# MA.7.NSO.2.1

Solve mathematical problems using multi-step order of operations with rational numbers including grouping symbols, whole-number exponents and absolute value.

### Clarifications

Clarification 1: Multi-step expressions are limited to 6 or fewer steps.
General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Number Sense and Operations
Status: State Board Approved

## Benchmark Instructional Guide

### Terms from the K-12 Glossary

• Absolute Value
• Exponent
• Order of Operations

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

In grade 6, students evaluated algebraic expressions using substitution and order of operations with integers, including use of absolute value and natural number exponents. In grade 7, students move to multi-step order of operations with rational numbers including grouping symbols, whole-number exponents and absolute value. In grade 8, students will solve problems involving order of operations involving radicals.
• Number sense and properties of operations should be emphasized during instruction as this benchmark is the completion of operations with rational numbers.
• Remind students that subtraction is addition of an opposite and division is multiplication by a reciprocal when working with order of operations (MTR.3.1).
• Avoid mnemonics, such as PEMDAS, that do not account for other grouping symbols and do not exercise proper number sense that allows for calculating accurately in a different order.
• Instruction includes the use of technology to help emphasize the proper use of grouping symbols for order of operations.
• With the completion of operations with rational numbers in grade 7, students should have experience using technology with decimals and fractions as they occur in the real world. This experience will help to prepare students working with irrational numbers in grade 8.

### Common Misconceptions or Errors

• Students may confuse when parentheses are used for grouping or multiplication.
• Some students may incorrectly apply the order of operations. In order to support students in moving beyond this misconception, be sure to review operations with rational numbers and order of operations.

### Strategies to Support Tiered Instruction

• Instruction includes the use of colors to highlight each step of the process used to evaluate an expression.
• Teacher co-creates a graphic organizer for different grouping symbols and provides examples when the grouping symbols indicate operator symbols.
• For example, students can be given the expressions below and discuss similarities and differences.
($\frac{\text{4}}{\text{6}}$ + 9) + 87 ($\frac{\text{4}}{\text{6}}$ + 9) 87 ($\frac{\text{4}}{\text{6}}$ + 9) −87
($\frac{\text{4}}{\text{6}}$ + 9) (+87) ($\frac{\text{4}}{\text{6}}$ + 9) (87) ($\frac{\text{4}}{\text{6}}$ + 9) (−87)
• Instruction includes reviewing operations with rational numbers and order of operations.

Part A. Using the integers −6 to 6 at most once, fill in the boxes to create an expression with the lowest value.

Part B. Compare your value with those in your group. Who has the lowest value? Explain why this value was less than the others.

Part A. Evaluate the expression .
Part B. Compare your strategy with a partner.

### Instructional Items

Instructional Item 1
What is the value of the expression $\frac{\text{(12−|8−5|)³}}{\text{36}}$ ?

Instructional Item 2
What is the value of the expression $\frac{\text{1}}{\text{2}}$(3² −4) + |7− $\frac{\text{1}}{\text{6}}$|?

Instructional Item 3
Evaluate the expression 18 − 3(4.12 + 7.6 ÷ 2).

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.

## Related Courses

This benchmark is part of these courses.
1205020: M/J Accelerated Mathematics Grade 6 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1205040: M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812020: Access M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.7.NSO.2.AP.1: Solve mathematical problems, using no more than four operations, with rational numbers including grouping symbols, whole-number exponents and absolute value.

## Related Resources

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

## Formative Assessment

A Rational Number Expression:

Students are given a numerical expression to evaluate.

Type: Formative Assessment

## Lesson Plans

Which van is the best buy?:

The students will have to decide which van is the "best buy" for a family. They will have to figure monthly payments and will also use critical thinking skills to decide which is the best van to purchase.

Type: Lesson Plan

Car Shopping:

In this Model Eliciting Activity, MEA, students will analyze and interpret data to recommend the best vehicle purchases for a school district. Students will work collaboratively to perform calculations that can be used to make comparisons and create composite scores for each vehicle.

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 processes. 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 MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

Say Cheese!:

In this Model Eliciting Activity, MEA, students will apply their knowledge of rational numbers and order of operations to analyze and compare data to provide recommendations on the best camera to use in an introductory photography class.

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 processes. 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 MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

Along for the Ride!:

In this Model Eliciting Activity, MEA, students will use the order of operations to develop and apply a scoring system to evaluate different lawn tractors for a company. Students will justify their rankings using their analysis, calculations, and scoring system.

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 processes. 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 MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

Multiplying with Common Bases:

This resource provides a Lesson Plan for teaching students how to apply the Product of Powers Property of exponents. They will be able to write equivalent exponential expressions and evaluate them when possible.

Type: Lesson Plan

Method to My Mathness:

In this lesson, students will complete proof tables to justify the steps taken to solve multi-step equations. Justifications include mathematical properties and definitions..

Type: Lesson Plan

Math in Mishaps:

Students will explore how percentages, proportions, and solving for unknowns are used in important jobs. This interactive activity will open their minds and address the question, "When is this ever used in real life?"

Type: Lesson Plan

Justly Justifying:

Students will review the properties used in solving simple equations through a quiz-quiz-trade activity. As a class, they will then associate these properties with individual steps in solving equations. The students will then participate in a Simultaneous Round Table to practice their justifications. Finish the lesson with a discussion on the different methods that students could use to acquire the correct answer. The following day, students will take a short quiz to identify misconceptions.

Type: Lesson Plan

## Original Student Tutorials

Order of Operations with Rational Numbers Part 2: Decimals:

Evaluate numerical expressions with rational numbers expressed as decimals using the order of operations and properties of operations in this interactive tutorial.

Type: Original Student Tutorial

Order of Operations with Rational Numbers Part 1: Fractions:

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

This is part 1 in a two-part series.

Type: Original Student Tutorial

## Perspectives Video: Teaching Idea

Absolute Value Progression:

Unlock an effective teaching strategy for making connections with absolute values to graphing in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

## 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

## STEM Lessons - Model Eliciting Activity

Along for the Ride!:

In this Model Eliciting Activity, MEA, students will use the order of operations to develop and apply a scoring system to evaluate different lawn tractors for a company. Students will justify their rankings using their analysis, calculations, and scoring system.

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 processes. 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 MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

Car Shopping:

In this Model Eliciting Activity, MEA, students will analyze and interpret data to recommend the best vehicle purchases for a school district. Students will work collaboratively to perform calculations that can be used to make comparisons and create composite scores for each vehicle.

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 processes. 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 MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

Say Cheese!:

In this Model Eliciting Activity, MEA, students will apply their knowledge of rational numbers and order of operations to analyze and compare data to provide recommendations on the best camera to use in an introductory photography class.

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 processes. 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 MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

Which van is the best buy?:

The students will have to decide which van is the "best buy" for a family. They will have to figure monthly payments and will also use critical thinking skills to decide which is the best van to purchase.

## MFAS Formative Assessments

A Rational Number Expression:

Students are given a numerical expression to evaluate.

## Original Student Tutorials Mathematics - Grades 6-8

Order of Operations with Rational Numbers Part 1: Fractions:

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

This is part 1 in a two-part series.

Order of Operations with Rational Numbers Part 2: Decimals:

Evaluate numerical expressions with rational numbers expressed as decimals using the order of operations and properties of operations in this interactive tutorial.

## Student Resources

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

## Original Student Tutorials

Order of Operations with Rational Numbers Part 2: Decimals:

Evaluate numerical expressions with rational numbers expressed as decimals using the order of operations and properties of operations in this interactive tutorial.

Type: Original Student Tutorial

Order of Operations with Rational Numbers Part 1: Fractions:

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

This is part 1 in a two-part series.

Type: Original Student Tutorial

## 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

## Parent Resources

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