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Unit 05 · Rational Numbers and CoordinatesLesson

Day 069Magnitude and Order

LearnClassworkAnswer keyPDF packet ↗
Standards 6.NS.C.7c6.NS.C.7d
LEARNING TARGET

I can distinguish a number from its distance to zero.

01 · LEARN

Build the idea

The absolute value |x| is the distance from x to zero, so it cannot be negative. A larger absolute value means farther from zero, but does not necessarily mean a greater number.

WORKED EXAMPLE 1

Find |-16|. Explain the distance meaning.

16

-16 is 16 units from 0; distance is nonnegative.

WORKED EXAMPLE 2

A diver is at -21 m and a bird is at 7/2 m relative to sea level. Who is farther from sea level? Who has greater elevation? Use absolute values.

Diver: 21 m from sea level; bird has greater elevation

|-21| = 21 > |7/2| = 7/2, but -21 < 7/2.

02 · PRACTICE

Your turn

Work in order. Start with the foundations, then build toward explanation and application.

  1. Find |-12|. Explain the distance meaning.

  2. Find |-8|. Explain the distance meaning.

  3. Find |-21|. Explain the distance meaning.

  4. Find |-8| and compare it with |2|.

  5. Find |-14| and compare it with |2|.

  6. Find |-12| and compare it with |4|.

  7. A diver is at -12 m and a bird is at 4 m relative to sea level. Who is farther from sea level? Who has greater elevation? Use absolute values.

  8. A diver is at -5 m and a bird is at 1 m relative to sea level. Who is farther from sea level? Who has greater elevation? Use absolute values.

  9. A diver is at -7 m and a bird is at 7/2 m relative to sea level. Who is farther from sea level? Who has greater elevation? Use absolute values.

  10. A diver is at -28 m and a bird is at 4 m relative to sea level. Who is farther from sea level? Who has greater elevation? Use absolute values.

03 · CHECK

Answers and reasoning

Reveal the teacher answer key
  1. 12

    -12 is 12 units from 0; distance is nonnegative.

  2. 8

    -8 is 8 units from 0; distance is nonnegative.

  3. 21

    -21 is 21 units from 0; distance is nonnegative.

  4. 8; 8 > 2

    -8 is 8 units from 0; distance is nonnegative.

  5. 14; 14 > 2

    -14 is 14 units from 0; distance is nonnegative.

  6. 12; 12 > 4

    -12 is 12 units from 0; distance is nonnegative.

  7. Diver: 12 m from sea level; bird has greater elevation

    |-12| = 12 > |4| = 4, but -12 < 4.

  8. Diver: 5 m from sea level; bird has greater elevation

    |-5| = 5 > |1| = 1, but -5 < 1.

  9. Diver: 7 m from sea level; bird has greater elevation

    |-7| = 7 > |7/2| = 7/2, but -7 < 7/2.

  10. Diver: 28 m from sea level; bird has greater elevation

    |-28| = 28 > |4| = 4, but -28 < 4.

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