Standard 1 : Write and interpret numerical expressions. (Additional Cluster) (Archived)



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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.

General Information

Number: MAFS.5.OA.1
Title: Write and interpret numerical expressions. (Additional Cluster)
Type: Cluster
Subject: Mathematics - Archived
Grade: 5
Domain-Subdomain: Operations and Algebraic Thinking

Related Standards

This cluster includes the following benchmarks
Code Description
MAFS.5.OA.1.1: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
MAFS.5.OA.1.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.


Related Access Points

This cluster includes the following access points.

Access Points

Access Point Number Access Point Title
MAFS.5.OA.1.AP.1a: Evaluate a simple expression involving one set of parenthesis.
MAFS.5.OA.1.AP.2a: Write a simple expression for a calculation.


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
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:

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.

Analyzing Polyhedra:

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

Sunshine Beach Restaurant:

This Model Eliciting Activity (MEA) asks students to develop a procedure to select a hurricane shutter company based on several data points.

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

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.

Order of Operations Example (No Exponents):

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

Introduction to the Order of Operations:

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

Unit/Lesson Sequence

Name Description
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.

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.

Order of Operations Example (No Exponents):

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

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.