### 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.

**Subject Area:**Mathematics (B.E.S.T.)

**Grade:**6

**Strand:**Number Sense and Operations

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

**Date Adopted or Revised:**08/20

**Status:**State Board Approved

## Benchmark Instructional Guide

### Connecting Benchmarks/Horizontal Alignment

### 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).*

- 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
- 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__7__degrees below zero.”

- 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
- 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?

### Instructional Tasks

*Instructional Task 1*

**(MTR.4.1, MTR.5.1)****(MTR.7.1)**

Month March April May June July Change in RainfallAmount from 5-YearAverage (inches)0.21 -1.64 -0.48 2.01 -2.30

*Instructional Item 3*

**(MTR.3.1)**- 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*

*Instructional Item 2*

*Instructional Item 3*

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

## Related Courses

## Related Access Points

## Related Resources

## Formative Assessments

## Lesson Plans

## Perspectives Video: Teaching Idea

## Problem-Solving Task

## Tutorials

## MFAS Formative Assessments

Students are asked to compare two elevations and their absolute values and then interpret these comparisons within a given real-world context.

Students are asked to identify a number’s possible locations on a number line when given the number’s absolute value.

## Student Resources

## 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

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

Type: Tutorial

## Parent Resources

## 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