MAFS.7.NS.1.3

Solve real-world and mathematical problems involving the four operations with rational numbers.

Clarifications

Examples of Opportunities for In-Depth Focus

When students work toward meeting this standard (which is closely connected to 7.NS.1.1 and 7.NS.1.2), they consolidate their skill and understanding of addition, subtraction, multiplication and division of rational numbers.
General Information
Subject Area: Mathematics
Grade: 7
Domain-Subdomain: The Number System
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. (Major 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
Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes
Test Item Specifications

  • Assessment Limits :
    Complex fractions may be used, but should contain fractions with single-digit numerators and denominators
  • Calculator :

    Neutral

  • Context :

    Allowable

Sample Test Items (3)
  • Test Item #: Sample Item 1
  • Question: At 8:00, the temperature was 6 degrees Celsius (°C). Three hours later, the temperature was -13°C. 

    By how many degrees Celsius did the temperature change?

  • Difficulty: N/A
  • Type: EE: Equation Editor

  • Test Item #: Sample Item 2
  • Question: The change in the price of a certain brand of cereal from 2010 to 2012 is shown in the table.

    In 2009 the price of cereal was $3.69.

    What was the price of the cereal at the end of 2012?

  • Difficulty: N/A
  • Type: EE: Equation Editor

  • Test Item #: Sample Item 3
  • Question:

    The total change in the price of a certain brand of cereal from 2008 to 2012 was -$0.20.

    Complete the table to show possible price changes in 2010 and 2012.

     

  • Difficulty: N/A
  • Type: TI: Table Item

Related Courses

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

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.7.NS.1.AP.3a: Solve real-world and mathematical problems involving the four operations with rational numbers from -100 to 100.

Related Resources

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

Assessments

Sample 3 - Seventh Grade Math State Interim Assessment:

This is a State Interim Assessment for seventh grade.

Type: Assessment

Sample 2 - Seventh Grade Math State Interim Assessment:

This is a State Interim Assessment for seventh grade.

Type: Assessment

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

Trail Mix Munchies:

Students are asked to solve a word problem involving division of fractions.

Type: Formative Assessment

A Rational Number Expression:

Students are given a numerical expression to evaluate.

Type: Formative Assessment

Monitoring Water Temperatures:

Students are asked to solve a word problem that involves finding the average of positive and negative decimal numbers.

Type: Formative Assessment

Lesson Plans

Water, Water Everywhere - Natural Disaster Water Filtration:

Students will be tasked with an engineering challenge to design an effective and efficient portable water filtration system. The designs will take dirty water and make it clear so it can be boiled for safe drinking. This lesson aligns to both math and science content standards.

Type: Lesson Plan

Irrigation Station:

This STEM lesson, complete with a design challenge, helps students design, build, and test irrigation methods. Students will incorporate and develop math skills through solving proportions as they work in teams to solve an engineering challenge.

Type: Lesson Plan

MEA NASA Salaries:

This is a NASA-themed, MEA (Model Eliciting Activity) lesson that challenges students to solve a real world open ended problem, while promoting collaboration through teamwork. This lesson asks each group of students to choose five positions and assign salaries to the positions with a given budget of $500,000. The students' original decision (and "twist") will be based on information from the client's letter(s) and data set(s). Groups are to write a detailed letter to the client of the procedure used.

Type: Lesson Plan

Rocket Repair:

Students will select the best type of coating for rockets given a set of data which will include temperature, hardness, resistance to corrosion and drag.

Type: Lesson Plan

Laura’s Babysitting Job:

In this 7th grade MEA Laura Banks requests a consulting firm, JJ Consulting, to help her make a decision on an employer. Students are to use the data table to calculate unit rates (nightly rate and hourly rate) and then rank her choices and write a recommendation with the procedure used to come up with the ranking.

Type: Lesson Plan

Johansson Family Travel Plans:

In this 7th grade MEA, students will form teams to rank the best vacation package for the Johansson family vacation. They will have to calculate the total cost of the vacation package making sure they don't go over budget. Teams will suggest what the family should do with any excess money. They will also suggest any deletion of activities if the package is over budget. Teams will make a presentation of the first choice recommendation.

Type: Lesson Plan

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

Increasing and Decreasing Quantities by a Percent:

This lesson unit is intended to help you assess how well students are able to interpret percent increase and decrease, and in particular, to identify and help students who have the following difficulties:

  • translating between percents
  • decimals and fractions
  • representing percent increase and decrease as multiplication
  • recognizing the relationship between increases and decreases

Type: Lesson Plan

Best Chicken Franchise for Me:

In this MEA, the students will compare data to decide which franchise would be best for a person who is moving into an area and wants to open up their own fried chicken franchise.

Type: Lesson Plan

Run For Your Life!:

Based on a student-focused scenario encouraging healthier lifestyles, students will perform a close and careful reading of an article encouraging active and healthy lifestyles. During the lesson, students will analyze data from Consumer Reports comparing and contrasting treadmills and elliptical exercisers. Using information gathered, students will compile data and persuade administrators to buy equipment that will align with the provided budget and fit in the given space.

Type: Lesson Plan

Using Positive and Negative Numbers in Context:

This lesson unit is intended to help you assess how well students are able to understand and use directed numbers in context. It is intended to help identify and aid students who have difficulties in ordering, comparing, adding, and subtracting positive and negative integers. Particular attention is paid to the use of negative numbers on number lines to explore the following structures:

  • starting temperature + change in temperature = final temperature
  • final temperature – change in temperature = starting temperature
  • final temperature – starting temperature = change in temperature

Type: Lesson Plan

Pricing The Twelve Days of Christmas:

Students will discover how much the items in the classic song, "The Twelve Days of Christmas," would cost in the current year; and then they will update the list for modern times.

Type: Lesson Plan

We're Going on Vacation!:

Teams of students act as travel agents in order to plan a vacation package for a family of 5. The students must create four vacation packages that include: hotel, car rental, and visits to three theme parks.

Type: Lesson Plan

Say Cheese!:

This resource provides a Model-Eliciting Activity where students will analyze a real-world scenario to solve a client's problem and provide the best possible solution based on a logically justified process. The students will consider a request from Simple Photography Classes to evaluate several digital cameras and help them decide which one they should purchase.

Type: Lesson Plan

Future Homes for America:

The students will need to look at data and make good decisions on which model home will be constructed for victims hurt by natural disasters.

Type: Lesson Plan

Ranking Banking:

In this activity, the students are given specifics and data tables to figure out which banking institution best fits the needs of the customer. Student have to figure out the company's monthly banking activities and use this information to rank the banks provided in the table(s) to determine which bank will give them the most service for the least cost. The twist adds a new situation to take into consideration that may or may not change their original recommendation.

Type: Lesson Plan

Along for the Ride!:

This resource provides a Model-Eliciting Activity where students will analyze a real-world scenario to solve a client's problem and provide the best possible solution based on a logically justified process. The students will consider a request from Cut It Out Section of the Building and Grounds Maintenance Department of a school district to evaluate several lawn tractor models and help them decide which unit they should purchase.

Type: Lesson Plan

Batteries Included:

This resource provides a Model-Eliciting Activity where students will analyze a real-world scenario to solve a client's problem and provide the best possible solution based on a logically justified process. The students will consider a request from E-Z Go Taxi Cab Service to evaluate several batteries and help them decide which battery they should purchase.

Type: Lesson Plan

Zany's Joke Shop Dilemma:

The main problem is that students will help rank products offered at Zany Joke Shop. They will be ranking the products from best overall to least. By helping rank the products, the student will help create a purchase order for the store. They will be expected to create a device to rank the products offered from best to worst. Students will be given tables that show: cost per product, customer rating, profits made and affordability. The second letter offers students a twist since new products are being introduced for the store to sell and a budget constraint will be introduced.

Type: Lesson Plan

Where in the world?:

This resource provides a Model-Eliciting Activity where students will analyze a real-world scenario to solve a client's problem and provide the best possible solution based on a logically justified process. The students will consider a request from Always On Time Delivery Service to evaluate several GPS units and help them decide which unit they should purchase.

Type: Lesson Plan

Forever Green Landscaping:

Students are asked to rank different types of mulch for a Landscaping company.

Type: Lesson Plan

All Around Fences:

Students use problem solving skills to determine how much fencing is needed and the type of fencing in order to secure a pool and recreational area.

Type: Lesson Plan

Whirl Wind:

The Whirl Wind Corporation would like to install Wind Turbines in the Mojave Desert. The company produces various models of these turbines and is looking for help in selecting the best one for the job.

Type: Lesson Plan

Cool Uniforms:

Students are asked to rank fabrics designated for a new women's volleyball team. Students must take into account the uniform color, Ultraviolet Protection Factor, weight of the fabric availability of material and cost. They will compare and contrast fabrics on these factors and calculate yardage needed to manufacture the team's 24 uniforms.

Type: Lesson Plan

Wallpaper Woes Money Math: Lessons for Life:

Students hear a story about a middle-school student who wants to redecorate his bedroom. They measure the classroom wall dimensions, draw a scale model, and incorporate measurements for windows and doors to determine the area that could be covered by wallpaper. Students then hear more about the student's redecorating adventure and learn about expenses, budget constraints, and tradeoffs.

Type: Lesson Plan

Predicting the decimal equivalent for a fraction - terminating or repeating?:

This lesson encourages students to make an important discovery. Will a given fraction yield a terminating or repeating decimal? Discussion includes why knowing this is important. The lesson is structured to allow exploration, discovery, and summarization.

Type: Lesson Plan

Problem-Solving Tasks

Sharing Prize Money:

Students are asked to determine how to distribute prize money among three classes based on the contribution of each class.

Type: Problem-Solving Task

Space Math: Lunar Cratering:

Students explore the formation of craters on the lunar surface using real world imaging data and mathematical reasoning. Students make observations and inferences about the time that impact craters were formed using probability and percentages.

Type: Problem-Solving Task

Teaching Idea

Feeding Time-SeaWorld Classroom Activity:

Students determine the cost to feed a group of ocean animals in captivity, thus solving a real-life problem.

Type: Teaching Idea

Tutorials

Multi-Step Word Problem :

Solve a multi-step word problem in the context of a cab fare.

Type: Tutorial

Rational Number Word Problem with Fractions:

In this example, you determine the volume of frozen water and express the answer as a fraction.

Type: Tutorial

Dividing Fractions Example 2:

This video demonstrates dividing fractions as multiplying by the reciprocal.

Type: Tutorial

Dividing Whole Numbers and Fractions: T-shirts:

This video demonstrates dividing a whole number by a fraction by multiplying by the reciprocal.

Type: Tutorial

Interpreting absolute value as distance:

In this video, we work through a bunch of examples that stretch our thinking on interpreting absolute value.

Type: Tutorial

Examples of Evaluating Variable Expressions:

This video tutorial shows examples of writing expressions in simplified form and evaluating expressions.

Type: Tutorial

STEM Lessons - Model Eliciting Activity

All Around Fences:

Students use problem solving skills to determine how much fencing is needed and the type of fencing in order to secure a pool and recreational area.

Along for the Ride!:

This resource provides a Model-Eliciting Activity where students will analyze a real-world scenario to solve a client's problem and provide the best possible solution based on a logically justified process. The students will consider a request from Cut It Out Section of the Building and Grounds Maintenance Department of a school district to evaluate several lawn tractor models and help them decide which unit they should purchase.

Batteries Included:

This resource provides a Model-Eliciting Activity where students will analyze a real-world scenario to solve a client's problem and provide the best possible solution based on a logically justified process. The students will consider a request from E-Z Go Taxi Cab Service to evaluate several batteries and help them decide which battery they should purchase.

Best Chicken Franchise for Me:

In this MEA, the students will compare data to decide which franchise would be best for a person who is moving into an area and wants to open up their own fried chicken franchise.

Cool Uniforms:

Students are asked to rank fabrics designated for a new women's volleyball team. Students must take into account the uniform color, Ultraviolet Protection Factor, weight of the fabric availability of material and cost. They will compare and contrast fabrics on these factors and calculate yardage needed to manufacture the team's 24 uniforms.

Forever Green Landscaping:

Students are asked to rank different types of mulch for a Landscaping company.

Future Homes for America:

The students will need to look at data and make good decisions on which model home will be constructed for victims hurt by natural disasters.

Johansson Family Travel Plans:

In this 7th grade MEA, students will form teams to rank the best vacation package for the Johansson family vacation. They will have to calculate the total cost of the vacation package making sure they don't go over budget. Teams will suggest what the family should do with any excess money. They will also suggest any deletion of activities if the package is over budget. Teams will make a presentation of the first choice recommendation.

Laura’s Babysitting Job:

In this 7th grade MEA Laura Banks requests a consulting firm, JJ Consulting, to help her make a decision on an employer. Students are to use the data table to calculate unit rates (nightly rate and hourly rate) and then rank her choices and write a recommendation with the procedure used to come up with the ranking.

MEA NASA Salaries:

This is a NASA-themed, MEA (Model Eliciting Activity) lesson that challenges students to solve a real world open ended problem, while promoting collaboration through teamwork. This lesson asks each group of students to choose five positions and assign salaries to the positions with a given budget of $500,000. The students' original decision (and "twist") will be based on information from the client's letter(s) and data set(s). Groups are to write a detailed letter to the client of the procedure used.

Ranking Banking:

In this activity, the students are given specifics and data tables to figure out which banking institution best fits the needs of the customer. Student have to figure out the company's monthly banking activities and use this information to rank the banks provided in the table(s) to determine which bank will give them the most service for the least cost. The twist adds a new situation to take into consideration that may or may not change their original recommendation.

Rocket Repair:

Students will select the best type of coating for rockets given a set of data which will include temperature, hardness, resistance to corrosion and drag.

Run For Your Life!:

Based on a student-focused scenario encouraging healthier lifestyles, students will perform a close and careful reading of an article encouraging active and healthy lifestyles. During the lesson, students will analyze data from Consumer Reports comparing and contrasting treadmills and elliptical exercisers. Using information gathered, students will compile data and persuade administrators to buy equipment that will align with the provided budget and fit in the given space.

Say Cheese!:

This resource provides a Model-Eliciting Activity where students will analyze a real-world scenario to solve a client's problem and provide the best possible solution based on a logically justified process. The students will consider a request from Simple Photography Classes to evaluate several digital cameras and help them decide which one they should purchase.

We're Going on Vacation!:

Teams of students act as travel agents in order to plan a vacation package for a family of 5. The students must create four vacation packages that include: hotel, car rental, and visits to three theme parks.

Where in the world?:

This resource provides a Model-Eliciting Activity where students will analyze a real-world scenario to solve a client's problem and provide the best possible solution based on a logically justified process. The students will consider a request from Always On Time Delivery Service to evaluate several GPS units and help them decide which unit they should purchase.

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.

Whirl Wind:

The Whirl Wind Corporation would like to install Wind Turbines in the Mojave Desert. The company produces various models of these turbines and is looking for help in selecting the best one for the job.

Zany's Joke Shop Dilemma:

The main problem is that students will help rank products offered at Zany Joke Shop. They will be ranking the products from best overall to least. By helping rank the products, the student will help create a purchase order for the store. They will be expected to create a device to rank the products offered from best to worst. Students will be given tables that show: cost per product, customer rating, profits made and affordability. The second letter offers students a twist since new products are being introduced for the store to sell and a budget constraint will be introduced.

MFAS Formative Assessments

Positive and Negative Fractions:

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

A Rational Number Expression:

Students are given a numerical expression to evaluate.

Complex Fractions:

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

Monitoring Water Temperatures:

Students are asked to solve a word problem that involves finding the average of positive and negative decimal numbers.

Trail Mix Munchies:

Students are asked to solve a word problem involving division of fractions.

Student Resources

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

Problem-Solving Task

Sharing Prize Money:

Students are asked to determine how to distribute prize money among three classes based on the contribution of each class.

Type: Problem-Solving Task

Tutorials

Multi-Step Word Problem :

Solve a multi-step word problem in the context of a cab fare.

Type: Tutorial

Rational Number Word Problem with Fractions:

In this example, you determine the volume of frozen water and express the answer as a fraction.

Type: Tutorial

Dividing Fractions Example 2:

This video demonstrates dividing fractions as multiplying by the reciprocal.

Type: Tutorial

Dividing Whole Numbers and Fractions: T-shirts:

This video demonstrates dividing a whole number by a fraction by multiplying by the reciprocal.

Type: Tutorial

Examples of Evaluating Variable Expressions:

This video tutorial shows examples of writing expressions in simplified form and evaluating expressions.

Type: Tutorial

Parent Resources

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

Problem-Solving Task

Sharing Prize Money:

Students are asked to determine how to distribute prize money among three classes based on the contribution of each class.

Type: Problem-Solving Task