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.

**Number:**MAFS.6.NS.3

**Title:**Apply and extend previous understandings of numbers to the system of rational numbers. (Major Cluster)

**Type:**Cluster

**Subject:**Mathematics - Archived

**Grade:**6

**Domain-Subdomain:**The Number System

## Related Standards

## Related Access Points

## Access Points

## Related Resources

## Educational Game

## Educational Software / Tool

## Formative Assessments

## Lesson Plans

## Original Student Tutorials

## Perspectives Video: Professional/Enthusiasts

## Problem-Solving Tasks

## Student Center Activity

## Tutorials

## Video/Audio/Animation

## Student Resources

## Original Student Tutorials

Follow Matteo as he explores opposite numbers, positive and negative rational numbers, and zero in real-world contexts while planning and going on a cruise in Alaska in this interactive tutorial.

Type: Original Student Tutorial

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

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

## Problem-Solving Tasks

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

Type: Problem-Solving Task

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

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

Type: Problem-Solving Task

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

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

Type: Problem-Solving Task

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

## 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

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

Type: Tutorial

This video demonstrates solving word problems involving the coordinate plane.

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

Let's order negative numbers from least to greatest in this video.

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

This video demonstrates solving absolute value inequality statements.

Type: Tutorial

This video is about interpreting absolute value in a real-life situation.

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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

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

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

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

Type: Tutorial

## Parent Resources

## Problem-Solving Tasks

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

Type: Problem-Solving Task

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

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

Type: Problem-Solving Task

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

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

Type: Problem-Solving Task

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

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

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

Type: Tutorial