the relationship between multiplication and division. (Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date Adopted or Revised: 02/14
Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes
Test Item Specifications

  • Assessment Limits :
    All values in items may not exceed whole number multiplication facts of 10 x 10 or the related division facts. 
    Items may contain no more than two properties in an equation  (e.g., a × (b + c) = (a × b) + (c × a)).
  • Calculator :

    No

  • Context :

    No context

Sample Test Items (3)


Related Courses

This benchmark is part of these courses.
5012050: Grade Three Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
7712040: Access Mathematics Grade 3 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022 (current), 2022 and beyond)
5012055: Grade 3 Accelerated Mathematics (Specifically in versions: 2019 - 2022 (current), 2022 and beyond)
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022 (current), 2022 and beyond)

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.3.OA.2.AP.5a: Recognize multiplication as commutative and associative.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Assessments

Sample 2 - Third Grade Math State Interim Assessment:

This is a State Interim Assessment for third grade.

Type: Assessment

Sample 1 - Third Grade Math State Interim Assessment:

This is a State Interim Assessment for third grade.

Type: Assessment

Educational Game

Who Wants to be a Mathionaire?:

This online game replicates the popular "Who Wants to be a Millionaire?" format, using multiplication facts. It's a fun way for kids to practice multiplication!

Type: Educational Game

Formative Assessments

Using the Associative Property of Multiplication:

Students are asked to find the product of three numbers and are observed to see if they use the Associative Property to find the product more easily.

Type: Formative Assessment

Break Apart and Put Together:

Students are given two arrays, one representing the equation 7 x 9 = 63 and the other representing the equation (5 + 2) x 9 = 63, to see if they recognize a relationship between the two.

Type: Formative Assessment

Meeting the Reading Goal:

Students are given two problems to solve, one represented by the equation 4 x 6 = 24 and the other by the equation 6 x 4 = 24, to see if they recognize the answer to the second problem based on the Commutative Property.

Type: Formative Assessment

Does It Work for Division?:

Students are asked if the Commutative Property holds for division.

Type: Formative Assessment

Lesson Plans

Partial Products with Arrays:

In this inquiry based lesson, students will find partial products of arrays to solve multiplication problems. They will also move from a concrete representation of arrays using manipulatives to a pictorial representation. 

Type: Lesson Plan

Candy Apple Fun:

Students will learn how to break down simple multiplication problems by using arrays to model the Distributive property.

Type: Lesson Plan

Simplifying Multiplication with the Distributive Property:

In this lesson, students will use arrays to understand the distributive property of multiplication and to demonstrate that multiplying a multiplicand by two factors of the multiplier and then adding their products is the same as finding the product of the multiplicand and the multiplier. For example: 5 x 9 = 5(6 + 3) = (5 x 6) + (5 x 3) = 30 + 15 = 45.

Type: Lesson Plan

Decomposing Arrays, an Introduction to the Distributive Property:

ResourceID: 73249
This lesson introduces students to the concept behind the Distributive Property of Multiplication. Students will decompose arrays into smaller parts and write the corresponding multiplication sentence for each smaller array.

Type: Lesson Plan

The Distributive Property, Revealed! with a 100-dot matrix:

This lesson is designed as an introduction into the use of a 100-dot matrix to visualize the Distributive property of multiplication for one-digit by one-digit multiplication problems.

Type: Lesson Plan

Zero on a Hero (Exploring the Zero Property of Multiplication):

Students will explore the Zero Property of Multiplication using array and equal-group models for multiplication. Students will model story problems, translate problems into multiplication facts, and identify patterns in a set of multiplication facts to develop understanding of the Zero Property of Multiplication.

Type: Lesson Plan

One with a Bun (Exploring the Multiplicative Identity Property of 1):

In this lesson students will explore the Multiplicative Identity Property of 1, using array and equal-group models for multiplication. Students will model story problems, translate problems into multiplication equations, and identify patterns in a set of multiplication facts to develop understanding of the Multiplicative Identity Property of 1.

Type: Lesson Plan

Hungry Zero:

The definition of the Zero Property of Multiplication will be analyzed, modeled and practiced.   

Type: Lesson Plan

Efficient Multiplication:

Students will engage with questions to evaluate the students' abilities to select and apply multiplication strategies with fluency and efficiency. The focus of the lesson is decomposing numbers to multiply using the Distributive property and understanding and applying the Commutative property. Then, students will reinforce decomposing of factors while playing Decomposition of Factors. The lesson concludes with a real world application problem on an Exit Slip.

Type: Lesson Plan

Fall Fun and Games! (Exploring the Commutative Property of Multiplication):

In this lesson, students will build and manipulate a variety of arrays in the context of creating games for a Fall Festival. They will practice using the Commutative Property of Multiplication to find related multiplication facts.

Type: Lesson Plan

Amazing Arrays:

This is a hands-on lesson for introducing and practicing building arrays to create models that represent the distributive property of multiplication, and then using those arrays to draw models of the equations they represent.

Type: Lesson Plan

Lesson Study Resource Kit

Operations and Algebraic Thinking Lesson Study Resource Kit – Third Grade:

This lesson study resource kit can be used to guide and support teams of third grade teachers as they engage in lesson study focused on the academic standards in the Operations and Algebraic Thinking domain.

Type: Lesson Study Resource Kit

Original Student Tutorial

Monkeying Around with Multiplication: Commutative Property:

Learn strategies, like the commutative property, to help you become better at multiplying in this interactive tutorial.

Type: Original Student Tutorial

Teaching Ideas

Shamu Math-SeaWorld Classroom Activity:

In this activity, the students demonstrate that numbers can be used to describe various quantities and relationships between quantities. Students gain experience adding, subtracting, multiplying, and dividing - building their understanding of how numbers are put together and taken apart. Students connect what they know to symbolic representation using number sentences.

Type: Teaching Idea

A Square of Numbers (problem to solve using addition, subtraction, multiplication, division):

A problem for students to solve using students' understanding of the operations of addition, subtraction, multiplication, and division. The problem presents an opportunity for students to appreciate the value of approaching a solution in a systematic way using what they know about the structure of operations.

Type: Teaching Idea

Tutorials

Explanation of the distributive property of multiplication:

In this video tutorial from Khan Academy, explore the distributive property of multiplication: Why does it work? How does it work? Why would I put it to use?

Type: Tutorial

Commutative and Associative Properties of Multiplication:

In this video tutorial from Khan Academy, use arrays to explore the commutative and associative properties of multiplication.

Type: Tutorial

Commutative and Associative Properties of Addition and Multiplication:


This lesson reviews the commutative and associative properties as it applies to addition and multiplication. These properties are useful with mental math and with solving equations. This resource includes a video lesson, video examples and a short quiz.

Type: Tutorial

Unit/Lesson Sequence

Computation Through Literature :

This collection of 10 lessons uses children's literature to engage students in addition, subtraction, multiplication, and division. The lesson arrangement is flexible and adaptable for any scope and sequence.

Type: Unit/Lesson Sequence

MFAS Formative Assessments

Break Apart and Put Together:

Students are given two arrays, one representing the equation 7 x 9 = 63 and the other representing the equation (5 + 2) x 9 = 63, to see if they recognize a relationship between the two.

Does It Work for Division?:

Students are asked if the Commutative Property holds for division.

Meeting the Reading Goal:

Students are given two problems to solve, one represented by the equation 4 x 6 = 24 and the other by the equation 6 x 4 = 24, to see if they recognize the answer to the second problem based on the Commutative Property.

Using the Associative Property of Multiplication:

Students are asked to find the product of three numbers and are observed to see if they use the Associative Property to find the product more easily.

Original Student Tutorials Mathematics - Grades K-5

Monkeying Around with Multiplication: Commutative Property:

Learn strategies, like the commutative property, to help you become better at multiplying in this interactive tutorial.

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Original Student Tutorial

Monkeying Around with Multiplication: Commutative Property:

Learn strategies, like the commutative property, to help you become better at multiplying in this interactive tutorial.

Type: Original Student Tutorial

Tutorials

Explanation of the distributive property of multiplication:

In this video tutorial from Khan Academy, explore the distributive property of multiplication: Why does it work? How does it work? Why would I put it to use?

Type: Tutorial

Commutative and Associative Properties of Multiplication:

In this video tutorial from Khan Academy, use arrays to explore the commutative and associative properties of multiplication.

Type: Tutorial

Commutative and Associative Properties of Addition and Multiplication:


This lesson reviews the commutative and associative properties as it applies to addition and multiplication. These properties are useful with mental math and with solving equations. This resource includes a video lesson, video examples and a short quiz.

Type: Tutorial

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

Tutorials

Explanation of the distributive property of multiplication:

In this video tutorial from Khan Academy, explore the distributive property of multiplication: Why does it work? How does it work? Why would I put it to use?

Type: Tutorial

Commutative and Associative Properties of Multiplication:

In this video tutorial from Khan Academy, use arrays to explore the commutative and associative properties of multiplication.

Type: Tutorial

Commutative and Associative Properties of Addition and Multiplication:


This lesson reviews the commutative and associative properties as it applies to addition and multiplication. These properties are useful with mental math and with solving equations. This resource includes a video lesson, video examples and a short quiz.

Type: Tutorial