Standard #: MAFS.6.NS.3.6 (Archived Standard)


This document was generated on CPALMS - www.cpalms.org



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
Grade: 6
Domain-Subdomain: The Number System
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 - 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





Related Courses

Course Number1111 Course Title222
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 Resources

Educational Game

Name Description
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.

Formative Assessments

Name Description
Graphing Points in the Plane

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

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.

What Is the Opposite?

Students are asked about numbers and their opposites.

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.

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.

Locating Quadrants

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

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.

Lesson Plans

Name Description
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.

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.

Modern Math Target Practice

The lesson uses the classroom as a coordinate plane then moves into plotting points on a graph. It culminates with a target-practice game.

Capture 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.

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 their understanding.

Original Student Tutorial

Name Description
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.

Perspectives Video: Professional/Enthusiast

Name Description
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]

Download the CPALMS Perspectives video student note taking guide.

Problem-Solving Task

Name Description
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

Name Description
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.

Tutorials

Name Description
Comparing Rational Numbers

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

The Coordinate Plane

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

Coordinate Plane

Students will become familiar with the coordinate plane.

Graphing Points and Naming Quadrants

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

Negative Symbol as Opposite

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

Decimals and Fractions on a Number Line

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

Ordering Rational Numbers

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

Comparing Variables with Negatives

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

Comparing Values on Number Line

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

Coordinate Plane: Quadrants

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

Opposite of a Number

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

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.  

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."

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.

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.

Video/Audio/Animation

Name Description
Number Opposites Practice

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

Student Resources

Original Student Tutorial

Name Description
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.

Educational Game

Name Description
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.

Problem-Solving Task

Name Description
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

Name Description
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.

Tutorials

Name Description
Comparing Rational Numbers:

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

The Coordinate Plane:

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

Coordinate Plane:

Students will become familiar with the coordinate plane.

Graphing Points and Naming Quadrants:

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

Negative Symbol as Opposite:

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

Decimals and Fractions on a Number Line:

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

Ordering Rational Numbers:

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

Comparing Variables with Negatives:

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

Comparing Values on Number Line:

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

Coordinate Plane: Quadrants:

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

Opposite of a Number:

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

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.  

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."

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.

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.



Parent Resources

Problem-Solving Task

Name Description
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.

Tutorial

Name Description
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.



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