# MAFS.6.NS.3.6Archived Standard Export Print
Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
1. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.
2. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
3. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.
General Information
Subject Area: Mathematics
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 of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes
Test Item Specifications
Also Assesses:
MAFS.6.NS.3.8

• Assessment Limits :
Plotting of points in the coordinate plane should include some negative values (not just first quadrant). Numbers in MAFS.6.NS.3.8 must be positive or negative rational numbers. Do not use polygons/vertices for MAFS.6.NS.3.8. Do not exceed a 10 × 10 coordinate grid, though scales can vary.
• Calculator :

No

• Context :

Allowable

Sample Test Items (3)

• Test Item #: Sample Item 3
• Question: Which ordered pair best describes the point plotted in Quadrant II on the coordinate plane shown? • Difficulty: N/A
• Type: MC: Multiple Choice

## Related Courses

This benchmark is part of these courses.
1205010: M/J Grade 6 Mathematics (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))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812015: Access M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
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.

## Educational Game

Maze Game:

In this activity, students enter coordinates to make a path to get to a target destination while avoiding mines. This activity allows students to explore Cartesian coordinates and the Cartesian coordinate plane. 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 Game

## Formative Assessments

Graphing Points in the Plane:

Students are asked to graph points given their coordinates and describe the coordinates of graphed points.

Type: Formative Assessment

Graphing on Cartesian Planes:

Students are asked to graph points given their coordinates and describe the coordinates of graphed points when the axes have different scales.

Type: Formative Assessment

What Is the Opposite?:

Type: Formative Assessment

Explaining Opposites:

Students are asked to graph -4, 0, and 4 on a number line and to explain the relationship between a number and its opposite in terms of the number line.

Type: Formative Assessment

Point Locations:

Students are asked to compare the graphs of coordinates that are opposite in sign on a number line and in the coordinate plane.

Type: Formative Assessment

Students are asked to determine in what quadrant or on which axis, points described algebraically, are located.

Type: Formative Assessment

Graphing Points on the Number Line:

Students are asked to find the coordinates of graphed points and graph points with rational coordinates on a number line.

Type: Formative Assessment

## Lesson Plans

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

Mapping the School:

This project is used to help students enhance their ability to use and understand the coordinate plane by creating a map of their school.

Type: Lesson Plan

Modern Math Warfare:

The lesson uses the classroom as a coordinate plane then moves into plotting points on a graph. It culminates with a game based on the "Battleship" game. All parts of the standard are covered in this lesson.

Type: Lesson Plan

Bomb the Boat - Sink the Teacher's Fleet!:

In this lesson, students learn about the four quadrants of a coordinate plane and how to plot points in those quadrants Students also learn how to use linear equations to predict future input and output pairs. Students work together to try to sink the teacher's fleet in a Battleship-type game while the teacher tries to sink theirs first.

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

Cartesian Classroom:

The classroom is turned into a human Cartesian coordinate plane, thereby introducing students to the characteristics of the Cartesian coordinate system.  The example given is for all 4 quadrants but the 5th grade standard may be addressed by designing the classroom as only the first quadrant.  In this case, questions regarding negative numbers would not be asked.

Type: Lesson Plan

## Original Student Tutorial

Golf: Where Negative Numbers are a Positive Thing:

Learn how to create and use number lines with positive and negative numbers, graph positive and negative numbers, find their distance from zero, find a number’s opposite using a number line and signs, and recognize that zero is its own opposite with this interactive, golf-themed tutorial.

Type: Original Student Tutorial

## Perspectives Video: Professional/Enthusiast

KROS Pacific Ocean Kayak Journey: GPS and Coordinates:

What's the shortest path between point A and B on the ocean? It depends on wind and currents, but coordinates can help you track your position.

Related Resources:
KROS Pacific Ocean Kayak Journey: GPS Data Set[.XLSX]
KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth[.KML]

Type: Perspectives Video: Professional/Enthusiast

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.

## Student Center Activity

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

## Tutorials

Comparing Rational Numbers:

In this tutorial, you will compare rational numbers using a number line.

Type: Tutorial

The Coordinate Plane:

Students will plot an ordered pair on the x (horizontal) axis and y (vertical) axis of the coordinate plane.

Type: Tutorial

Coordinate Plane:

Students will become familiar with the coordinate plane.

Type: Tutorial

This video contains examples of plotting coordinate pairs and identifying their quadrant.

Type: Tutorial

Negative Symbol as Opposite:

This video discusses the negative sign as meaning "opposite."

Type: Tutorial

Decimals and Fractions on a Number Line:

Locate fractions and decimals on the same number line in this tutorial.

Type: Tutorial

Ordering Rational Numbers:

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

Type: Tutorial

Comparing Variables with Negatives:

This video guides you through comparisons of values, including opposites.

Type: Tutorial

Comparing Values on Number Line:

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

Type: Tutorial

Students will learn how to identify the four quadrants in the coordinate plane.

Type: Tutorial

Opposite of a Number:

This video uses a number line to describe the opposite of a number.

Type: Tutorial

The Cartesian Coordinate System:

The Cartesian Coordinate system, formed from the Cartesian product of the real number line with itself, allows algebraic equations to be visualized as geometric shapes in two or three dimensions.  While this tutorial includes the basis of Coordinate system, it also includes ideas beyond fifth grade standards.  Most likely only advanced fifth graders would find the video engaging.

Type: Tutorial

Pre-Algebra - Fractions and Rational Numbers:

The first fractions used by ancient civilizations were "unit fractions." Later, numerators other than one were added, creating "vulgar fractions" which became our modern fractions. Together, fractions and integers form the "rational numbers."

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

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

Number Opposites Practice:

This video provides sample questions about the concept of opposite numbers.

Type: Video/Audio/Animation

## MFAS Formative Assessments

Explaining Opposites:

Students are asked to graph -4, 0, and 4 on a number line and to explain the relationship between a number and its opposite in terms of the number line.

Graphing on Cartesian Planes:

Students are asked to graph points given their coordinates and describe the coordinates of graphed points when the axes have different scales.

Graphing Points in the Plane:

Students are asked to graph points given their coordinates and describe the coordinates of graphed points.

Graphing Points on the Number Line:

Students are asked to find the coordinates of graphed points and graph points with rational coordinates on a number line.

Students are asked to determine in what quadrant or on which axis, points described algebraically, are located.

Point Locations:

Students are asked to compare the graphs of coordinates that are opposite in sign on a number line and in the coordinate plane.

What Is the Opposite?:

## Original Student Tutorials Mathematics - Grades 6-8

Golf: Where Negative Numbers are a Positive Thing:

Learn how to create and use number lines with positive and negative numbers, graph positive and negative numbers, find their distance from zero, find a number’s opposite using a number line and signs, and recognize that zero is its own opposite with this interactive, golf-themed tutorial.

## Student Resources

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

## Original Student Tutorial

Golf: Where Negative Numbers are a Positive Thing:

Learn how to create and use number lines with positive and negative numbers, graph positive and negative numbers, find their distance from zero, find a number’s opposite using a number line and signs, and recognize that zero is its own opposite with this interactive, golf-themed tutorial.

Type: Original Student Tutorial

## Educational Game

Maze Game:

In this activity, students enter coordinates to make a path to get to a target destination while avoiding mines. This activity allows students to explore Cartesian coordinates and the Cartesian coordinate plane. 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 Game

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.

## Student Center Activity

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

## Tutorials

Comparing Rational Numbers:

In this tutorial, you will compare rational numbers using a number line.

Type: Tutorial

The Coordinate Plane:

Students will plot an ordered pair on the x (horizontal) axis and y (vertical) axis of the coordinate plane.

Type: Tutorial

Coordinate Plane:

Students will become familiar with the coordinate plane.

Type: Tutorial

This video contains examples of plotting coordinate pairs and identifying their quadrant.

Type: Tutorial

Negative Symbol as Opposite:

This video discusses the negative sign as meaning "opposite."

Type: Tutorial

Decimals and Fractions on a Number Line:

Locate fractions and decimals on the same number line in this tutorial.

Type: Tutorial

Ordering Rational Numbers:

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

Type: Tutorial

Comparing Variables with Negatives:

This video guides you through comparisons of values, including opposites.

Type: Tutorial

Comparing Values on Number Line:

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

Type: Tutorial

Students will learn how to identify the four quadrants in the coordinate plane.

Type: Tutorial

Opposite of a Number:

This video uses a number line to describe the opposite of a number.

Type: Tutorial

The Cartesian Coordinate System:

The Cartesian Coordinate system, formed from the Cartesian product of the real number line with itself, allows algebraic equations to be visualized as geometric shapes in two or three dimensions.  While this tutorial includes the basis of Coordinate system, it also includes ideas beyond fifth grade standards.  Most likely only advanced fifth graders would find the video engaging.

Type: Tutorial

Pre-Algebra - Fractions and Rational Numbers:

The first fractions used by ancient civilizations were "unit fractions." Later, numerators other than one were added, creating "vulgar fractions" which became our modern fractions. Together, fractions and integers form the "rational numbers."

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

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.

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.