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

Lesson 7.37.3 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can find the absolute value of a rational number — an integer, fraction, or decimal — as its distance from zero — one step at a time, with support.

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 1

Group 1Supported practice

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

Learning target With my small group, I can find the absolute value of a rational number — an integer, fraction, or decimal — as its distance from zero — one step at a time, with support.

  1. 1Complete each step, then write the final answer.
    −10−8−6−4−20246810? units−8
    Count from −8 to 0.

    Find |−8|, the absolute value of −8.

    1. 1Is −8 to the left or right of 0?
    2. 2Count the units from −8 to 0. How many?
    3. 3So what is |−8|?
    Final answer:
  2. 2Complete each step, then write the final answer.
    −5−4−3−2−1012345? units−3.5
    This time the number is a decimal.

    Find |−3.5|, the absolute value of −3.5.

    1. 1Where is −3.5 on the number line?
    2. 2How many units is −3.5 from 0?
    3. 3Can a distance be negative?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Find |−11|.

    Show your work

    Hint How many units is −11 from 0?

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

    Find |−3/4|.

    Show your work

    Hint −3/4 is between −1 and 0. How far is it from 0?

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

    A town is at an elevation of −20 feet. Sea level is 0. How far is the town from sea level?

    Show your work

    Hint Distance from sea level is the absolute value of the elevation.

    Final answer:
  6. 6Complete each step, then write the final answer.

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

    Show your work

    Hint Absolute value is a distance. Can a distance be negative?

    Final answer:

Explain your thinkingBen wrote |−5| = −5. Explain his mistake. Why is an absolute value never negative?

Sentence starter An absolute value is never negative because ___. · |−5| = ___ because −5 is ___ units from 0.

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