# MA.6.NSO.1.3

Given a mathematical or real-world context, interpret the absolute value of a number as the distance from zero on a number line. Find the absolute value of rational numbers.

### Clarifications

Clarification 1: Instruction includes the connection of absolute value to mirror images about zero and to opposites.

Clarification 2: Instruction includes vertical and horizontal number lines and context referring to distances, temperature and finances.

General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Number Sense and Operations
Status: State Board Approved

## Benchmark Instructional Guide

### Terms from the K-12 Glossary

• Absolute Value
• Integers
• Number Line
• Rational Number
• Whole Number

### Vertical Alignment

Previous Benchmarks

• This is the first introduction to the concept of absolute value.
http://flbt5.floridaearlylearning.com/standards.html

Next Benchmarks

### Purpose and Instructional Strategies

In elementary grades, students plotted positive numbers on a number line and related addition of positive numbers to distance on a number line. In grade 6, students determine the absolute values, both in the context of the distance from zero and determining the distance between two points on the coordinate plane with the same x- or y-coordinate. In grade 7, students will use the concept of opposites when solving problems involving order of operations and absolute value.
• Instruction includes developing the understanding that absolute value explains the magnitude of a real number without regard to its sign, and is denoted by |x| and reads “the absolute value of x.”
• Absolute value in real-life situations can help students understand the concept of absolute value.
• For example, distance is not depicted as a negative number; absolute value context should be used to describe a distance in the opposite direction. Students can draw pictures or diagrams, including vertical or horizontal number lines, to mathematically demonstrate what is happening in the real-life situation (MTR.2.1, MTR.7.1).
• Using sentence frames can help students describe relationships and reasoning with absolute value (MTR.4.1).
• For example, when given the statement |x| = 6, students may benefit from frame such as: The distance from x to 0 is _____, so x can be located at _____ or _____.
• Instruction includes the use of technology to explore, interpret and define absolute value.

### Common Misconceptions or Errors

• Students may incorrectly state the absolute value of a negative number has a negative value. Students need to understand the total distance you traveled is not dependent on which direction you travel. To help address this misconception, instruction includes students talking about absolute value as distance and asking students questions such as:
• If your parent drives a car backwards, does the odometer show how far the car traveled by counting backwards?
• If you walk from your desk to the door backwards (your back is facing the door), about how far would you walk?
• You stand in line for a ride at an amusement park. You walk forward 10 feet in line then the line makes a U-turn and you walk 30 feet. A U-turn happens in the line again and you travel an additional 16 feet before boarding the ride. Do you subtract the distance when you travel the opposite direction in line, or do you still add it because you are still traveling over a specific distance?
• Do you describe how far you traveled with a negative number because a person was walking or driving backwards?

### Strategies to Support Tiered Instruction

• Instruction includes providing students with a sentence stem to interpret the meaning of the absolute value. Some students may require additional reading support.
• For example, if given “If the temperature in Chicago, IL, is −7°, how many degrees below zero is the temperature?” the teacher can provide the sentence stem: “The absolute value of −7 is 7 units from zero, so the temperature is  degrees below zero.”
• Instruction includes providing students error analysis problems for which the absolute value of a positive number is incorrectly given as its opposite, rather than its distance from zero. Teacher reinforces the absolute value as the distance from zero and provides opportunities for students to plot the value on a number line and record the number of units the point is from zero. Instruction begins with integers and moves toward rational numbers.
• Teacher co-creates a graphic organizer with the students while providing instruction on the definitions of “absolute value,” “opposite value,” and “negative number.” Instruction includes helping students to develop a definition in their own words, identify key characteristics, examples, and non-examples of each term.
• Teacher provides students with flash cards to practice and reinforce academic vocabulary.
• Instruction includes students talking about absolute value as distance and asking students questions such as:
• If your parent drives a car backwards, does the odometer show how far the car traveled by counting backwards?
• If you walk from your desk to the door backwards (your back is facing the door), about how far would you walk?
• You stand in line for a ride at an amusement park. You walk forward 10 feet in line then the line makes a U-turn and you walk 30 feet. A U-turn happens in the line again and you travel an additional 16 feet before boarding the ride. Do you subtract the distance when you travel the opposite direction in line, or do you still add it because you are still traveling over a specific distance?
• Do you describe how far you traveled with a negative number because a person was walking or driving backwards?

The absolute value of an unknown number is 11.2. Where could the unknown number be located on a number line? Explain how you know.

The table below shows the change in rainfall for each month from the month’s average over the past 5 years. Find the absolute value of each month and determine which month had the greatest change in rainfall.
 Month March April May June July Change in Rainfall  Amount from 5-Year  Average (inches) 0.21 -1.64 -0.48 2.01 -2.30
Instructional Item 3 (MTR.3.1
Plot 4, −4 and 0 on the same number line. Compare 4 and −4 in relation to 0.
• Part A. Plot 4, −4 and 0 on the same number line.
• Part B. Compare 4 and −4 in relation to 0.

### Instructional Items

Instructional Item 1
What is the value of the expression |− $\frac{\text{7}}{\text{8}}$| ?

Instructional Item 2
If the temperature in Chicago, IL is −7°, how many degrees below zero is the temperature?

Instructional Item 3
What is the value of the expression −|12.75|?

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.

## 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))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.6.NSO.1.AP.3: Find absolute value of a rational number ranging from –30 to 30 using a number line.

## Related Resources

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

## Formative Assessments

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

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

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

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.

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, 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

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

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).

Type: Lesson Plan

## 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

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 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 Values on Number Line:

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

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.

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.

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 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 Values on Number Line:

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

Type: Tutorial

## Parent Resources

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