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Unit 05 · Rational Numbers and CoordinatesLesson

Day 068Absolute Value as Distance

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 |-28|. Explain the distance meaning.

28

-28 is 28 units from 0; distance is nonnegative.

WORKED EXAMPLE 2

A diver is at -18 m and a bird is at 3 m relative to sea level. Who is farther from sea level? Who has greater elevation? Use absolute values.

Diver: 18 m from sea level; bird has greater elevation

|-18| = 18 > |3| = 3, but -18 < 3.

02 · PRACTICE

Your turn

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

  1. Find |-16|. Explain the distance meaning.

  2. Find |-35|. Explain the distance meaning.

  3. Find |-6|. Explain the distance meaning.

  4. Find |-3| and compare it with |3/2|.

  5. Find |-6| and compare it with |3|.

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

  7. 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.

  8. A diver is at -14 m and a bird is at 2 m relative to sea level. Who is farther from sea level? Who has greater elevation? Use absolute values.

  9. A diver is at -16 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.

  10. A diver is at -25/2 m and a bird is at 5/2 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. 16

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

  2. 35

    -35 is 35 units from 0; distance is nonnegative.

  3. 6

    -6 is 6 units from 0; distance is nonnegative.

  4. 3; 3 > 3/2

    -3 is 3 units from 0; distance is nonnegative.

  5. 6; 6 > 3

    -6 is 6 units from 0; distance is nonnegative.

  6. 8; 8 > 4

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

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

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

  8. Diver: 14 m from sea level; bird has greater elevation

    |-14| = 14 > |2| = 2, but -14 < 2.

  9. Diver: 16 m from sea level; bird has greater elevation

    |-16| = 16 > |4| = 4, but -16 < 4.

  10. Diver: 25/2 m from sea level; bird has greater elevation

    |-25/2| = 25/2 > |5/2| = 5/2, but -25/2 < 5/2.

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