MA.6.AR.1.3

Evaluate algebraic expressions using substitution and order of operations.

Examples

Evaluate the expression begin mathsize 12px style 2 a squared minus b over 5 end style, where a=-1 and b=15.

Clarifications

Clarification 1: Within this benchmark, the expectation is to perform all operations with integers.

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

General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 6
Strand: Algebraic Reasoning
Status: State Board Approved

Related Courses

This benchmark is part of these courses.
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
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.3: Solve an expression using substitution with no more than two operations.

Related Resources

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

Formative Assessments

Substitution Resolution:

Students are asked to evaluate formulas for given values of the variables.

Type: Formative Assessment

Exponent Priorities:

Students are asked to evaluate numerical expressions with exponents.

Type: Formative Assessment

Lesson Plans

Going The Distance:

This lesson provides a hands-on activity where students can apply solving one-step multiplication and division equations to a real-world problem. The lesson focuses on the relationship between distance, rate, and time. The students will also represent data on graphs and draw conclusions and make interpretations based on the graphs.

Type: Lesson Plan

Using Nets to Find the Surface Area of Pyramids:

In this lesson, students will explore and apply the use of nets to find the surface area of pyramids.

Type: 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 Tutorials

Order of Operations with Decimals:

Evaluate numerical expressions with decimals using the order of operations and properties of operations in this interactive tutorial.

Type: Original Student Tutorial

Order of Operations with Whole Numbers: Part 2:

Evaluate numerical expressions with whole numbers using the order of operations and properties of operations in this interactive tutorial. This is part 2 of a series on evaluating expressions with whole numbers.

Type: Original Student Tutorial

Order of Operations with Whole Numbers:

Evaluate numerical expressions with whole numbers using the order of operations and properties of operations in this interactive tutorial.

Type: Original Student Tutorial

Order of Operations with Integers:

Evaluate numerical expressions with integers using the order of operations and properties of operations in this interactive tutorial. 

Type: Original Student Tutorial

MacCoder’s Farm Part 1: Declare Variables:

Explore computer coding on the farm by declaring and initializing variables in this interactive tutorial. You'll also get a chance to practice your long division skills.

Type: Original Student Tutorial

Tutorials

How to Evaluate an Expression with Variables:

Learn how to evaluate an expression with variables using a technique called substitution.

Type: Tutorial

How to Evaluate Expressions with Two Variables:

This video demonstrates evaluating expressions with two variables.

Type: Tutorial

Thinking About the Changing Values of Variables and Expressions:

Explore how the value of an algebraic expression changes as the value of its variable changes. 

Type: Tutorial

How to Evaluate an Expression Using Substitution:

In this example, we have a formula for converting a Celsius temperature to Fahrenheit. 

Type: Tutorial

Introduction to Order of Operations:

Students will evaluate expressions using the order of operations.

Type: Tutorial

Order of Operations: PEMDAS:

Work through a 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

Examples of evaluating variable expressions:

Examples of evaluating variable expressions

Type: Tutorial

How to evaluate an expression using substitution:

In this example we have a formula for converting Celsius temperature to Fahrenheit. Let's substitute the variable with a value (Celsius temp) to get the degrees in Fahrenheit. Great problem to practice with us!

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

Virtual Manipulative

Order of Operations Quiz:

In this activity, students practice solving algebraic expressions using order of operations. The applet records their score so the student can track their progress. This activity allows students to practice applying the order of operations when solving problems. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Virtual Manipulative

MFAS Formative Assessments

Exponent Priorities:

Students are asked to evaluate numerical expressions with exponents.

Substitution Resolution:

Students are asked to evaluate formulas for given values of the variables.

Original Student Tutorials Mathematics - Grades 6-8

Order of Operations with Decimals:

Evaluate numerical expressions with decimals using the order of operations and properties of operations in this interactive tutorial.

Order of Operations with Integers:

Evaluate numerical expressions with integers using the order of operations and properties of operations in this interactive tutorial. 

Order of Operations with Whole Numbers:

Evaluate numerical expressions with whole numbers using the order of operations and properties of operations in this interactive tutorial.

Order of Operations with Whole Numbers: Part 2:

Evaluate numerical expressions with whole numbers using the order of operations and properties of operations in this interactive tutorial. This is part 2 of a series on evaluating expressions with whole numbers.

Computer Science Original Student Tutorials

MacCoder’s Farm Part 1: Declare Variables:

Explore computer coding on the farm by declaring and initializing variables in this interactive tutorial. You'll also get a chance to practice your long division skills.

Student Resources

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

Original Student Tutorials

Order of Operations with Decimals:

Evaluate numerical expressions with decimals using the order of operations and properties of operations in this interactive tutorial.

Type: Original Student Tutorial

Order of Operations with Whole Numbers: Part 2:

Evaluate numerical expressions with whole numbers using the order of operations and properties of operations in this interactive tutorial. This is part 2 of a series on evaluating expressions with whole numbers.

Type: Original Student Tutorial

Order of Operations with Whole Numbers:

Evaluate numerical expressions with whole numbers using the order of operations and properties of operations in this interactive tutorial.

Type: Original Student Tutorial

Order of Operations with Integers:

Evaluate numerical expressions with integers using the order of operations and properties of operations in this interactive tutorial. 

Type: Original Student Tutorial

MacCoder’s Farm Part 1: Declare Variables:

Explore computer coding on the farm by declaring and initializing variables in this interactive tutorial. You'll also get a chance to practice your long division skills.

Type: Original Student Tutorial

Tutorials

How to Evaluate an Expression with Variables:

Learn how to evaluate an expression with variables using a technique called substitution.

Type: Tutorial

How to Evaluate Expressions with Two Variables:

This video demonstrates evaluating expressions with two variables.

Type: Tutorial

Thinking About the Changing Values of Variables and Expressions:

Explore how the value of an algebraic expression changes as the value of its variable changes. 

Type: Tutorial

How to Evaluate an Expression Using Substitution:

In this example, we have a formula for converting a Celsius temperature to Fahrenheit. 

Type: Tutorial

Introduction to Order of Operations:

Students will evaluate expressions using the order of operations.

Type: Tutorial

Order of Operations: PEMDAS:

Work through a 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

How to evaluate an expression using substitution:

In this example we have a formula for converting Celsius temperature to Fahrenheit. Let's substitute the variable with a value (Celsius temp) to get the degrees in Fahrenheit. Great problem to practice with us!

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

Virtual Manipulative

Order of Operations Quiz:

In this activity, students practice solving algebraic expressions using order of operations. The applet records their score so the student can track their progress. This activity allows students to practice applying the order of operations when solving problems. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Virtual Manipulative

Parent Resources

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