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

Lesson 7.37.3 Small Group · Group 2

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, explain why the method works, and use it on a problem I have not seen before.

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. +5 means 5 above zero, like 5 floors above ground level
NegativeSpanish: Negativo A number smaller than zero, to the left of zero on a number line. -3 means 3 below zero, like 3 floors underground
Absolute valueSpanish: Valor absoluto How far a number is from zero. It is never negative. |−3| = 3 and |3| = 3
OppositeSpanish: Opuesto Two numbers the same distance from zero, on opposite sides, like 3 and -3. −3 and 3 are opposites
Rational numberSpanish: Número racional A number that can be written as a fraction of two integers, with a bottom number that is not zero. −3/4, 0.5, 7, −50

How it worksWorked exampleusing absolute value to see which number is closer to 0

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

One freezer logged −23 degrees and another logged 17 degrees. Which reading sits closer to 0?

  1. Absolute value measures distance from 0, so the sign does not matter here.
  2. Distance from 0 for the first reading: −23 = 23
  3. Distance from 0 for the second reading: 17 = 17
  4. Compare the two distances; the shorter distance sits closer to 0.

Answer: |−23

Now you trySame steps, your turn

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

A fish swims at −31 meters and a gull flies at 28 meters. Which one is closer to the water surface at 0?

  1. Absolute value measures from 0, so the sign does not matter.
  2. Distance from 0 for the fish: −31 =
  3. Distance from 0 for the gull: 28 =
  4. Compare the distances; the distance is closer, so the is closer.
Answer:which one is closer to 0

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 because it sits units from zero.
  • and share the same absolute value because .
  • An absolute value is never negative because .
  • The number closer to zero is because its distance is .

Word bank absolute valuedistancemagnitudezeronumber lineoppositeunitscloserfarthernegativepositivesign

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 7.37.3 Small Group · Group 2

Group 2Challenge 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, explain why the method works, and use it on a problem I have not seen before.

  1. 1Complete each step, then write the final answer.
    −3−2−101230
    Start at 0. Look both ways.

    Which two numbers have an absolute value of 1.75?

    1. 1Start at 0. Count 1.75 units to the right. What number is there?
    2. 2Now count 1.75 units to the left. What number is there?
    Final answer:
  2. 2Complete each step, then write the final answer.
    −40−30−20−10010203040cavesea levelhilltop
    Compare each distance from 0.

    A cave is at −35 meters. A hilltop is at 28 meters. Sea level is 0. Which one is farther from sea level?

    1. 1What is |−35|?
    2. 2What is |28|?
    3. 3Which one is farther from sea level?
    4. 4−35 is less than 28. Why is the cave still farther from 0?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Find |−2 2/5|.

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.

    |x| = 13, and x is to the left of 0. What is x?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.

    A diver is at −12.5 meters. A pelican flies at 9 meters. How much farther from sea level is the diver than the pelican?

    Show your work
    Final answer:
  6. 6Circle 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

Explain your thinking−35 is less than 28, but the cave is farther from sea level. When is "less" not the same as "closer to 0"?

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help