MAFS.5.OA.1.1Archived Standard

loading spinner
Export Print
Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
General Information
Subject Area: Mathematics
Grade: 5
Domain-Subdomain: Operations and Algebraic Thinking
Cluster: Level 1: Recall
Cluster: Write and interpret numerical expressions. (Additional Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date Adopted or Revised: 02/14
Content Complexity Rating: Level 1: Recall - More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes
Test Item Specifications

  • Assessment Limits :
    Expressions may contain whole numbers and up to one fraction with a denominator of 10 or less. Items may not require division with fractions. Items may not contain nested grouping symbols.
  • Calculator :

    No

  • Context :

    No context

Sample Test Items (3)
  • Test Item #: Sample Item 2
  • Question:

    A numerical expression is evaluated as shown.

    begin mathsize 12px style 1 half space cross times space left parenthesis 6 cross times 1 plus 7 right parenthesis space plus 11 end style

    Step 1: begin mathsize 12px style 1 half space cross times space left parenthesis 6 cross times 8 right parenthesis space plus space 11 end style

    Step 2: begin mathsize 12px style 1 half space cross times space 48 space plus space 11 end style

    Step 3: begin mathsize 12px style 24 space plus space 11 end style

    Step 4: begin mathsize 12px style 35 end style

    In which step does a mistake first appear?

     

  • Difficulty: N/A
  • Type: MC: Multiple Choice

Related Courses

This benchmark is part of these courses.
5012070: Grade Five Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712060: Access Mathematics Grade 5 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012065: Grade 4 Accelerated Mathematics (Specifically in versions: 2019 - 2022, 2022 and beyond (current))
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022, 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

Related Resources

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

Formative Assessments

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

Lesson Plans

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

Fly Runners Order of Operations MEA:

This MEA is designed so that students will practice knowledge learned from Order of Operations. In the process, students will analyze marketing and advertising data in order to help Fly Runners Running Shoes choose the appropriate magazine to advertise with.

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

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

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

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

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

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

Order of Operations Example (No Exponents):

In this video, you will work through an example to correctly use the order of operations.

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

Unit/Lesson Sequence

Using the Laws of Arithmetic:

This lesson unit helps teachers assess how students perform arithmetic operations, write and evaluate numerical expression s from diagrammatic representations, apply the distributive and commutative properties, and find areas of compound rectangles. The time for the lesson is broken into a 15 minute pre-lesson task, an 80 minute lesson (or two 40 minute lessons), and a 15 minute follow up lesson or homework. Individual students will need a copy of the two tasks, a mini-whiteboard, a pen, and an eraser. Each small group will need cut-up copies of the card sets, a large sheet of poster-sized paper, and a glue stick.

Type: Unit/Lesson Sequence

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

STEM Lessons - Model Eliciting Activity

Fly Runners Order of Operations MEA:

This MEA is designed so that students will practice knowledge learned from Order of Operations. In the process, students will analyze marketing and advertising data in order to help Fly Runners Running Shoes choose the appropriate magazine to advertise with.

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.

MFAS Formative Assessments

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.

Place The Parentheses:

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

With and Without Parentheses:

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

Original Student Tutorials Mathematics - Grades K-5

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.

Computer Science Original Student Tutorials

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.

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 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.

Student Resources

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

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

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 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

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

Order of Operations Example (No Exponents):

In this video, you will work through an example to correctly use the order of operations.

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 benchmark.

Problem-Solving Tasks

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

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