# MA.6.AR.1.4

Apply the properties of operations to generate equivalent algebraic expressions with integer coefficients.

### Examples

Example: The expression 5(3x+1) can be rewritten equivalently as 15x+5.

Example: If the expression 2x+3x represents the profit the cheerleading team can make when selling the same number of cupcakes, sold for \$2 each, and brownies, sold for \$3 each. The expression 5x can express the total profit.

### Clarifications

Clarification 1: Properties include associative, commutative and distributive.

Clarification 2: Refer to Properties of Operations, Equality and Inequality (Appendix D).

General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Algebraic Reasoning
Status: State Board Approved

## Related Courses

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

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.6.AR.1.AP.4: Use tools or models to combine like terms in an expression with no more than four operations.

## Related Resources

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

## Formative Assessments

Property Combinations:

Students are asked to identify expressions equivalent to a given expression and justify their responses.

Type: Formative Assessment

Generating Equivalent Expressions:

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

Type: Formative Assessment

Equivalent Expressions:

Students are asked to determine if pairs of expressions are equivalent and to justify their responses.

Type: Formative Assessment

Equivalent Exponents:

Students are asked to identify expressions equivalent to a given exponential expression and justify their responses.

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

Identifying Equivalent Expressions:

Students are asked to identify expressions equivalent to a given expression and justify their responses.

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 Plan

Have You Met Your Match?-Understanding Equivalent Expressions :

In this lesson, students will use the properties of operations to generate and identify equivalent algebraic expressions. Students will apply their prior knowledge of the distributive property and combining like terms to create equivalent algebraic expressions. The hands-on memory "match" game will engage students and support student understanding of algebraic thinking.

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

## 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

How to Simplify an Expression by Combining Like Terms:

Students will simplify an expression by combining like terms.

Type: Tutorial

How to Combine Like Terms:

This tutorial is an explanation on how to combine like terms in algebra.

Type: Tutorial

Combining Like Terms Introduction:

This is an introduction to combining like terms in this tutorial.

Type: Tutorial

Why aren't we using the multiplication sign?:

Great question. In algebra, we do indeed avoid using the multiplication sign. We'll explain it for you here.

Type: Tutorial

## 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.

Type: Video/Audio/Animation

## 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.

Equivalent Exponents:

Students are asked to identify expressions equivalent to a given exponential expression and justify their responses.

Equivalent Expressions:

Students are asked to determine if pairs of expressions are equivalent and to justify their responses.

Generating Equivalent Expressions:

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

Identifying Equivalent Expressions:

Students are asked to identify expressions equivalent to a given expression and justify their responses.

Property Combinations:

Students are asked to identify expressions equivalent to a given expression and justify their responses.

## 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

## 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

How to Simplify an Expression by Combining Like Terms:

Students will simplify an expression by combining like terms.

Type: Tutorial

How to Combine Like Terms:

This tutorial is an explanation on how to combine like terms in algebra.

Type: Tutorial

Combining Like Terms Introduction:

This is an introduction to combining like terms in this tutorial.

Type: Tutorial

Why aren't we using the multiplication sign?:

Great question. In algebra, we do indeed avoid using the multiplication sign. We'll explain it for you here.

Type: Tutorial

## Parent Resources

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