Standard 2: Demonstrate an understanding of equality, the order of operations and equivalent numerical expressions.

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General Information
Number: MA.5.AR.2
Title: Demonstrate an understanding of equality, the order of operations and equivalent numerical expressions.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Grade: 5
Strand: Algebraic Reasoning

Related Benchmarks

This cluster includes the following benchmarks.

Related Access Points

This cluster includes the following access points.

Access Points

MA.5.AR.2.AP.1
Translate mathematical descriptions (e.g., five plus two; the product of three and four) into numerical expressions with two terms.
MA.5.AR.2.AP.2
Evaluate an expression containing three terms and one set of parentheses.
MA.5.AR.2.AP.3
Determine whether an equation (with no more than four terms and up to one set of parentheses) involving any of the four operations with whole numbers is true or false. Limit addition and subtraction to within 100 and limit multiplication and division to the products of two single-digit whole numbers and their related division facts.
MA.5.AR.2.AP.4
Given a mathematical or real-world context, generate an equation involving any of the four operations to determine the unknown sum, difference, product or quotient. Sums may not exceed 100 and their related subtraction facts. Multiplication and division may not exceed two digit by one digit.

Related Resources

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

Formative Assessments

Write the Expression:

Students are presented with a verbal description of a numerical expression and are asked to write the expression and then compare it to a similar expression.

Type: Formative Assessment

Brayden’s Video Game:

Students are asked to write an expression requiring more than one operation and the use of parentheses to model a word problem.

Type: Formative Assessment

Evaluating Expressions:

Students are asked to evaluate two similar expressions and explain why the answers are different.

Type: Formative Assessment

More Expressions:

Students are asked to insert parentheses into an expression in two different ways, evaluate each way, and explain why the answers are different.

Type: Formative Assessment

With and Without Parentheses:

Students consider two different yet similar equations and determine if they are true.

Type: Formative Assessment

Place The Parentheses:

Students are given an equation and asked to place parentheses within the equation to make the equation true.

Type: Formative Assessment

How Much Greater Is The Product?:

Students are asked to model an expression that is a multiple of a sum and to compare the expression to the sum.

Type: Formative Assessment

Comparing Products:

Students are asked to analyze and compare two related products.

Type: Formative Assessment

Lesson Plans

Gimme Two Steps!:

In this lesson, students will create representations for different multi-step word problems. One of these representations will be an expression with a variable.

Type: Lesson Plan

Please Excuse My Dear Aunt Sally:

The students will learn and use the order of operations. In groups, the students will work together to discover the importance of following step-by-step instructions and apply that knowledge in solving algebraic equations by correctly using the order of operations. Students should accurately use the mathematical steps of the PEMDAS model to solve mathematical expressions.

Type: Lesson Plan

Field Trip Fundraiser:

This 5th grade MEA asks students to work as a team to figure out which product would be the best choice for their fundraiser for their field trip. They will compare vendors' products and rank the vendors according to which would be the best option for their school.

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.

Type: Lesson Plan

“Express Yourself!” with Math Story Chains:

Students work in small groups to write math story chains (multi-step real world problems) and write expressions or equations for their story chains.

Type: Lesson Plan

Original Student Tutorials

Bee A Coder Part 4: Repeat Loops:

Learn how to use repeat loops in this interactive tutorial. Repeat loops iterate though a list of instructions based on a desired number of times. Combined with variables, condition statements, if statements, and repeat loops we practice using order of operations to code.

This is part 1 of a 4-part series. Click below to check out the other tutorials in the series.

Type: Original Student Tutorial

Bee A Coder Part 3: If Statements:

Learn how to perform instructions using an if statement and explore relational operators (less than, greater than, equal and not equal to) and how they are used to compare to values in this interactive tutorial.

Type: Original Student Tutorial

Bee A Coder Part 2: Condition Statements:

Construct efficient lines of code using condition- and if-statements to solve equations as you complete this interactive tutorial. You'll also review the order of operations in expressions.

This is part 2 of a 4-part series on coding. Click below to open the other tutorials in the series.

Type: Original Student Tutorial

Expressions: Not Just for Faces:

Learn how to write mathematical expressions while making faces in this interactive tutorial!

Type: Original Student Tutorial

The Expression Debate:

Learn to evaluate expressions that have all four operations (multiplication, division, addition, and subtraction) and parentheses as you settle debates in this interactive tutorial.

Type: Original Student Tutorial

Perspectives Video: Teaching Idea

Deciphering Cryptic Operations through Mathematical Reasoning:

Sideways or wayside, math word problems can be a ton of fun, no matter how you look at them.

Type: Perspectives Video: Teaching Idea

Problem-Solving Tasks

Video Game Scores:

This task asks students to exercise both of these complementary skills, writing an expression in part (a) and interpreting a given expression in (b). The numbers given in the problem are deliberately large and "ugly" to discourage students from calculating Eric's and Leila's scores. The focus of this problem is not on numerical answers, but instead on building and interpreting expressions that could be entered in a calculator or communicated to another student unfamiliar with the context.

Type: Problem-Solving Task

Seeing is Believing:

The purpose of this task is to help students see that 4×(9+2) is four times as big as (9+2). Though this task may seem very simple, it provides students and teachers with a very useful visual for interpreting an expression without evaluating it because they can see for themselves that 4×(9+2) is four times as big as (9+2).

Type: Problem-Solving Task

Comparing Products:

The purpose of this task is to generate a classroom discussion that helps students synthesize what they have learned about multiplication in previous grades. It builds on applying properties of operations as strategies to multiply and divide and interpreting a multiplication equation as a comparison.

Type: Problem-Solving Task

Bowling for Numbers:

The purpose of this game is to help students think flexibly about numbers and operations and to record multiple operations using proper notation. Students eager to knock down all of the pins quickly develop patterns in their expressions. They may re-use parts of an expression, perhaps changing just the final operation.

Type: Problem-Solving Task

Words to Expressions 1:

This problem allows student to see words that can describe an expression although the solution requires nested parentheses.  Additionally , the words (add, sum) and (product, multiply) are all strategically used so that the student can see that these words have related meanings.

Type: Problem-Solving Task

Watch Out for Parentheses 1:

This problem asks the student to evaluate six numerical expressions that contain the same integers and operations yet have differing results due to placement of parentheses. This type of problem helps students to see structure in numerical expressions. In later grades they will be working with similar ideas in the context of seeing and using structure in algebraic expressions.

Type: Problem-Solving Task

Tutorials

Translating Expressions with Parentheses:

This Khan Academy tutorial video interprets written statements and writes them as mathematical expressions.

Type: Tutorial

Evaluate an Expression With and Without Parentheses:

This Khan Academy tutorial video presents the impact of parentheses notation in an expression.  As the tutorial does the same problem with and without parenthesis, negative numbers are part of the solution.  

Type: Tutorial

Constructing a Numerical Expression Example:

This Khan Academy tutorial video demonstrates how to write a simple expression from a word problem.

Type: Tutorial

Number Pattern Example: Growing Sequence:

In this Khan Academy tutorial video a table is used to track a growing sequence of design.

Type: Tutorial

Introduction to the Order of Operations:

In this video, you will see why it is important to have one agreed upon order of operations.

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

Student Resources

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

Original Student Tutorials

Bee A Coder Part 4: Repeat Loops:

Learn how to use repeat loops in this interactive tutorial. Repeat loops iterate though a list of instructions based on a desired number of times. Combined with variables, condition statements, if statements, and repeat loops we practice using order of operations to code.

This is part 1 of a 4-part series. Click below to check out the other tutorials in the series.

Type: Original Student Tutorial

Bee A Coder Part 3: If Statements:

Learn how to perform instructions using an if statement and explore relational operators (less than, greater than, equal and not equal to) and how they are used to compare to values in this interactive tutorial.

Type: Original Student Tutorial

Bee A Coder Part 2: Condition Statements:

Construct efficient lines of code using condition- and if-statements to solve equations as you complete this interactive tutorial. You'll also review the order of operations in expressions.

This is part 2 of a 4-part series on coding. Click below to open the other tutorials in the series.

Type: Original Student Tutorial

Expressions: Not Just for Faces:

Learn how to write mathematical expressions while making faces in this interactive tutorial!

Type: Original Student Tutorial

The Expression Debate:

Learn to evaluate expressions that have all four operations (multiplication, division, addition, and subtraction) and parentheses as you settle debates in this interactive tutorial.

Type: Original Student Tutorial

Problem-Solving Tasks

Video Game Scores:

This task asks students to exercise both of these complementary skills, writing an expression in part (a) and interpreting a given expression in (b). The numbers given in the problem are deliberately large and "ugly" to discourage students from calculating Eric's and Leila's scores. The focus of this problem is not on numerical answers, but instead on building and interpreting expressions that could be entered in a calculator or communicated to another student unfamiliar with the context.

Type: Problem-Solving Task

Seeing is Believing:

The purpose of this task is to help students see that 4×(9+2) is four times as big as (9+2). Though this task may seem very simple, it provides students and teachers with a very useful visual for interpreting an expression without evaluating it because they can see for themselves that 4×(9+2) is four times as big as (9+2).

Type: Problem-Solving Task

Comparing Products:

The purpose of this task is to generate a classroom discussion that helps students synthesize what they have learned about multiplication in previous grades. It builds on applying properties of operations as strategies to multiply and divide and interpreting a multiplication equation as a comparison.

Type: Problem-Solving Task

Words to Expressions 1:

This problem allows student to see words that can describe an expression although the solution requires nested parentheses.  Additionally , the words (add, sum) and (product, multiply) are all strategically used so that the student can see that these words have related meanings.

Type: Problem-Solving Task

Watch Out for Parentheses 1:

This problem asks the student to evaluate six numerical expressions that contain the same integers and operations yet have differing results due to placement of parentheses. This type of problem helps students to see structure in numerical expressions. In later grades they will be working with similar ideas in the context of seeing and using structure in algebraic expressions.

Type: Problem-Solving Task

Tutorials

Translating Expressions with Parentheses:

This Khan Academy tutorial video interprets written statements and writes them as mathematical expressions.

Type: Tutorial

Evaluate an Expression With and Without Parentheses:

This Khan Academy tutorial video presents the impact of parentheses notation in an expression.  As the tutorial does the same problem with and without parenthesis, negative numbers are part of the solution.  

Type: Tutorial

Constructing a Numerical Expression Example:

This Khan Academy tutorial video demonstrates how to write a simple expression from a word problem.

Type: Tutorial

Number Pattern Example: Growing Sequence:

In this Khan Academy tutorial video a table is used to track a growing sequence of design.

Type: Tutorial

Introduction to the Order of Operations:

In this video, you will see why it is important to have one agreed upon order of operations.

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.

Problem-Solving Tasks

Video Game Scores:

This task asks students to exercise both of these complementary skills, writing an expression in part (a) and interpreting a given expression in (b). The numbers given in the problem are deliberately large and "ugly" to discourage students from calculating Eric's and Leila's scores. The focus of this problem is not on numerical answers, but instead on building and interpreting expressions that could be entered in a calculator or communicated to another student unfamiliar with the context.

Type: Problem-Solving Task

Seeing is Believing:

The purpose of this task is to help students see that 4×(9+2) is four times as big as (9+2). Though this task may seem very simple, it provides students and teachers with a very useful visual for interpreting an expression without evaluating it because they can see for themselves that 4×(9+2) is four times as big as (9+2).

Type: Problem-Solving Task

Comparing Products:

The purpose of this task is to generate a classroom discussion that helps students synthesize what they have learned about multiplication in previous grades. It builds on applying properties of operations as strategies to multiply and divide and interpreting a multiplication equation as a comparison.

Type: Problem-Solving Task

Bowling for Numbers:

The purpose of this game is to help students think flexibly about numbers and operations and to record multiple operations using proper notation. Students eager to knock down all of the pins quickly develop patterns in their expressions. They may re-use parts of an expression, perhaps changing just the final operation.

Type: Problem-Solving Task

Words to Expressions 1:

This problem allows student to see words that can describe an expression although the solution requires nested parentheses.  Additionally , the words (add, sum) and (product, multiply) are all strategically used so that the student can see that these words have related meanings.

Type: Problem-Solving Task

Watch Out for Parentheses 1:

This problem asks the student to evaluate six numerical expressions that contain the same integers and operations yet have differing results due to placement of parentheses. This type of problem helps students to see structure in numerical expressions. In later grades they will be working with similar ideas in the context of seeing and using structure in algebraic expressions.

Type: Problem-Solving Task