MA.7.NSO.2.2

Add, subtract, multiply and divide rational numbers with procedural fluency.
General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 7
Strand: Number Sense and Operations
Date Adopted or Revised: 08/20
Status: State Board Approved

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

 

Terms from the K-12 Glossary

  • Rational Number

 

Vertical Alignment

Previous Benchmarks

Next Benchmarks

 

Purpose and Instructional Strategies

In grade 6, students performed operations with integers, multiplied and divided positive multi-digit numbers with decimals to the thousandths and computed products and quotients of positive fractions by positive fractions, including mixed numbers with procedural fluency. In grade 7, students perform all four operations with positive and negative rational numbers with procedural fluency. In grade 8, they will expand to operations with rational numbers including exponents and radicals, and will perform operations with rational numbers expressed in scientific notation. 
  • This benchmark is the completion of arithmetic operations with rational numbers (MTR.3.1).
  • Instruction includes the possibility that the division of two fractions can be written as a complex fraction. This connection will be important when students work with algebraic expressions in later grades.
  • Students should develop fluency with and without the use of a calculator when performing operations with rational numbers.

 

Common Misconceptions or Errors

  • Students may think the product of a fraction and another fraction is greater than either factor. Use manipulatives or models referenced in previous grade levels to support conceptual understanding (MTR.2.1).
  • Students may incorrectly believe that dividing by 12 is the same as dividing by 2.
  • Students may incorrectly solve complex fractions by multiplying the two fractions.

 

Strategies to Support Tiered Instruction

  • Instruction includes the use of fraction tiles to represent operations with positive fractions while simultaneously recording the equivalent numerical expressions.
  • Instruction includes the use of base ten blocks to represent operations with positive decimals while simultaneously recording the equivalent numerical expressions.
  • Instruction includes the use of two-color counters to represent operations with positive and negative whole numbers while simultaneously recording the equivalent numerical expressions.
  • Teacher co-creates a graphic organizer with students to review operations with positive fractions and operations with integers to assist when applying operations with rational numbers.
  • Instruction includes using manipulatives or models referenced in previous grade levels to support conceptual understanding.

 

Instructional Tasks

Instructional Task 1 (MTR.7.1)
Daliah purchases eggs by the dozen for her two children. Each day, Zane eats 14 carton and Amare eats 16 carton. A carton of 12 eggs costs $1.65.
  • Part A. How much does Daliah spend on eggs for her two children in 30 days?
  • Part B. During one of her shopping trips, Daliah finds that her grocery store has started to sell cartons of 18 eggs for $2.25. If she begins to purchase these cartons, how much does Daliah spend on eggs for her two children in 30 days? After how many days will Daliah spend more than $50? Explain your reasoning.

Instructional Task 2 (MTR.3.1)

Given a = −235 and b = 23, calculate the following:
  • a + b
  • ab
  • a · b
  • ab

 

Instructional Items

Instructional Item 1
Determine the product of 156 and −1.2.

Instructional Item 2
What is the value of the expression 7.24 − 5.01 − 78.4?
 
Instructional Item 3
What is the value of the expression 
− 
245
19
 ?

 

*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.
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
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.2: Using tools or models, add, subtract, multiply and divide rational numbers.

Related Resources

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

Educational Game

Fraction Quiz:

Test your fraction skills by answering questions on this site. This quiz asks you to simplify fractions, convert fractions to decimals and percentages, and answer algebra questions involving fractions. You can even choose difficulty level, question types, and time limit.

Type: Educational Game

Educational Software / Tool

Arithmetic Quiz:

In this activity, students solve arithmetic problems involving whole numbers, integers, addition, subtraction, multiplication, and division. This activity allows students to track their progress in learning how to perform arithmetic on whole numbers and integers. 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: Educational Software / Tool

Formative Assessments

Complex Fractions:

Students are asked to rewrite complex fractions as simple fractions in lowest terms.

Type: Formative Assessment

Positive and Negative Fractions:

Students are asked to add, subtract, multiply, and divide positive and negative fractions.

Type: Formative Assessment

Rational Water Management:

Students are asked to combine rational numbers, including fractions and decimals, and use the properties of operations to simplify calculations.

Type: Formative Assessment

Understanding Products:

Students are asked to explain why the product of a positive and a negative rational number is negative.

Type: Formative Assessment

Negatives Explained:

Students are asked to describe a real-world context for a given expression involving the product of two rational numbers.

Type: Formative Assessment

Applying Rational Number Properties:

Students are asked to evaluate expressions involving multiplication of rational numbers and use the properties of operations to simplify calculations.

Type: Formative Assessment

Lesson Plans

Which Services can we Afford? Part 2 of 3:

In this lesson, students will be presented with the same scenario as lesson 1. Now there are additional taxes revenues that came in due to new developments in the area. The budget has a 12.5% increase but due to the new developments, there are allocation constraints to the budget. After dispersing their new funds students will compare their results with their original analysis. This is lesson 2 of 3 in a mini-unit integrating math and civics.

Type: Lesson Plan

Which Services can we Afford? Part 3 of 3:

In this lesson, students will peer review their assignments from lessons 1 and 2 to compare their solutions and determine the validity of the classmate’s process according to the provided rubric. This is lesson 3 of 3 in a mini-unit integrating math and civics.

Type: Lesson Plan

Which Services can we Afford? Part 1of 3:

In this lesson, students will be re-introduced to ratios and percentages and explain how we use them for budgeting and taxes. Students will get information on tax income funds and use the information to allocate funds for providing the different services in a community (Police, Fire, Schools, Hospitals, Roads, etc.) This is lesson 1 of 3 in a mini-unit integrating civics and math.

Type: Lesson Plan

Breaking Up is Hard to Do:

Student will use geoboards to decompose composite figures and polygons into squares, rectangles, and triangles in order to find the total area.

Type: Lesson Plan

Independent Compound Probability:

During this lesson, students will use Punnett Squares to determine the probability of an offspring's characteristics.

Type: Lesson Plan

Building Graduation Caps:

Students will apply skills from the Geometry Domain to build graduation caps for themselves using heavyweight poster paper. They will also apply some basic mathematical skills to determine dimensions and to determine minimum cost. Some of the Geometric skills reinforced in Building Graduation Caps: Cooperative Assignment are finding area, applying the concept of similarity, and the application of the properties of parallelograms. Other skills also involved in this application are measuring, and statistical calculations, such as finding the mean and the range. In addition to the hands-on group project that takes place during the lesson, there is the Prerequisite Skills Assessment: Area that should be administered before the group activity and a home-learning activity. Building Graduation Caps: Individual Assignment is the home-learning assignment; it is designed to reinforce the skills learned in the group activity.

Type: Lesson Plan

Decisions, Decisions!:

In this Model Eliciting Activity, MEA, students will research a list of companies to invest in through purchasing stocks. Students will calculate the amount invested and readjust their investment choices.

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

Selecting a Sample Population:

The student explores several strategies for selecting a sample population to support making inferences about the population.

Type: Lesson Plan

Generating Multiple Samples to Gauge Variation:

Students explore variation in random samples and use random samples to make generalizations about the population.

Type: Lesson Plan

Finding Area with Hands-On Measurement:

This lesson allows students to apply the area of triangles, quadrilaterals, and trapezoids to composite figures, and gives students a chance to work with classmates to find the area by taking measurements and making the necessary calculations. Students will also see the relationship between the area formulas for rectangles, triangles, trapezoids, and polygons. 

Type: Lesson Plan

Perspectives Video: Experts

Fluency vs. Automaticity:

How are fluency and automaticity defined? Dr. Lawrence Gray explains fluency and automaticity in the B.E.S.T. mathematics benchmarks in this Expert Perspectives video.

Type: Perspectives Video: Expert

B.E.S.T. Journey:

What roles do exploration, procedural reliability, automaticity, and procedural fluency play in a student's journey through the B.E.S.T. benchmarks? Dr. Lawrence Gray explains the path through the B.E.S.T. maththematics benchmarks in this Expert Perspectives video.

Type: Perspectives Video: Expert

What is Fluency?:

What is fluency? What are the ingredients required to become procedurally fluent in mathematics? Dr. Lawrence Gray explores what it means for students to be fluent in mathematics in this Expert Perspectives video.

Type: Perspectives Video: Expert

Why Isn't Getting the "Right" Answer Good Enough?:

Why is it important to look beyond whether a student gets the right answer? Dr. Lawrence Gray explores the importance of understanding why we perform certain steps or what those steps mean, and the impact this understanding can have on our ability to solve more complex problems and address them in the context of real life in this Expert Perspectives video.

Type: Perspectives Video: Expert

Tutorial

Adding and Subtracting Numbers in Different Formats:

In this example, we will work with three numbers in different formats: a percent, a decimal, and a mixed number.

Type: Tutorial

Video/Audio/Animation

Interpreting Negative Number Statements:

Explore negative numbers to represent real world situations in this tutorial.

Type: Video/Audio/Animation

STEM Lessons - Model Eliciting Activity

Decisions, Decisions!:

In this Model Eliciting Activity, MEA, students will research a list of companies to invest in through purchasing stocks. Students will calculate the amount invested and readjust their investment choices.

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

Positive and Negative Fractions:

Students are asked to add, subtract, multiply, and divide positive and negative fractions.

Applying Rational Number Properties:

Students are asked to evaluate expressions involving multiplication of rational numbers and use the properties of operations to simplify calculations.

Complex Fractions:

Students are asked to rewrite complex fractions as simple fractions in lowest terms.

Negatives Explained:

Students are asked to describe a real-world context for a given expression involving the product of two rational numbers.

Rational Water Management:

Students are asked to combine rational numbers, including fractions and decimals, and use the properties of operations to simplify calculations.

Understanding Products:

Students are asked to explain why the product of a positive and a negative rational number is negative.

Student Resources

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

Educational Game

Fraction Quiz:

Test your fraction skills by answering questions on this site. This quiz asks you to simplify fractions, convert fractions to decimals and percentages, and answer algebra questions involving fractions. You can even choose difficulty level, question types, and time limit.

Type: Educational Game

Educational Software / Tool

Arithmetic Quiz:

In this activity, students solve arithmetic problems involving whole numbers, integers, addition, subtraction, multiplication, and division. This activity allows students to track their progress in learning how to perform arithmetic on whole numbers and integers. 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: Educational Software / Tool

Tutorial

Adding and Subtracting Numbers in Different Formats:

In this example, we will work with three numbers in different formats: a percent, a decimal, and a mixed number.

Type: Tutorial

Parent Resources

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