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

Lesson 7.3Understand Absolute Value of Rational Numbers

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.

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?

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 example

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

Find |−13| and |6|. Which number is farther from 0?

  1. −13 is 13 units left of 0, so |−13| = 13.
  2. 6 is 6 units right of 0, so |6| = 6.
  3. Compare the distances: 13 > 6.

Answer: −13 is farther from 0

Now you trySame steps, your turn

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

Now let's find |3|. Where is 3 on the number line? It is 3 steps to the right of zero.

Answer:

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 out!A common mistake

A common mistake in Integers and Absolute Value is judging size by the digits alone instead of position on the number line

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

Lesson 7.3Understand Absolute Value of Rational Numbers

Level 0Most support · every hint printed

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?

How it worksWorked example

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

Find |−13| and |6|. Which number is farther from 0?

  1. −13 is 13 units left of 0, so |−13| = 13.
  2. 6 is 6 units right of 0, so |6| = 6.
  3. Compare the distances: 13 > 6.

Answer: −13 is farther from 0

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

    What is the absolute value of -9?

    1. A-9
    2. B0
    3. C1
    4. D9
    Steps to try
    1. Absolute value asks: how FAR is -9 from zero? It's about distance, not direction.
    2. Picture -9 on a number line and count the hops back to 0. A distance is never negative.
    3. Start at -9 and count the steps to reach 0: 1, 2, 3, ... How many hops does it take in all?
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    Which integer has the GREATEST absolute value: -3, 7, -5, 2?

    1. A-5
    2. B-3
    3. C2
    4. D7
    Steps to try
    1. 'Greatest absolute value' means farthest from zero — the sign doesn't matter.
    2. Find each number's distance from 0: |-3|, |7|, |-5|, |2|. Then pick the biggest distance.
    3. Start with |-3| = 3 and |-5| = 5. Now find the distances for 7 and 2 and compare all four.
    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    What is |0|?

    1. A1
    2. B-1
    3. C0
    4. DThere is no answer
    Steps to try
    1. Absolute value = distance from zero. Here the number inside the bars IS zero.
    2. Ask: how many units do you travel from 0 to reach 0 on the number line?
    3. Place your finger on 0. Count the hops needed to get to 0 — that count is the value of |0|.
    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    What is |−2.5|?

    1. A0
    2. B2.5
    3. C−2.5
    4. D25
    Steps to try
    1. Where does −2.5 sit on the number line?
    2. How far is that from zero?
    3. Distance ignores direction.
    Show your work

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