Grade 6 Mathematics · Unit 7: Integers, Rational Numbers, and the Coordinate PlaneStandard 6.NOS.8

Lesson 7.3Understand Absolute Value of Rational Numbers

Set B · Version ASecond form · supported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can find the absolute value of a rational number — an integer, fraction, or decimal — as its distance from zero.

Why This Matters Claire is performing a science experiment with two liquids. The temperatures of the two liquids in Celsius are shown. She needs to use the beaker with the temperature that is closer to 0°C. Which beaker should Claire use?

RememberUnderstand Absolute Value of Rational Numbers

Absolute Value. Formula: |a| = Distance of a from 0 (always ≥ 0) A rational number is any number that can be written as a fraction: integers like -6, fractions like -3/4, and decimals like 2.5 are all rational numbers. The absolute value of a number is how far it is from zero on the number line. Distance is never negative.

  1. Absolute value represents distance on a number line, never direction.
  2. Distance is always positive or zero: |-7| = 7 and |7| =
  3. Context: Magnitude of temperature, debt, elevation regardless of sign

Words: Integer (Número entero)Positive (Positivo)Negative (Negativo)Absolute value (Valor absoluto)Opposite (Opuesto)

Part 1Apply itreal-world problems
  1. 1Circle the letter of the best answer. Show how you know.

    What is |−3/4|?

    1. A0
    2. B3/4
    3. C−3/4
    4. D4/3

    Hint Mark −3/4 on a number line between −1 and 0.

    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    Which number sits between 2 and 3 on a number line?

    1. A1.9
    2. B2.4
    3. C−2.5
    4. D3.2
    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    What is the opposite of 3/4?

    1. A0
    2. B−3/4
    3. C3/4
    4. D4/3
    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    Between which two integers does −1/2 sit on a number line?

    1. A0 and 1
    2. B−1 and 0
    3. C−1/2 is not on the number line
    4. D−2 and −1
    Show your work
  5. 5Circle the letter of the best answer. Show how you know.

    The opposite of a number sits the same distance from 0 but on the…

    1. Aother side of 0
    2. Bsame side of 0
    3. Cexact same point
    4. Dfar end of the line
    Show your work
Part 2Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    The Missing Sign Mistake

    1. 1ProblemFind the absolute value of -9.
    2. 2Student's thinkingThe number inside the bars is negative, so I should keep the negative sign in my answer.
    3. 3Student's answer|-9| = -9

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Hint Can you walk backward -5 steps? Distance is always zero or positive, no matter which direction you moved.

    Correct work
    Correct answer:

Explain your thinkingHow does the number line help you see the difference between an integer and its absolute value?

Sentence starter The integer ___ is located ___ units from zero, so its absolute value is ___. Even though ___ is negative, its distance from zero is still ___.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 7: Integers, Rational Numbers, and the Coordinate PlaneStandard 6.NOS.8

Lesson 7.3Understand Absolute Value of Rational Numbers

Set B · Version BSecond form · core practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can find the absolute value of a rational number — an integer, fraction, or decimal — as its distance from zero.

Why This Matters Claire is performing a science experiment with two liquids. The temperatures of the two liquids in Celsius are shown. She needs to use the beaker with the temperature that is closer to 0°C. Which beaker should Claire use?

  1. 1Circle the letter of the best answer. Show how you know.

    A submarine is at -150 meters (below sea level) and a helicopter is at +200 meters (above sea level). A rescue team needs to know how far each is from sea level to plan a mission. What is |−150|?

    1. A0
    2. B150
    3. C−150
    4. D300
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    A submarine is at -150 meters (below sea level) and a helicopter is at +200 meters (above sea level). A rescue team needs to know how far each is from sea level to plan a mission. Which craft is FARTHER from sea level?

    1. AThe helicopter, because 200 > 150
    2. BThe submarine, because −150 < 200
    3. CThey are the same distance
    4. DYou cannot compare them
    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    A submarine is at -150 meters (below sea level) and a helicopter is at +200 meters (above sea level). A rescue team needs to know how far each is from sea level to plan a mission. Which craft is at the LOWER position?

    1. AThe helicopter, because 200 > 150
    2. BThey are equal
    3. CThe submarine, because 150 < 200
    4. DThe submarine, because −150 < 200
    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    On a frosty morning at the mountain cache, the thermometer reads -8 degrees. What is the absolute value of -8?

    1. A-8
    2. B0
    3. C8
    4. D16
    Show your work
  5. 5Circle the letter of the best answer. Show how you know.

    Two treasure sites report their temperatures: -5 degrees F at the Ice Cave and -2 degrees F at the Frozen Dock. Which site is COLDER?

    1. A-5 degrees F (Ice Cave)
    2. B-2 degrees F (Frozen Dock)
    3. CThey are the same
    4. DNeither is below zero
    Show your work
  6. 6Circle the letter of the best answer. Show how you know.

    Captain Vega compares |-12| (a deep cave) and |7| (a hilltop). Which absolute value is GREATER?

    1. A|7| because 7 is positive
    2. BThey are equal
    3. C|-12| = -12, so |7| is greater
    4. D|-12| because 12 > 7
    Show your work

Explain your thinkingHow does the number line help you see the difference between an integer and its absolute value?

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help