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



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

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
Code Description
MA.5.AR.2.1: Translate written real-world and mathematical descriptions into numerical expressions and numerical expressions into written mathematical descriptions.
Clarifications:
Clarification 1: Expressions are limited to any combination of the arithmetic operations, including parentheses, with whole numbers, decimals and fractions. 

Clarification 2: Within this benchmark, the expectation is not to include exponents or nested grouping symbols.

MA.5.AR.2.2: Evaluate multi-step numerical expressions using order of operations.
Clarifications:
Clarification 1: Multi-step expressions are limited to any combination of arithmetic operations, including parentheses, with whole numbers, decimals and fractions.

Clarification 2: Within this benchmark, the expectation is not to include exponents or nested grouping symbols.

Clarification 3: Decimals are limited to hundredths. Expressions cannot include division of a fraction by a fraction.

MA.5.AR.2.3: Determine and explain whether an equation involving any of the four operations is true or false.
Clarifications:
Clarification 1: Problem types include equations that include parenthesis but not nested parentheses.

Clarification 2: Instruction focuses on the connection between properties of equality and order of operations.

MA.5.AR.2.4: Given a mathematical or real-world context, write an equation involving any of the four operations to determine the unknown whole number with the unknown in any position.
Clarifications:
Clarification 1: Instruction extends the development of algebraic thinking where the unknown letter is recognized as a variable.

Clarification 2: Problems include the unknown and different operations on either side of the equal sign



Related Access Points

This cluster includes the following access points.

Access Points

Access Point Number Access Point Title
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.

Original Student Tutorials

Name Description
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.

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.

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.

Expressions: Not Just for Faces:

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

Formative Assessments

Name Description
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.

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.

Evaluating Expressions:

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

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.

With and Without Parentheses:

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

Place The Parentheses:

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

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.

Comparing Products:

Students are asked to analyze and compare two related products.

Lesson Plans

Name Description
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.

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.

Fly Runners Order of Operations MEA:

In this Model Eliciting Activity, MEA, the students will determine the best ad for a tennis shoe company.

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

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.

“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.

Perspectives Video: Teaching Idea

Name Description
Deciphering Cryptic Operations through Mathematical Reasoning: <p>Sideways or wayside, math word problems can be a ton of fun, no matter how you look at them.</p>

Problem-Solving Tasks

Name Description
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.

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).

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.

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.

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.

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.

Tutorials

Name Description
Translating Expressions with Parentheses:

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

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.  

Constructing a Numerical Expression Example:

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

Number Pattern Example: Growing Sequence:

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

Introduction to the Order of Operations:

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

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
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.

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.

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.

Expressions: Not Just for Faces:

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

Problem-Solving Tasks

Title Description
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.

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).

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.

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.

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.

Tutorials

Title Description
Translating Expressions with Parentheses:

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

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.  

Constructing a Numerical Expression Example:

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

Number Pattern Example: Growing Sequence:

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

Introduction to the Order of Operations:

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

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
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.

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).

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.

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.

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.

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.