Rational Numbers

Lesson 9

Math

Unit 4

6th Grade

Lesson 9 of 13

Objective


Define absolute value as the distance from zero on a number line. 

Common Core Standards


Core Standards

  • 6.NS.C.7.C — Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of -30 dollars, write |-30| = 30 to describe the size of the debt in dollars.

Criteria for Success


  • Define absolute value as the distance from zero on a number line. 
  • Understand that absolute value is a distance or magnitude and, therefore, is always positive or zero. Absolute value is never negative.
  • Understand that the absolute value of a number is equal to the absolute value of the number’s opposite because a number and its opposite are the same distance from zero.
  • Represent absolute value as $${|x|}$$.

Tips for Teachers


Common misconceptions with absolute value involve confusing absolute value with opposites or with distinct locations on the number line. To support the understanding of absolute value as a distance, use points to show locations of numbers or values, but use line segments or horizontal brackets to show distance/magnitude for absolute value (MP.6).

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Anchor Problems


Problem 1

A flea is jumping around on the number line.

a.   If he starts at 1 and jumps 3 units to the right, then where is he on the number line? How far away from zero is he?

b.   If he starts at 1 and jumps 3 units to the left, then where is he on the number line? How far away from zero is he?

c.   If the flea starts at 0 and jumps 5 units away, where might he have landed?

d.   If the flea jumps 2 units and lands at zero, where might he have started?

e.   The absolute value of a number is the distance it is from zero. The absolute value of the flea’s location is 4, and he is to the left of zero. Where is he on the number line?

Guiding Questions

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References

Illustrative Mathematics Jumping Flea

Jumping Flea, accessed on Aug. 11, 2017, 12:47 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Problem 2

For each number in the table:

  • Locate the number on a number line.
  • Find its absolute value and show it on a number line.
  • Name another number with the same absolute value, and locate it on the number line.

Number

Absolute Value

(show with symbol)

Number Line Diagram

Number with Same Absolute Value

5  

     

 
-7  

     

 

Guiding Questions

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References

EngageNY Mathematics Grade 6 Mathematics > Module 3 > Topic B > Lesson 11Exercises 1-3

Grade 6 Mathematics > Module 3 > Topic B > Lesson 11 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem 3

Absolute value and opposites are related but not the same. Consider each statement below and answer with always, sometimes, or never. Be prepared to defend your reasoning.

a.   Finding the absolute value of a number is the same thing as changing its sign.

b.   The absolute value of a number is positive.

c.   The absolute value of a number is not negative.

d.   The opposite of a number is positive. 

e.   $${|a| = |-a|}$$

f.   You and a friend are both 2 miles from school, so that means you’re both in the same location.

Guiding Questions

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Problem Set

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Target Task


Problem 1

On the number line, show all of the values that have an absolute value of 2.5.


 

How is the opposite of -2.5 different from the absolute value of -2.5?

Problem 2

Compare the following values using the symbols $${<}$$, $${>}$$, or $$=$$.

a.     $${|{-2}|}$$    ________       $${-2}$$

 

b.     $${|-5|}$$    ________     $${|-8|}$$

 

c.     $${-1.4}$$     ________    $${|-1.3|}$$

 

d.         $$7$$       ________      $$|7|$$

Student Response

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Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Students can do a variation of “Jumping Flea” from Anchor Problem #1 in pairs with individual number lines.
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Lesson 8

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Lesson 10

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Understanding Positive and Negative Rational Numbers

Topic B: Order and Absolute Value

Topic C: Rational Numbers in the Coordinate Plane

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