# Standard 1: Extend knowledge of numbers to negative numbers and develop an understanding of absolute value.

General Information
Number: MA.6.NSO.1
Title: Extend knowledge of numbers to negative numbers and develop an understanding of absolute value.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Strand: Number Sense and Operations

## Related Benchmarks

This cluster includes the following benchmarks.

## Related Access Points

This cluster includes the following access points.

## Access Points

MA.6.NSO.1.AP.1
Plot, order and compare rational numbers (positive and negative integers within 10 from 0, fractions with common denominators, decimals up to the hundredths and percentages) in the same form.
MA.6.NSO.1.AP.2
Represent positive and negative numbers in the same form on a number line given a real-world situation and explain the meaning of zero within its context.
MA.6.NSO.1.AP.3
Find absolute value of a rational number ranging from –30 to 30 using a number line.
MA.6.NSO.1.AP.4
Use manipulatives, models or tools to compare absolute value in mathematical and real-world problems.

## Related Resources

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

## Formative Assessments

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

South Pole:

Students are asked to interpret an inequality relating two temperatures.

Type: Formative Assessment

Visualizing Absolute Value:

Students are asked to identify a numberâ€™s possible locations on a number line when given the numberâ€™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

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

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

Positive or Negative? Does It Matter?:

This lesson aligns to the Mathematics Formative Assessment System (MFAS) Task Submarines (CPALMS Resource ID# ). 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

Are You Invited to the Party?:

Students will write and graph inequalities that represent real-world constraints involving whole numbers, negative numbers, and/or rational numbers. The distinction between continuous and discrete variables is made.

Type: Lesson Plan

Introducing Inequalities:

Students are introduced to simple inequalities and their graphs as they write inequalities to represent real-world constraints.

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 use the concept of lines of symmetry to select the best rangoli design for a school event.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

Discovering How to Subtract Rational Numbers Using the Additive Inverse:

In this lesson, students will develop an understanding that opposite quantities combine to make zero-sum pairs and will learn how to subtract rational numbers using a horizontal number line and the additive inverse

Type: Lesson Plan

Where's The POINT? What's The POINT? The Point is... a DECIMAL. "Multiply with Decimals":

Multiply efficiently and fluently with multi-digit decimals using a standard algorithm for the operation.

Type: Lesson Plan

Batteries Included:

In this Model Eliciting Activity, MEA, students will evaluate batteries using empirical data and customer comments to help a Taxi Cab Service decide which battery brand to purchase. In this real-world scenario, students will communicate with the client in letter format stating their suggested ranking. They will also provide calculations and justification for each decision.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

Profit Plaza:

This lesson requires students to use mathematical data and logic/reasoning to place vendors into retail spaces in a shopping plaza. Students will first rank five vendor types on their profitability (based on average sales and average overhead/upkeep costs), then place the vendor types into the 11-13 retail spaces. They are also required to find the area of each space and calculate the total leasing charges. The plans for the plaza are given on a coordinate plane, so students will need to find the lengths of horizontal and vertical line segments (using the coordinates of the endpoints) to calculate the areas of the rectangular and composite spaces.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

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 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.

Type: Lesson Plan

Where in the world?:

This resource provides a Model-Eliciting Activity where students will analyze a real-world scenario to solve a client's problem and provide the best possible solution based on a logically justified process. The students will consider a request from Always On Time Delivery Service to evaluate several GPS units and help them decide which unit they should purchase.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

In this lesson, students will use T-charts as a strategy to add and subtract positive and negative numbers.

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

Rational vs Irrational:

Students will organize the set of real numbers and be able to identify when a number is rational or irrational. They will also learn the process of how to change a repeating decimal to its equivalent fraction.

Type: Lesson Plan

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.

Type: Lesson Plan

Plotting Rectangles:

Students are challenged to plot coordinates on a graph in order to create a rectangle, and then find the length of its horizontal and vertical sides using the coordinates to calculate the area and perimeter.Â

Type: Lesson Plan

Discovering Our Rules for Addition of Integers:

In this lesson, students will develop an understanding of the rules for adding integers by using the absolute value of integers and number lines.

Type: Lesson Plan

Plotting Polygons with GeoGebra:

This introductory lesson guides students through the process of graphing polygons on the coordinate plane and finding vertical and horizontal side lengths. Explicit instructions are given for teachers who are new to GeoGebra. A detailed summative assessment includes extensions and an answer key is provided.

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

Dogpound Graphing:

Students will graph ordered pairs within all four quadrants of a coordinate plane in order to complete the picture of a bulldog.

Type: Lesson Plan

Coordinate Grids: The Key to the City (solving real-world problems using the coordinate grid):

This lesson contains a small group activity in which students use knowledge of graphing in a 4-quadrant coordinate grid. Students will individually solve a real-world problem to find the distance between two points on a coordinate grid. Students must utilize their knowledge of absolute value and subtracting integers to determine distances between points.

Type: Lesson Plan

Decoding Word Phrases-Translating verbal phrases to variable expressions:

This lesson is designed to help students decode word phrases and then translate them from word form into numerical form. It provides a resource, in the form of a foldable, that can be kept all year and used anytime the students need to decode word phrases.

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 their understanding.

Type: Lesson Plan

Discovering Integer Addition Rules by Hand:

In this lesson students will use physical and digital manipulatives to help them discover patterns when adding positive and negative integers.

Type: Lesson Plan

The Mystery of Crop Circles...on a coordinate plane:

In this lesson, students will use their knowledge of plotting points on quadrant I of the coordinate plane to figure out other coordinate pairs within quadrants II, III, and IV. Students are challenged to match description cards to the matching "map" (four-coordinate grid).Â

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Type: Lesson Plan

## 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

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

## Perspectives Video: Teaching Ideas

Unlock an effective teaching strategy for using patterns to help students make generalizations when adding integers in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

Absolute Value Progression:

Unlock an effective teaching strategy for making connections with absolute values to graphing in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

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.

Mile High:

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

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.

Comparing Temperatures:

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

Fractions on the Number Line:

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

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.

It's Warmer in Miami:

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

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.

## Tutorials

Comparing Rational Numbers:

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

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 Negative Numbers:

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

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

Comparing Variables with Negatives:

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

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:

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

Type: Tutorial

Opposite of a Number:

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

Type: Tutorial

## Video/Audio/Animation

Number Opposites Practice:

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

Type: Video/Audio/Animation

## Student Resources

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

## 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

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

Mile High:

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

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.

Comparing Temperatures:

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

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.

It's Warmer in Miami:

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

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.

## Tutorials

Comparing Rational Numbers:

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

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 Negative Numbers:

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

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

Comparing Variables with Negatives:

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

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:

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

Type: Tutorial

Opposite of a Number:

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

Type: Tutorial

## Parent Resources

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

Mile High:

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

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.

Comparing Temperatures:

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

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.