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

Lesson 7.3Absolute Value and Total Distance

Start hereWords, worked example, and sentence starters

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.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
IntegerSpanish: Número entero Whole numbers and their opposites, like -2, -1, 0, 1, 2. ... -3, -2, -1, 0, 1, 2, 3 ... shown on a number line with 0 in the center
PositiveSpanish: Positivo A number bigger than zero, to the right of zero on a number line. 50 sits right of zero
NegativeSpanish: Negativo A number smaller than zero, to the left of zero on a number line. −50 sits left of zero
Absolute valueSpanish: Valor absoluto How far a number is from zero. It is never negative. |−50| = 50
OppositeSpanish: Opuesto Two numbers the same distance from zero, on opposite sides, like 3 and -3. 3 and -3 are opposites — both are 3 units from 0
Rational numberSpanish: Número racional A number that can be written as a fraction of two integers, with a bottom number that is not zero. −1/2, 0 and 5/4 each sit at one exact point.

How it worksWorked examplefinding the swing between a negative and a positive reading

These numbers are not on your problems. The steps are. Follow them with your own numbers.

In one day a town's temperature rose from −38 degrees to 46 degrees. How great was the temperature swing?

  1. One reading sits left of 0 and one sits right, so 0 falls between them.
  2. Distance from the low reading to 0: −38 = 38
  3. Distance from 0 to the high reading: 46 = 46
  4. Join the two distances to cover the whole trip: 38 + 46 = 84

Answer: The temperature swing was 84 degrees.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

In one day a town's temperature rose from −27 degrees to 55 degrees. How great was the temperature swing?

  1. Where does 0 sit compared with the two readings?
  2. Distance from the low reading to 0: −27 =
  3. Distance from 0 to the high reading: 55 =
  4. Join the two distances: + =
Answer:size of the temperature swing, in degrees

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • The absolute value of is , so it sits units from zero.
  • Zero falls between and , so I the two distances.
  • The total distance is because .
  • Magnitude tells me , but it does not tell me .

Word bank absolute valuemagnitudedistancetotalzerobetweenaddunitsnegativepositivenumber lineopposite sides

Watch outA common mistake

A common mistake in Integers and Absolute Value is judging size by the digits alone instead of position on the number line — students think -8 is 'more' than -3 because 8 > 3, when really -8 sits farther left (colder, deeper, or lower) and is actually the SMALLER integer. Absolute value measures distance from zero and is always positive or zero, but that distance does not decide which integer is greater — only left-to-right order on the number line does. Before you submit, ask: am I comparing distance from zero (absolute value) or position on the number line (greater/less than)?

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

Lesson 7.3Absolute Value and Total Distance

Apply Day · Version ASupported 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.

  1. 1Complete each step, then write the final answer.

    Find |−16|.

    Show your work

    Hint Count the units from −16 to 0.

    Final answer:
  2. 2Complete each step, then write the final answer.

    Find |10|.

    Show your work

    Hint 10 is to the right of 0. How far is it?

    Final answer:
  3. 3Complete each step, then write the final answer.

    A fish swims at −1.5 meters. The surface is 0. How far is the fish from the surface?

    Show your work

    Hint Find |−1.5|.

    Final answer:
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 7.3Absolute Value and Total Distance

Apply Day · Version BCore 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.

  1. 1Complete each step, then write the final answer.

    Ben says |−5| = −5. Is he right? What is |−5|?

    Show your work
    Final answer:
  2. 2Complete each step, then write the final answer.

    Find |−2 2/5|.

    Show your work
    Final answer:
  3. 3Complete each step, then write the final answer.

    Find |−14|.

    Show your work
    Final answer:
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 7.3Absolute Value and Total Distance

Apply Day · ChallengeExtension

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.

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

    What is the value of |−12|?

    1. A0
    2. B1/12
    3. C12
    4. D−12
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    Which number is farthest from 0: −8.2, 7.9, −0.5 or 8?

    1. A−8.2
    2. B8
    3. C7.9
    4. D−0.5
    Show your work
  3. 3Complete each step, then write the final answer.

    Find |−5 1/3|.

    Show your work
    Final answer:
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help