Standard 1 : Apply previous understanding of arithmetic expressions to algebraic expressions.



This document was generated on CPALMS - www.cpalms.org

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.)
Grade: 6
Strand: Algebraic Reasoning

Related Benchmarks

This cluster includes the following benchmarks
Code Description
MA.6.AR.1.1: Given a mathematical or real-world context, translate written descriptions into algebraic expressions and translate algebraic expressions into written descriptions.
MA.6.AR.1.2:

Translate a real-world written description into an algebraic inequality in the form of x > a, x < a, x ≥ a or x ≤ a. Represent the inequality on a number line.

Clarifications:
Clarification 1: Variables may be on the left or right side of the inequality symbol.
MA.6.AR.1.3: Evaluate algebraic expressions using substitution and order of operations.
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).

MA.6.AR.1.4: Apply the properties of operations to generate equivalent algebraic expressions with integer coefficients.
Clarifications:
Clarification 1: Properties include associative, commutative and distributive.

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



Related Access Points

This cluster includes the following access points.

Access Points

Access Point Number Access Point Title
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.

Original Student Tutorials

Name Description
Order of Operations with Fractions:

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

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 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.

Order of Operations with Integers:

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

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. 

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.

Balancing the Machine:

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

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.

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.

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.

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.

Theme Park Inequalities: Part 1:

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

Formative Assessments

Name Description
Property Combinations:

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

Generating Equivalent Expressions:

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

Equivalent Expressions:

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

Equivalent Exponents:

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

Equal Sides, Equivalent Expressions:

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

Identifying Equivalent Expressions:

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

Associative and Commutative Expressions:

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

Substitution Resolution:

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

Writing Real-World Expressions:

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

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.

Inventing X:

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

Parts of Expressions:

Students are asked to identify key parts of algebraic expressions.

Cube House:

Students are asked to write a numerical expression using exponents.

Exponent Priorities:

Students are asked to evaluate numerical expressions with exponents.

Transportation Number Lines:

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

Rational Number Lines:

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

Roadway Inequalities:

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

Acres and Altitudes:

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

Writing Expressions:

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

Lesson Plans

Name Description
Order Matters:

Students will analyze a Scratch program and compare its computerized algorithm to the mathematical order of operations, in this lesson plan.

Power of a Right Triangle: Day 1 Proving Pythagoras:

In this first of three lessons on the Pythagorean Theorem students work to prove the Pythagorean theorem and verify that the theorem works.

Expressions and Art:

Students will design a color-by-expression picture in order to practice evaluating algebraic expressions including substitution and order of operations.

Dissecting an Expression:

This lesson will focus on how to write, translate, and interpret an algebraic expression. Students will be able to identify the parts of an algebraic expression and the meaning of those parts.

Are You Invited to the Party?:

Students will write and graph inequalities that represent real-world constraints involving whole numbers, negative numbers, and/or rational numbers. The distinction between continuous and discrete variables is made.

Introducing Inequalities:

Students are introduced to simple inequalities and their graphs as they write inequalities to represent real-world constraints.

Equivalent Expressions with Candies:

In this lesson, students use small round candies and equation mats to explore the equivalency of pairs of expressions. Then they show pairs of expressions are equivalent using properties of operations. For those that are not equivalent, they provide a counterexample.

It's All About Balance!:

Students will use a balance scale graphic organizer to solve for the unknown (variable) in addition and subtraction equations with one variable.

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.

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.

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.

The "Power" of Exponents:

The students will use square tiles or cubes to explore the meaning of "squared" and "cubed" numbers. They will model squared and cubed numbers to build a strong foundation for working with exponents. The students will learn the connections between area and volume models and the related positive exponents. This is an introductory lesson.

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.

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).

It's Hip 2b^2 eXponent^s:

Meaning of Exponents... Students will write and simplify numerical and algebraic expressions with natural number exponents. Bases are limited to positive integers.

Sticks and Stones May Break My Bones:

In this Model Eliciting Activity, MEA, "Sticks and Stones May Break My Bones", teams of students work as forensic anthropologists and use equations to determine the height and gender of persons to whom a series of newly discovered bones may belong.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Can You Find the Relationship?:

In this lesson students will first define in their own words what the greatest common factor (GCF) and least common multiple (LCM) mean. They will take this understanding and apply it to solving GCF and LCM word problems. Students will then illustrate their understanding by creating posters based on their word problems. There are examples of different types of methods, online games, a rubric, and a power point to summarize this two-day lesson.

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.

Expressions, Phrases and Word Problems, Oh My!:

This lesson focuses on using appropriate mathematical language when reading or writing expressions, with students applying this knowledge to translate written phrases into algebraic expressions and vice versa. Students will analyze word problems for key words and write the representative expressions.

Digesting the Distributive Property:

This lesson will show the student how to use the distributive property to express a sum of two whole numbers 1-100.

You Can Never Have Too Many Shoes!:

This lesson teaches Least Common Multiples.

Finding the Greatest Crush Factor:

This lesson uses a real-life approach to exploring the use of Greatest Common Factors (GCF). The students will utilize math practice standards as they analyze math solutions and explain their own solutions.

Factoring out the Greatest:

This lesson teaches students how to find the GCF and LCM by factoring. This is a different method than is normally seen in textbooks. This method easily leads to solving GCF word problems and using the distributive property to express a sum of two whole numbers.

Power of a Right Triangle: Day 1 Proving Pythagoras:

In this first of three lessons on the Pythagorean Theorem students work to prove the Pythagorean theorem and verify that the theorem works.

Decoding Word Phrases-Translating verbal phrases to variable expressions:

This lesson is designed to help students decode word phrases and then translate them from word form into numerical form. It provides a resource, in the form of a foldable, that can be kept all year and used anytime the students need to decode word phrases.

Analyzing Polyhedra:

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

Let's Translate!!:

Students will translate verbal phrases into algebraic expressions. Students are given practice in writing expressions that record operations with numbers and variables. Special attention is given to writing operations in the correct order. Class work and homework worksheets are provided with answer keys for each.

The Distributive Property:

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

Writing Inequalities to Represent Situations:

Students will learn how to write inequalities through guided practice, cooperative learning, and comparing the solutions of inequalities to those of equations.

Perspectives Video: Expert

Name Description
Improving Hurricane Scales:

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

Download the CPALMS Perspectives video student note taking guide.

Perspectives Video: Professional/Enthusiast

Name Description
Using Algebra to Program Robots and Microcontrollers:

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

Download the CPALMS Perspectives video student note taking guide.

Perspectives Video: Teaching Ideas

Name Description
Adding Integers:

Unlock an effective teaching strategy for using patterns to help students make generalizations when adding integers in this Teacher Perspectives video for educators.

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.

Download the CPALMS Perspectives video student note taking guide.

Problem-Solving Tasks

Name Description
Triangular Tables:

Students are asked to use a diagram or table to write an algebraic expression and use the expression to solve problems.

Rectangle Perimeter 1:

This tasks gives a verbal description for computing the perimeter of a rectangle and asks the students to find an expression for this perimeter. They then have to use the expression to evaluate the perimeter for specific values of the two variables.

Rectangle Perimeter 2:

Students are asked to determine if given expressions are equivalent.

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.

Distance to School:

This task asks students to find equivalent expressions by visualizing a familiar activity involving distance. The given solution shows some possible equivalent expressions, but there are many variations possible.

Equivalent Expressions:

Students are asked to use properties of operations to match expressions that are equivalent and to write equivalent expressions for any expressions that do not have a match.

Firefighter Allocation:

In this task students are asked to write an equation to solve a real-world problem.

Text Resources

Name Description
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.

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.

Tutorials

Name Description
Applying Arithmetic Properties with Negative Numbers:

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

How to Write Basic Expressions with Variables:

Learn how to write basic algebraic expressions.

How to Represent Real-World Situations with Inequalities:

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

How to Write Expressions with Variables:

Learn how to write simple algebraic expressions.

How to Write Basic Algebraic Expressions from Word Problems:

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

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.

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.

How to Use the Distributive Property with Variables:

Learn how to apply the distributive property to algebraic expressions.

What is a Variable?:

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

How to Evaluate an Expression with Variables:

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

How to Evaluate Expressions with Two Variables:

This video demonstrates evaluating expressions with two variables.

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. 

How to Evaluate an Expression Using Substitution:

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

How to Simplify an Expression by Combining Like Terms:

Students will simplify an expression by combining like terms.  

How to Combine Like Terms:

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

Combining Like Terms Introduction:

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

 

Introduction to Order of Operations:

Students will evaluate expressions using the order of operations.

Order of Operations: PEMDAS:

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

Order of Operations :

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

Order of Operations :

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

 

Examples of evaluating variable expressions:

Examples of evaluating variable expressions

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!

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.

Video/Audio/Animation

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

Learn how to apply the distributive property to factor numerical expressions.

Virtual Manipulative

Name Description
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.



Student Resources

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

Original Student Tutorials

Title Description
Order of Operations with Fractions:

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

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 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.

Order of Operations with Integers:

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

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. 

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.

Balancing the Machine:

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

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.

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.

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.

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.

Theme Park Inequalities: Part 1:

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

Problem-Solving Tasks

Title Description
Triangular Tables:

Students are asked to use a diagram or table to write an algebraic expression and use the expression to solve problems.

Rectangle Perimeter 1:

This tasks gives a verbal description for computing the perimeter of a rectangle and asks the students to find an expression for this perimeter. They then have to use the expression to evaluate the perimeter for specific values of the two variables.

Rectangle Perimeter 2:

Students are asked to determine if given expressions are equivalent.

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.

Distance to School:

This task asks students to find equivalent expressions by visualizing a familiar activity involving distance. The given solution shows some possible equivalent expressions, but there are many variations possible.

Equivalent Expressions:

Students are asked to use properties of operations to match expressions that are equivalent and to write equivalent expressions for any expressions that do not have a match.

Firefighter Allocation:

In this task students are asked to write an equation to solve a real-world problem.

Tutorials

Title Description
Applying Arithmetic Properties with Negative Numbers:

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

How to Write Basic Expressions with Variables:

Learn how to write basic algebraic expressions.

How to Represent Real-World Situations with Inequalities:

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

How to Write Expressions with Variables:

Learn how to write simple algebraic expressions.

How to Write Basic Algebraic Expressions from Word Problems:

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

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.

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.

How to Use the Distributive Property with Variables:

Learn how to apply the distributive property to algebraic expressions.

What is a Variable?:

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

How to Evaluate an Expression with Variables:

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

How to Evaluate Expressions with Two Variables:

This video demonstrates evaluating expressions with two variables.

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. 

How to Evaluate an Expression Using Substitution:

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

How to Simplify an Expression by Combining Like Terms:

Students will simplify an expression by combining like terms.  

How to Combine Like Terms:

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

Combining Like Terms Introduction:

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

 

Introduction to Order of Operations:

Students will evaluate expressions using the order of operations.

Order of Operations: PEMDAS:

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

Order of Operations :

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

Order of Operations :

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

 

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!

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.

Virtual Manipulative

Title Description
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.



Parent Resources

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

Problem-Solving Tasks

Title Description
Triangular Tables:

Students are asked to use a diagram or table to write an algebraic expression and use the expression to solve problems.

Rectangle Perimeter 1:

This tasks gives a verbal description for computing the perimeter of a rectangle and asks the students to find an expression for this perimeter. They then have to use the expression to evaluate the perimeter for specific values of the two variables.

Rectangle Perimeter 2:

Students are asked to determine if given expressions are equivalent.

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.

Distance to School:

This task asks students to find equivalent expressions by visualizing a familiar activity involving distance. The given solution shows some possible equivalent expressions, but there are many variations possible.

Equivalent Expressions:

Students are asked to use properties of operations to match expressions that are equivalent and to write equivalent expressions for any expressions that do not have a match.

Firefighter Allocation:

In this task students are asked to write an equation to solve a real-world problem.