MAFS.6.NS.3.7

Understand ordering and absolute value of rational numbers.
  1. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret -3 > -7 as a statement that -3 is located to the right of -7 on a number line oriented from left to right.

  2. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write -3 oC > -7 oC to express the fact that -3 oC is warmer than -7 oC.

  3. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of -30 dollars, write |-30| = 30 to describe the size of the debt in dollars.

  4. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than -30 dollars represents a debt greater than 30 dollars.
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 :

    N/A

  • Calculator :

    No

  • Context :

    Allowable

Sample Test Items (3)

  • Test Item #: Sample Item 2
  • Question:

    The elevations of several cities are shown.

    Select which city has the greatest elevation and which city is farthest from sea level.

     

     

  • Difficulty: N/A
  • Type: MI: Matching Item

  • Test Item #: Sample Item 3
  • Question:

    Chicago has a temperature of begin mathsize 12px style negative 10 end style degrees Fahrenheit (ºF). It is colder in Minneapolis than in Chicago.

    Select all the values that could represent the temperature of Minneapolis.

     

  • 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.
MAFS.6.NS.3.AP.7a: Compare two numbers on a number line (e.g., -2 > -9) between -30 and 30.
MAFS.6.NS.3.AP.7b: Determine the meaning of absolute value using numbers from -30 to 30.

Related Resources

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

Assessments

Sample 4 - Sixth Grade Math State Interim Assessment:

This is a State Interim Assessment for sixth grade.

Type: Assessment

Sample 2 - 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

Formative Assessments

South Pole:

Students are asked to interpret an inequality relating two temperatures.

Type: Formative Assessment

Visualizing Absolute Value:

Students are asked to identify a number’s possible locations on a number line when given the number’s absolute value.

Type: Formative Assessment

Submarines:

Students are asked to write integers to represent quantities given in context and to relate the integers with an inequality.

Type: Formative Assessment

Positions of Numbers:

Students are asked to describe the positions of numbers relative to each other on a number line.

Type: Formative Assessment

Absolute Altitudes:

Students are asked to compare two elevations and their absolute values and then interpret these comparisons within a given real-world context.

Type: Formative Assessment

Lesson Plans

Positive or Negative? Does It Matter?:

This lesson aligns to the Mathematics Formative Assessment System (MFAS) Task Submarines (CPALMS Resource ID# 57915). In this lesson, students with similar instructional needs are grouped according to MFAS rubric levels: Getting Started, Moving Forward, Almost There, and Got It. Students in each group complete an exercise designed to move them toward a better understanding of the ordering of rational numbers.

Type: Lesson Plan

Absolutely Integers:

Students will review how to graph positive numbers and then negative numbers on a number line. The students will review absolute value and apply this to different integers. They will then play a fun game to check understanding.

Type: Lesson Plan

Problem-Solving Tasks

Above and below sea level:

The purpose of this task is to help students interpret signed numbers in a context as a magnitude and a direction and to make sense of the absolute value of a signed number as its magnitude. The questions about the elevation of New Orleans are fairly natural: it is a standard convention to use positive numbers to represent elevations above sea level and negative numbers below sea level. However, it is possible to represent them the other way around.

Type: Problem-Solving Task

Comparing Temperatures:

The purpose of the task is for students to compare signed numbers in a real-world context.

Type: Problem-Solving Task

Fractions on the Number Line:

The purpose of this task is to help students get a better understanding of fractions on a number line.

Type: Problem-Solving Task

Integers on the Number Line 2:

The purpose of this task is for students to get a better understanding of the relative positions and values of positive and negative numbers.

Type: Problem-Solving Task

Jumping Flea:

This purpose of this task is to help students understand the absolute value of a number as its distance from 0 on the number line. The context is not realistic, nor is meant to be; it is a thought experiment to help students focus on the relative position of numbers on the number line.

Type: Problem-Solving Task

Tutorials

Ordering Negative Numbers:

Is -40 bigger than -10? When ordering negative numbers from least to greatest, be careful that you don't get hung up on the "amount" of the number. Think about what that negative sign really means!

Type: Tutorial

Ordering Rational Numbers:

In this tutorial, you will learn how to order rational numbers using a number line.

Type: Tutorial

Comparing Absolute Values:

In this tutorial you will compare the absolute value of numbers using the concepts of greater than (>), less than (<), and equal to (=).

Type: Tutorial

Sorting Values on Number Line:

This video demonstrates sorting values including absolute value from least to greatest using a number line.

Type: Tutorial

Comparing Values on Number Line:

This video demonstrates evaluating inequality statements, some involving absolute value, using a number line.

Type: Tutorial

Values to Make Absolute Value Inequality True:

This video demonstrates solving absolute value inequality statements.

Type: Tutorial

Interpreting Absolute Value:

Practice interpreting absolute value in a real-life situation.

Type: Tutorial

Pre-Algebra - Whole Numbers, Integers, and the Number Line:

Number systems evolved from the natural "counting" numbers, to whole numbers (with the addition of zero), to integers (with the addition of negative numbers), and beyond. These number systems are easily understood using the number line.

Type: Tutorial

Ordering Numeric Expressions :

The video demonstrates rewriting given numbers in a common format (as decimals), so they can be compared and ordered.

Type: Tutorial

MFAS Formative Assessments

Absolute Altitudes:

Students are asked to compare two elevations and their absolute values and then interpret these comparisons within a given real-world context.

Positions of Numbers:

Students are asked to describe the positions of numbers relative to each other on a number line.

South Pole:

Students are asked to interpret an inequality relating two temperatures.

Submarines:

Students are asked to write integers to represent quantities given in context and to relate the integers with an inequality.

Visualizing Absolute Value:

Students are asked to identify a number’s possible locations on a number line when given the number’s absolute value.

Student Resources

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

Problem-Solving Tasks

Comparing Temperatures:

The purpose of the task is for students to compare signed numbers in a real-world context.

Type: Problem-Solving Task

Integers on the Number Line 2:

The purpose of this task is for students to get a better understanding of the relative positions and values of positive and negative numbers.

Type: Problem-Solving Task

Jumping Flea:

This purpose of this task is to help students understand the absolute value of a number as its distance from 0 on the number line. The context is not realistic, nor is meant to be; it is a thought experiment to help students focus on the relative position of numbers on the number line.

Type: Problem-Solving Task

Tutorials

Ordering Negative Numbers:

Is -40 bigger than -10? When ordering negative numbers from least to greatest, be careful that you don't get hung up on the "amount" of the number. Think about what that negative sign really means!

Type: Tutorial

Ordering Rational Numbers:

In this tutorial, you will learn how to order rational numbers using a number line.

Type: Tutorial

Comparing Absolute Values:

In this tutorial you will compare the absolute value of numbers using the concepts of greater than (>), less than (<), and equal to (=).

Type: Tutorial

Sorting Values on Number Line:

This video demonstrates sorting values including absolute value from least to greatest using a number line.

Type: Tutorial

Comparing Values on Number Line:

This video demonstrates evaluating inequality statements, some involving absolute value, using a number line.

Type: Tutorial

Values to Make Absolute Value Inequality True:

This video demonstrates solving absolute value inequality statements.

Type: Tutorial

Interpreting Absolute Value:

Practice interpreting absolute value in a real-life situation.

Type: Tutorial

Pre-Algebra - Whole Numbers, Integers, and the Number Line:

Number systems evolved from the natural "counting" numbers, to whole numbers (with the addition of zero), to integers (with the addition of negative numbers), and beyond. These number systems are easily understood using the number line.

Type: Tutorial

Ordering Numeric Expressions :

The video demonstrates rewriting given numbers in a common format (as decimals), so they can be compared and ordered.

Type: Tutorial

Parent Resources

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

Problem-Solving Tasks

Comparing Temperatures:

The purpose of the task is for students to compare signed numbers in a real-world context.

Type: Problem-Solving Task

Integers on the Number Line 2:

The purpose of this task is for students to get a better understanding of the relative positions and values of positive and negative numbers.

Type: Problem-Solving Task

Jumping Flea:

This purpose of this task is to help students understand the absolute value of a number as its distance from 0 on the number line. The context is not realistic, nor is meant to be; it is a thought experiment to help students focus on the relative position of numbers on the number line.

Type: Problem-Solving Task

Tutorial

Ordering Numeric Expressions :

The video demonstrates rewriting given numbers in a common format (as decimals), so they can be compared and ordered.

Type: Tutorial