# Standard 1: Apply previous understanding of arithmetic expressions to algebraic expressions. Export Print
General Information
Number: MA.6.AR.1
Title: Apply previous understanding of arithmetic expressions to algebraic expressions.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Strand: Algebraic Reasoning

## Related Benchmarks

This cluster includes the following benchmarks.

## Related Access Points

This cluster includes the following access points.

## Access Points

MA.6.AR.1.AP.1
Write or select an algebraic expression that represents a real-world situation.
MA.6.AR.1.AP.2
Write or select an inequality that represents a real-world situation.
MA.6.AR.1.AP.3
Solve an expression using substitution with no more than two operations.
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 topic.

## 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

Substitution Resolution:

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

Type: Formative Assessment

Writing Real-World Expressions:

Students are asked to use variables to write expressions that represent quantities described in context.

Type: Formative Assessment

Gavin’s Pocket:

Students are asked to interpret the significance of a variable and its possible values when given a variable expression in a real-world context.

Type: Formative Assessment

Inventing X:

Students are asked to write and explain a real-world situation to accompany an algebraic expression.

Type: Formative Assessment

Parts of Expressions:

Students are asked to identify key parts of algebraic expressions.

Type: Formative Assessment

Cube House:

Students are asked to write a numerical expression using exponents.

Type: Formative Assessment

Exponent Priorities:

Students are asked to evaluate numerical expressions with exponents.

Type: Formative Assessment

Transportation Number Lines:

Students are given an inequality to graph and asked to list sample solutions.

Type: Formative Assessment

Rational Number Lines:

Students are given an inequality to graph and asked to select sample solutions.

Type: Formative Assessment

Students are given a context from which to write an inequality statement.

Type: Formative Assessment

Acres and Altitudes:

Students are given a context from which to write an inequality statement.

Type: Formative Assessment

Writing Expressions:

Students are asked to write expressions that record operations with numbers and variables.

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

Analyzing Polyhedra:

Students will construct several simple polyhedra, then count the number of faces, edges, and vertices. These data should suggest Euler's formula.

Type: Lesson Plan

Gummy vs. Gum (Number Pattern):

In this lesson from the Beacon Learning Center, students use gummy bears and sticks of gum to discover a number pattern and write an representation that describes it.

This lesson can be adapted for several grade levels and instead of writing an equation, students can write a "rule" or expression based on the pattern or relationship between number of pieces of gum and gummy bears.  Consider scaffolding this activity to meet your grade-level needs.

Type: Lesson Plan

## Original Student Tutorials

Order of Operations with Fractions:

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

Type: Original Student Tutorial

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

Theme Park Inequalities: Part 2:

Follow Jamal as he represents algebraic inequalities on a number line while visiting a theme park with his family in this interactive tutorial.

This is part 2 in a two-part series on inequalities. Click HERE to open part 1.

Type: Original Student Tutorial

Theme Park Inequalities: Part 1:

Follow Jamal as he translates theme park written descriptions into algebraic inequalities in this interactive tutorial.

Type: Original Student Tutorial

Algebraic Expressions Part 2: Multiplication and Division:

Help Oscar translate written real-world descriptions of multiplication and division into algebraic expressions in this interactive tutorial.

This is part 2 of 3. Click below to open the other tutorials in this series.

Type: Original Student Tutorial

Algebraic Expressions Part 1: Addition and Subtraction:

Follow Oscar as he writes algebraic expressions of addition and subtraction about his new puppy Scooter in this interactive tutorial.

Type: Original Student Tutorial

Balancing the Machine:

Use models to solve balance problems on a space station in this interactive, math and science tutorial.

Type: 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

MacCoder’s Farm Part 3: If Statements:

Explore computer coding on the farm by using relational operators and IF statements to evaluate 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

MacCoder’s Farm Part 2: Condition Statements:

Explore computer coding on the farm by using condition and IF statements in this interactive tutorial. You'll also get a chance to apply the order of operations as you using coding to solve problems.

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

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

## Perspectives Video: Expert

Improving Hurricane Scales:

Meteorologist, Michael Kozar, discusses the limitations to existing hurricane scales and how he is helping to develop an improved scale.

Type: Perspectives Video: Expert

## Perspectives Video: Professional/Enthusiast

Using Algebra to Program Robots and Microcontrollers:

There are 10 ways to use algebra to program a binary-counting circuit: fun and more fun.

Type: Perspectives Video: Professional/Enthusiast

## Perspectives Video: Teaching Idea

Programming Mathematics: Algebra, and Variables to control Open-source Hardware:

If you are having trouble understanding variables, this video might help you see the light.

Type: Perspectives Video: Teaching Idea

## Text Resources

Pythagoras Explained:

This informational text resource is intended to support reading in the content area. The text describes a method for predicting the win-loss record for baseball teams based on runs scored and runs allowed, using the "Pythagorean Expectation" formula invented by Bill James. The text goes on to show the relationship of the prediction formula to the Pythagorean theorem, pointing out a very cool application of the theorem to the world of sports.

Type: Text Resource

Kangaroos Have "Green" Farts:

This informational text resource is intended to support reading in the content area. Researchers in Australia have found kangaroos to produce more acetate in their flatulence than methane. Cows and goats produce methane-heavy flatulence twenty times more potent than carbon dioxide, adding to the greenhouse gases contributing to global warming. Scientists are trying to use this research on kangaroo farts to discover a way to alter the amount of greenhouse gases in animal flatulence worldwide.

Type: Text Resource

## 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

How to Write Basic Expressions with Variables:

Learn how to write basic algebraic expressions.

Type: Tutorial

How to Represent Real-World Situations with Inequalities:

Learn how to write inequalities to model real-world situations.

Type: Tutorial

How to Write Expressions with Variables:

Learn how to write simple algebraic expressions.

Type: Tutorial

How to Write Basic Algebraic Expressions from Word Problems:

Learn how to write basic expressions with variables to portray situations described in word problems.

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

What is a Variable?:

The focus here is understanding that a variable is just a symbol that can represent different values in an expression.

Type: Tutorial

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

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

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

## 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

## 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

## Student Resources

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

## Original Student Tutorials

Order of Operations with Fractions:

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

Type: Original Student Tutorial

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

Theme Park Inequalities: Part 2:

Follow Jamal as he represents algebraic inequalities on a number line while visiting a theme park with his family in this interactive tutorial.

This is part 2 in a two-part series on inequalities. Click HERE to open part 1.

Type: Original Student Tutorial

Theme Park Inequalities: Part 1:

Follow Jamal as he translates theme park written descriptions into algebraic inequalities in this interactive tutorial.

Type: Original Student Tutorial

Algebraic Expressions Part 2: Multiplication and Division:

Help Oscar translate written real-world descriptions of multiplication and division into algebraic expressions in this interactive tutorial.

This is part 2 of 3. Click below to open the other tutorials in this series.

Type: Original Student Tutorial

Algebraic Expressions Part 1: Addition and Subtraction:

Follow Oscar as he writes algebraic expressions of addition and subtraction about his new puppy Scooter in this interactive tutorial.

Type: Original Student Tutorial

Balancing the Machine:

Use models to solve balance problems on a space station in this interactive, math and science tutorial.

Type: 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

MacCoder’s Farm Part 3: If Statements:

Explore computer coding on the farm by using relational operators and IF statements to evaluate 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

MacCoder’s Farm Part 2: Condition Statements:

Explore computer coding on the farm by using condition and IF statements in this interactive tutorial. You'll also get a chance to apply the order of operations as you using coding to solve problems.

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

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

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

How to Write Basic Expressions with Variables:

Learn how to write basic algebraic expressions.

Type: Tutorial

How to Represent Real-World Situations with Inequalities:

Learn how to write inequalities to model real-world situations.

Type: Tutorial

How to Write Expressions with Variables:

Learn how to write simple algebraic expressions.

Type: Tutorial

How to Write Basic Algebraic Expressions from Word Problems:

Learn how to write basic expressions with variables to portray situations described in word problems.

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

What is a Variable?:

The focus here is understanding that a variable is just a symbol that can represent different values in an expression.

Type: Tutorial

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

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

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 topic.