MAFS.6.NS.3.5

Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
General Information
Subject Area: Mathematics
Grade: 6
Domain-Subdomain: The Number System
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Apply and extend previous understandings of numbers to the system of 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 :
    Items should not require the student to perform an operation.
  • Calculator :

    No

  • Context :

    Required

Sample Test Items (3)
  • Test Item #: Sample Item 1
  • Question: Chicago, Illinois has an elevation of 600 feet above sea level. The elevation of Desert Shores, California is −200 feet. 

    Select all the true statements. 

     

  • Difficulty: N/A
  • Type: MS: Multiselect

  • Test Item #: Sample Item 2
  • Question: Desert Shores, California is located at an elevation that is below sea level. 

    What is a possible elevation of Desert Shores, California? 

     

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

  • Test Item #: Sample Item 3
  • Question: Chicago, Illinois, has an elevation of 600 feet above sea level. The elevation of Desert Shores, California, is 800 feet less than the elevation of Chicago. 

    Select all options that apply to Desert Shores. 

     

  • Difficulty: N/A
  • Type: MS: Multiselect

Related Courses

This benchmark is part of these courses.
1205010: M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1205020: M/J Grade 6 Accelerated Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022 (current), 2022 and beyond)
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
7812015: Access M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 and beyond)
7912110: Fundamental Explorations in Mathematics 1 (Specifically in versions: 2013 - 2015, 2015 - 2017 (course terminated))

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.

Assessments

Sample 3 - Sixth Grade Math State Interim Assessment:

This is a State Interim Assessment for sixth grade.

Type: Assessment

Sample 1 - Sixth Grade Math State Interim Assessment:

This is a State Interim Assessment for sixth grade.

Type: Assessment

Educational Game

Circle 0 (Addition of Integers):

This addition game encourages some logical analysis as well as addition skills. This particular circle game uses positive and negative integers. There is only one way to combine all the given numbers so that every circle sums to zero.
(source: NLVM grade 6-8 "Circle 0")

Type: Educational Game

Formative Assessments

Relative Fractions:

Students are given positive and negative fractions and asked to explain their meanings within the context of a problem.

Type: Formative Assessment

Relative Integers:

Students are asked to use numbers to represent gains/losses and to interpret the meaning of zero in the context of football.

Type: Formative Assessment

Relative Decimals:

Students are asked to explain the meaning of positive and negative decimals within the context of a problem.

Type: Formative Assessment

Rainfall Change:

Students are asked to interpret values given in a chart that represent positive and negative deviations from average rainfall.

Type: Formative Assessment

Lesson Plans

Too Hot, Too Cold-6th Grade STEM Lesson:

A two day STEM lesson where students get a hands-on experience understanding positive and negative integers. Students will understand how temperature demonstrations and their own created models are used to visualize positive and negative integers in relation to 0 in real-world settings. Students will summarize their understanding of the relationship between positive and negative integers in relation to 0 for the evaluation of this lesson in a journal format.

Type: Lesson Plan

The Layers of the Atmosphere, Guest Starring the Integers! :

Students will learn the functions and characteristics of the four main layers of Earth's atmosphere. They will also determine the thickness of each layer and display them to scale. Students will plot the layers' temperatures, noting the change in temperature from the bottom to the top on a number line.

Type: Lesson Plan

Raja Rangoli:

Rangoli is a traditional Indian art that is used in decorating the entrance of the house to welcome guests. In this activity students will explore and practice the concepts of positive numbers, negative numbers, absolute value, origin, coordinates etc. and will create their own Rangoli design at the end.

Type: Lesson Plan

Let's Ride!:

Let's Ride! is a model-eliciting activity that asks students to use pluses and minuses to indicate if eight models of 4-door sedans meet specific standards based on gas mileage, seating capacity, warranty, and type of engine. The students then have to rank the cars and indicate their top four choices.

Type: Lesson Plan

Understanding Integers:

This lesson is an introduction to integers. Students will compare, order, and describe real-life situations using positive and negative whole numbers. The concepts of opposites and vertical as well as horizontal number lines are addressed.

Type: Lesson Plan

Positive or Negative, It's All About Shopping!:

This lesson introduces students to the concept of negative and positive integers as opposites and as indicators of movement, beginning with elevation and ending with real-world application to money.

Type: Lesson Plan

Positive, Zero, or Negative?:

This lesson involves students using positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of zero in each situation. Students will understand the positive and negative numbers are used together to describe quantities having opposite values.

Type: Lesson Plan

Problem-Solving Tasks

Mile High:

Students are asked to reason about and explain the position of two locations relative to sea level.

Type: Problem-Solving Task

Distances on the Number Line 2:

The purpose of this task is meant to reinforce students' understanding of rational numbers as points on the number line and to provide them with a visual way of understanding that the sum of a number and its additive inverse (usually called its "opposite") is zero.

Type: Problem-Solving Task

It's Warmer in Miami:

The purpose of this task is for students to apply their knowledge of integers in a real-world context.

Type: Problem-Solving Task

Student Center Activity

Edcite: Mathematics Grade 6:

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

Tutorial

Adding Integers:

Students will be able to see examples of addition of integers while watching a short video, and practice adding integers using an online quiz.

Type: Tutorial

Video/Audio/Animation

Interpreting Negative Number Statements:

The examples in this video use negative numbers to represent real world situations. What are these negative numbers really telling us?

Type: Video/Audio/Animation

STEM Lessons - Model Eliciting Activity

Let's Ride!:

Let's Ride! is a model-eliciting activity that asks students to use pluses and minuses to indicate if eight models of 4-door sedans meet specific standards based on gas mileage, seating capacity, warranty, and type of engine. The students then have to rank the cars and indicate their top four choices.

Raja Rangoli:

Rangoli is a traditional Indian art that is used in decorating the entrance of the house to welcome guests. In this activity students will explore and practice the concepts of positive numbers, negative numbers, absolute value, origin, coordinates etc. and will create their own Rangoli design at the end.

MFAS Formative Assessments

Rainfall Change:

Students are asked to interpret values given in a chart that represent positive and negative deviations from average rainfall.

Relative Decimals:

Students are asked to explain the meaning of positive and negative decimals within the context of a problem.

Relative Fractions:

Students are given positive and negative fractions and asked to explain their meanings within the context of a problem.

Relative Integers:

Students are asked to use numbers to represent gains/losses and to interpret the meaning of zero in the context of football.

Student Resources

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

Educational Game

Circle 0 (Addition of Integers):

This addition game encourages some logical analysis as well as addition skills. This particular circle game uses positive and negative integers. There is only one way to combine all the given numbers so that every circle sums to zero.
(source: NLVM grade 6-8 "Circle 0")

Type: Educational Game

Problem-Solving Tasks

Mile High:

Students are asked to reason about and explain the position of two locations relative to sea level.

Type: Problem-Solving Task

Distances on the Number Line 2:

The purpose of this task is meant to reinforce students' understanding of rational numbers as points on the number line and to provide them with a visual way of understanding that the sum of a number and its additive inverse (usually called its "opposite") is zero.

Type: Problem-Solving Task

It's Warmer in Miami:

The purpose of this task is for students to apply their knowledge of integers in a real-world context.

Type: Problem-Solving Task

Student Center Activity

Edcite: Mathematics Grade 6:

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

Tutorial

Adding Integers:

Students will be able to see examples of addition of integers while watching a short video, and practice adding integers using an online quiz.

Type: Tutorial

Parent Resources

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

Educational Game

Circle 0 (Addition of Integers):

This addition game encourages some logical analysis as well as addition skills. This particular circle game uses positive and negative integers. There is only one way to combine all the given numbers so that every circle sums to zero.
(source: NLVM grade 6-8 "Circle 0")

Type: Educational Game

Problem-Solving Tasks

Mile High:

Students are asked to reason about and explain the position of two locations relative to sea level.

Type: Problem-Solving Task

Distances on the Number Line 2:

The purpose of this task is meant to reinforce students' understanding of rational numbers as points on the number line and to provide them with a visual way of understanding that the sum of a number and its additive inverse (usually called its "opposite") is zero.

Type: Problem-Solving Task

It's Warmer in Miami:

The purpose of this task is for students to apply their knowledge of integers in a real-world context.

Type: Problem-Solving Task

Tutorial

Adding Integers:

Students will be able to see examples of addition of integers while watching a short video, and practice adding integers using an online quiz.

Type: Tutorial