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

Lesson 7.37.1–7.3 Catch-Up

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can show I am caught up on Lessons 7.1–7.3 by using each lesson's big idea in mixed practice.

Start hereWords for this lesson

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

WordWhat it meansExample
IntegerSpanish: Número entero The counting numbers, their opposites, and 0. ..., -3, -2, -1, 0, 1, 2, 3, ...
OppositeSpanish: Opuesto A number that is the same distance from 0 as another number, but on the other side of 0. −3 and 3 are opposites
Negative numberSpanish: Número negativo A number less than 0, written with a − sign. On a number line it sits to the left of 0. -86 meters means 86 meters BELOW sea level
Positive numberSpanish: Número positivo A number greater than 0. On a number line it sits to the right of 0. 9°C is 9 degrees ABOVE zero
Number lineSpanish: Recta numérica A straight line where numbers are placed in order. It extends to the left of 0 to show values less than 0. -3, -2, -1, 0, 1, 2, 3 marked in order from left to right
Rational Numbers on the Number LineSpanish: Números racionales en la recta numérica Every rational number has one exact spot on the number line. Writing it as a fraction, a decimal, or an integer does not change where it sits. −3/2 = −1.5 and 1/2 = 0.5 each sit at one exact point.

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 7.37.1–7.3 Catch-Up

Catch-UpSkill bridge

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

Learning target I can show I am caught up on Lessons 7.1–7.3 by using each lesson's big idea in mixed practice.

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

    (Lesson 7.1) Badwater Basin is 86 meters below sea level, and sea level is 0. Which integer represents that elevation?

    1. A-86
    2. B-68
    3. C0
    4. D86

    Hint Sea level is 0. Is 'below sea level' more than 0 or less than 0?

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

    (Lesson 7.1) In Reykjavik the temperature was -9°C. What is the opposite of -9?

    1. A-18
    2. B-9
    3. C0
    4. D9

    Hint 'Opposite' means the same distance from 0, but on the other side of 0.

    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    (Lesson 7.2) Which point is located between -1 and -2 on the number line?

    1. A-2.5
    2. B-1.5
    3. C-0.5
    4. D1.5

    Hint 'Between -1 and -2' is on the NEGATIVE side, in the gap from -1 to -2.

    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    (Lesson 7.2) Which fraction is equivalent to 0.25?

    1. A1/4
    2. B1/2
    3. C1/3
    4. D2/5

    Hint Read 0.25 as a place-value number: 25 hundredths.

    Show your work
  5. 5Circle the letter of the best answer. Show how you know.

    (Lesson 7.3) What is the absolute value of -9?

    1. A-9
    2. B0
    3. C1
    4. D9

    Hint Absolute value asks: how FAR is -9 from zero? It's about distance, not 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 ___.

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