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

Lesson 7.4Ordering Integers and Rational Numbers

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can compare and order integers using a number line.

Start hereWords for this lesson

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

WordWhat it meansExample
Number lineSpanish: Recta numérica A straight line where numbers are placed in order; numbers get smaller to the left and larger to the right. ← -3 -2 -1 0 1 2 3 →
CompareSpanish: Comparar To see if a number is bigger, smaller, or equal to another. -3 < 2 because -3 is farther left on the number line than 2
OrderSpanish: Ordenar To arrange numbers by size, from least to greatest or greatest to least. −9, −2, 0, 6
Greater thanSpanish: Mayor que The > sign, showing one number is bigger. 4 > -1 because 4 is to the right of -1 on the number line
Less thanSpanish: Menor que The < sign, showing one number is smaller. -6 < -2 because -6 is farther left — it is farther from zero
Negative integerSpanish: Entero negativo A whole number smaller than zero, like -5. -4 is 4 units to the LEFT of zero on the number line

How it worksWorked exampleordering three negative depths

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

Three wells have floors at −418 feet, −96 feet, and −1,240 feet. Order the depths from least to greatest.

  1. All three numbers are negative, so every point lands to the left of 0.
  2. Farther left means less. Sketch a line and place the three points on it.
  3. Read the line left to right: −1,240 , −418 , −96
  4. Check with absolute value: the least number sits farthest from 0.

Answer: −1,240 < −418 < −96, so the order is −1,240 , −418 , −96.

Now you trySame steps, your turn

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

Three wells have floors at −275 feet, −53 feet, and −809 feet. Order the depths from least to greatest.

  1. All three numbers are , so every point lands to the of 0.
  2. Farther left means . Sketch a line and place the three points.
  3. Read the line left to right: , ,
  4. Check with absolute value: the number sits farthest from 0.
Answer:the three depths in order, least to greatest

Say it and write itSentence starters

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

  • I placed before because .
  • From least to greatest the order is , , .
  • The absolute value of is , which measures .
  • The number farthest from zero is , but the greatest number is .

Word bank orderleastgreatestabsolute valuedistancepositionnumber linenegativepositiveinequalityleftright

Watch outA common mistake

A common mistake in Compare and Order Integers is thinking that a negative number with a bigger digit is the bigger value — for example, believing -15 is greater than -8 because 15 is greater than 8. It's the opposite for negatives: the number farther to the left on the number line (farther from zero) is always the LESSER value, so -15 < -8. Before you submit, check your comparison against the number line, not just the digits.

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

Lesson 7.4Ordering Integers and Rational Numbers

Apply Day · Version ASupported practice

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

Learning target I can compare and order integers using a number line.

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

    Which is greater: −16 or −8?

    Show your work

    Hint The number farther right on a number line is greater.

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

    Which symbol goes in −4 ___ 2? Use < or >.

    Show your work

    Hint A negative number is always left of a positive number.

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

    Which is less: 0 or −19?

    Show your work

    Hint Negative numbers are left of 0.

    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 7.4Ordering Integers and Rational Numbers

Apply Day · Version BCore practice

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

Learning target I can compare and order integers using a number line.

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

    Max writes −10 > −2 because 10 > 2. Which symbol should go in −10 ___ −2?

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

    Which is greater: −4.2 or −4.25?

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

    Which is greater: −14 or −20?

    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 7.4Ordering Integers and Rational Numbers

Apply Day · ChallengeExtension

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

Learning target I can compare and order integers using a number line.

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

    Order these numbers from LEAST to GREATEST: −2, 1.5, −4.5, 0, 3.

    1. A−2, −4.5, 0, 1.5, 3
    2. B3, 1.5, 0, −2, −4.5
    3. C−4.5, −2, 0, 1.5, 3
    4. D−4.5, −2, 0, 3, 1.5
    Show your work
  2. 2Complete each step, then write the final answer.

    Eva says −0.6 < −0.55 is false because 0.55 has more digits. Which is greater: −0.6 or −0.55?

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

    Which is less: −5.6 or −5.65?

    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