# MAFS.6.EE.1.3

Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

### Clarifications

Examples of Opportunities for In-Depth Focus

By applying properties of operations to generate equivalent expressions, students use properties of operations that they are familiar with from previous grades’ work with numbers — generalizing arithmetic in the process.
General Information
Subject Area: Mathematics
Domain-Subdomain: Expressions & Equations
Cluster: Level 1: Recall
Cluster: Apply and extend previous understandings of arithmetic to algebraic expressions. (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 of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes
Test Item Specifications

• Assessment Limits :
Positive rational numbers, values may include exponents. Variables must be included in the expression. For items using distribution, coefficients may be fractions before distribution but must be integer values after simplification. Only positive rational numbers may be distributed.
• Calculator :

No

• Context :

Allowable

Sample Test Items (2)
• Test Item #: Sample Item 1
• Question:

Alyssa attends football games at her school. At each football game, she buys a bottle of water for \$0.75 and a candy bar for \$0.90.

Select all the expressions that represent the amount of money, in dollars, Alyssa spends after attending 6 football games.

• Difficulty: N/A
• Type: MS: Multiselect

• Test Item #: Sample Item 2
• Question: Tina sells lampshades for \$7 each and paper lanterns for \$4 each at a one-day craft fair. She sells k lampshades and (k + 4) paper lanterns. The expression 7k + 4(k + 4) represents Tina’s total sales.

Select all the equivalent expressions for Tina's total sales at the fair.

• Difficulty: N/A
• Type: MS: Multiselect

## Related Courses

This benchmark is part of these courses.
1205010: M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1205020: M/J Grade 6 Accelerated Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022 (current), 2022 and beyond)
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
7812015: Access M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 and beyond)
7912110: Fundamental Explorations in Mathematics 1 (Specifically in versions: 2013 - 2015, 2015 - 2017 (course terminated))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.6.EE.1.AP.3a: Use properties to produce equivalent expressions.

## Related Resources

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

## Assessments

Sample 4 - Sixth Grade Math State Interim Assessment:

This is a State Interim Assessment for sixth grade.

Type: Assessment

Sample 2 - Sixth Grade Math State Interim Assessment:

This is a State Interim Assessment for sixth grade.

Type: Assessment

## Formative Assessments

Generating Equivalent Expressions:

Students are asked to write equivalent expressions using the Distributive Property.

Type: Formative Assessment

Equal Sides, Equivalent Expressions:

Students are asked to generate and justify an expression equivalent to a given one using the properties of operations.

Type: Formative Assessment

Associative and Commutative Expressions:

Students are asked to write expressions equivalent to a given one by using the Associative and Commutative Properties.

Type: Formative Assessment

## Lesson Plans

Extending the Distributive Property:

In this lesson, students will build upon their arithmetic experiences with the distributive property to equate algebraic expressions through a series of questions related to real world situations and the use of manipulatives. Activities include the use of Algebra Tiles for moving the concrete learner to the abstract level and the use of matching cards.
This is an introductory lesson that only includes producing equivalent expressions such as 3(2 + x) = 6 + 3x.

Type: Lesson Plan

Collectively Collecting:

In this lesson, students will examine and experience collecting like terms through an analogy to real world situations and the use of manipulatives. Activities include the use of Algebra Tiles for transitioning a concrete experience to the abstract level and a card-matching activity.

Type: Lesson Plan

Interpreting Algebraic Expressions:

This lesson unit is intended to help you assess how well students are able to translate between words, symbols, tables, and area representations of algebraic expressions. It will help you to identify and support students who have difficulty in recognizing the order of algebraic operations, recognizing equivalent expressions and understanding the distributive laws of multiplication and division over addition (expansion of parentheses).

Type: Lesson Plan

Have You Met Your Match?-Understanding Equivalent Expressions Using the Distributive Property:

In this lesson, students will use the properties of operations to generate and identify equivalent expressions. Students will apply their knowledge of the distributive property to an expression to produce equivalent expressions. The guided inquiry and hands-on memory "match" game will engage students and support student understanding of algebraic thinking.

Type: Lesson Plan

The Distributive Property:

Introductory lesson on the distributive property using word problems as context for area models.

Type: Lesson Plan

## Original Student Tutorial

MacCoder's Farm Part 4: Repeat Loops:

Explore computer coding on the farm by using IF statements and repeat loops to evaluate mathematical expressions. In this interactive tutorial, you'll also solve problems involving inequalities.

Click below to check out the other tutorials in the series.

Type: Original Student Tutorial

Rectangle Perimeter 3:

The purpose of this task is to ask students to write expressions and to consider what it means for two expressions to be equivalent.

Watch out for Parentheses:

This problem asks the student to evaluate three numerical expressions that contain the same integers yet have differing results due to placement of parentheses.

Anna in D.C.:

The purpose of this task is to give students an opportunity to solve a challenging multistep percentage problem that can be approached in several different ways. Students are asked to find the cost of a meal before tax and tip when given the total cost of the meal. The task can illustrate multiple standards depending on the prior knowledge of the students and the approach used to solve the problem.

## Student Center Activity

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

## Tutorials

Applying Arithmetic Properties with Negative Numbers:

In this video, you will practice using arithmetic properties with integers to determine if expressions are equivalent.

Type: Tutorial

The Distributive Law of Multiplication over Addition:

Learn how to apply the distributive law of multiplication over addition and why it works. This is sometimes just called the distributive law or the distributive property.

Type: Tutorial

The Distributive Law of Multiplication over Subtraction:

Learn how to apply the distributive property of multiplication over subtraction. This is sometimes just called the distributive property or distributive law.

Type: Tutorial

How to Use the Distributive Property with Variables:

Learn how to apply the distributive property to algebraic expressions.

Type: Tutorial

Introduction to order of operations:

Students will evaluate expressions using the order of operations.

Type: Tutorial

Order of operations: PEMDAS:

Work through another challenging order of operations example with only positive numbers.

Type: Tutorial

Order of Operations :

Work through a challenging order of operations example with only positive numbers.

Type: Tutorial

Order of Operations :

This video will show how to evaluate expressions with exponents using the order of operations.

Type: Tutorial

The Distributive Property and Mental Math:

The distributive property states that the terms of addition or subtraction statements within parentheses may be separately multiplied by a value outside the parentheses. In this tutorial, students will learn the distributive property, which is very helpful with mental math calculations and solving equations.

Type: Tutorial

Pre-Algebra - Associative & Distributive Properties of Multiplication:

Take a look at the logic behind the associative and distributive properties of multiplication.

Type: Tutorial

Pre-Algebra - Commutative & Associative Properties of Addition:

A look behind the fundamental properties of the most basic arithmetic operation, addition

Type: Tutorial

Pre-Algebra - Commutative Property of Multiplication:

The commutative property is common to the operations of both addition and multiplication and is an important property of many mathematical systems.

Type: Tutorial

## Unit/Lesson Sequence

Using the Laws of Arithmetic:

This lesson unit helps teachers assess how students perform arithmetic operations, write and evaluate numerical expression s from diagrammatic representations, apply the distributive and commutative properties, and find areas of compound rectangles. The time for the lesson is broken into a 15 minute pre-lesson task, an 80 minute lesson (or two 40 minute lessons), and a 15 minute follow up lesson or homework. Individual students will need a copy of the two tasks, a mini-whiteboard, a pen, and an eraser. Each small group will need cut-up copies of the card sets, a large sheet of poster-sized paper, and a glue stick.

Type: Unit/Lesson Sequence

## Video/Audio/Animation

How to Use the Distributive Property to Factor Out the Greatest Common Factor:

Learn how to apply the distributive property to factor numerical expressions (no variables).

Type: Video/Audio/Animation

## Virtual Manipulative

Math Match - Concepts Review Game:

This interactive game allows students to review math concepts, including shapes, shape names, addition, multiplication, negative numbers, and equivalent expressions.

Type: Virtual Manipulative

## MFAS Formative Assessments

Associative and Commutative Expressions:

Students are asked to write expressions equivalent to a given one by using the Associative and Commutative Properties.

Equal Sides, Equivalent Expressions:

Students are asked to generate and justify an expression equivalent to a given one using the properties of operations.

Generating Equivalent Expressions:

Students are asked to write equivalent expressions using the Distributive Property.

## Computer Science Original Student Tutorials

MacCoder's Farm Part 4: Repeat Loops:

Explore computer coding on the farm by using IF statements and repeat loops to evaluate mathematical expressions. In this interactive tutorial, you'll also solve problems involving inequalities.

Click below to check out the other tutorials in the series.

## Student Resources

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

## Original Student Tutorial

MacCoder's Farm Part 4: Repeat Loops:

Explore computer coding on the farm by using IF statements and repeat loops to evaluate mathematical expressions. In this interactive tutorial, you'll also solve problems involving inequalities.

Click below to check out the other tutorials in the series.

Type: Original Student Tutorial

Rectangle Perimeter 3:

The purpose of this task is to ask students to write expressions and to consider what it means for two expressions to be equivalent.

Anna in D.C.:

The purpose of this task is to give students an opportunity to solve a challenging multistep percentage problem that can be approached in several different ways. Students are asked to find the cost of a meal before tax and tip when given the total cost of the meal. The task can illustrate multiple standards depending on the prior knowledge of the students and the approach used to solve the problem.

## Student Center Activity

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

## Tutorials

Applying Arithmetic Properties with Negative Numbers:

In this video, you will practice using arithmetic properties with integers to determine if expressions are equivalent.

Type: Tutorial

The Distributive Law of Multiplication over Addition:

Learn how to apply the distributive law of multiplication over addition and why it works. This is sometimes just called the distributive law or the distributive property.

Type: Tutorial

The Distributive Law of Multiplication over Subtraction:

Learn how to apply the distributive property of multiplication over subtraction. This is sometimes just called the distributive property or distributive law.

Type: Tutorial

How to Use the Distributive Property with Variables:

Learn how to apply the distributive property to algebraic expressions.

Type: Tutorial

Introduction to order of operations:

Students will evaluate expressions using the order of operations.

Type: Tutorial

Order of operations: PEMDAS:

Work through another challenging order of operations example with only positive numbers.

Type: Tutorial

Order of Operations :

Work through a challenging order of operations example with only positive numbers.

Type: Tutorial

Order of Operations :

This video will show how to evaluate expressions with exponents using the order of operations.

Type: Tutorial

The Distributive Property and Mental Math:

The distributive property states that the terms of addition or subtraction statements within parentheses may be separately multiplied by a value outside the parentheses. In this tutorial, students will learn the distributive property, which is very helpful with mental math calculations and solving equations.

Type: Tutorial

Pre-Algebra - Associative & Distributive Properties of Multiplication:

Take a look at the logic behind the associative and distributive properties of multiplication.

Type: Tutorial

Pre-Algebra - Commutative & Associative Properties of Addition:

A look behind the fundamental properties of the most basic arithmetic operation, addition

Type: Tutorial

Pre-Algebra - Commutative Property of Multiplication:

The commutative property is common to the operations of both addition and multiplication and is an important property of many mathematical systems.

Type: Tutorial

## Parent Resources

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

Rectangle Perimeter 3:

The purpose of this task is to ask students to write expressions and to consider what it means for two expressions to be equivalent.

Anna in D.C.:

The purpose of this task is to give students an opportunity to solve a challenging multistep percentage problem that can be approached in several different ways. Students are asked to find the cost of a meal before tax and tip when given the total cost of the meal. The task can illustrate multiple standards depending on the prior knowledge of the students and the approach used to solve the problem.