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

Lesson 7.4Compare and Order 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.

Why This Matters Lucy and Yuzuki are playing a trivia game with these rules: if a player answers a question correctly, they receive 1 point; if they answer incorrectly, they lose 0.25 point. The player with the greatest score wins the game. The final scores for two games are shown in the table. Who is the winner of each game?

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. left is less, right is more
CompareSpanish: Comparar To see if a number is bigger, smaller, or equal to another. −7 compared with −3
OrderSpanish: Ordenar To arrange numbers by size, from least to greatest or greatest to least. Least to greatest: -5, -2, 0, 3, 7 (left to right on the number line)
Greater thanSpanish: Mayor que The > sign, showing one number is bigger. −3 > −7
Less thanSpanish: Menor que The < sign, showing one number is smaller. −7 < −3
Negative integerSpanish: Entero negativo A whole number smaller than zero, like -5. −7, −3, −100

How it worksWorked example

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

Compare −14 degrees and −5 degrees.

  1. Plot −14 and −5 on a number line.
  2. −5 is to the right of −14.
  3. Write the comparison: −14 < −5.

Answer: −5 is greater; −14 is colder

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 compare -2 and 3. Which one is to the left on the number line? The -2 is left of zero.

Answer:

Say it and write itSentence starters

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

  • On the number line, sits to the of , so is greater.
  • I can write the comparison as .
  • The least number in this set is because .
  • Comparing two negative numbers is different from counting because .

Word bank compareordergreater thanless thannumber lineleftrightnegativepositiveleastgreatestinequality

Watch out!A common mistake

A common mistake in Compare and Order Integers is thinking that a negative number with a bigger digit is the bigger value

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

Lesson 7.4Compare and Order Integers and Rational Numbers

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.

Why This Matters Lucy and Yuzuki are playing a trivia game with these rules: if a player answers a question correctly, they receive 1 point; if they answer incorrectly, they lose 0.25 point. The player with the greatest score wins the game. The final scores for two games are shown in the table. Who is the winner of each game?

Part 1Understand the ideamodels and meaning
  1. 1Circle the letter of the best answer. Show how you know.

    Which statement is TRUE?

    1. A-5 < -2
    2. B-4 > 0
    3. C-3 > -1
    4. D-1 < -6

    Hint Sketch a quick number line. For negatives, 'greater' means closer to zero, not a bigger digit.

    Show your work
  2. 2Write the name of the correct group on each line.

    Drag to order these integers from LEAST to GREATEST.

    Groups:
    • 3
    • -1
    • -6
    • 0
    • -4
    • 5

    Hint Least to greatest reads left to right on a number line — all the negatives come before 0.

  3. 3Mark and label each value on the number line.

    Plot -3, 1, -7, 4, and -1 on the number line to help you compare them.

    -8-7-6-5-4-3-2-10123456

    Hint Negatives (-3, -7, -1) go left of 0; positives (1, 4) go right.

    Show your thinking
Part 2Apply itreal-world problems
  1. 4Circle the letter of the best answer. Show how you know.

    Which integer is the LEAST: -3, 5, -8, 2, 0?

    1. A-8
    2. B-3
    3. C0
    4. D5

    Hint 'Least' means farthest LEFT on the number line — for negatives, that's the one farthest below zero.

    Show your work
  2. 5Circle the letter of the best answer. Show how you know.

    What is |−8|?

    1. A0
    2. B8
    3. C−8
    4. D−16

    Hint The bars |...| mean absolute value: the distance from 0, which is never negative.

    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1ReadCompare -5 and -2. Write the comparison using > or <.
    2. 2AttemptThe student wrote -5 > -2, reasoning that 5 is bigger than 2, so -5 must be bigger than -2.
    3. 3CheckOn a number line, -5 is farther LEFT than -2, so -5 is actually less. The correct comparison is -5 < -2.

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Hint Where do -5 and -2 sit on the number line?

    Correct work
    Correct answer:

Explain your thinkingHow does plotting on the number line help you compare and order integers?

Sentence starter On the number line, ___ is to the left of ___, so ___ < ___. The order from least to greatest is ___.

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

Lesson 7.4Compare and Order Integers and Rational Numbers

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.

Why This Matters Lucy and Yuzuki are playing a trivia game with these rules: if a player answers a question correctly, they receive 1 point; if they answer incorrectly, they lose 0.25 point. The player with the greatest score wins the game. The final scores for two games are shown in the table. Who is the winner of each game?

Part 1Understand the ideamodels and meaning
  1. 1Mark and label each value on the number line.

    Plot these integers and write them in order from greatest to least: -8, 4, -3, 1, -1, 6

    -10-8-6-4-202468
    Show your thinking
  2. 2Complete the table. Show how you found each value.

    Compare each pair of integers using < , > , or =.

    Integer AInteger BComparison (< , > , or =)
    -42
    -7-3
    0-5
    -1-1
    6-9
    Show your work
  3. 3Write the name of the correct group on each line.

    Sort these integers from GREATEST to LEAST.

    Groups:
    • -10
    • 5
    • -2
    • 8
    • 0
    • -6
Part 2Apply itreal-world problems
  1. 4Circle the letter of the best answer. Show how you know.

    Three cities have temperatures of -12°F, -5°F, and 3°F. Which city is warmest?

    1. A-5°F
    2. B-12°F
    3. C3°F
    4. DThey are equal
    Show your work
Part 3Explain and correctreasoning
  1. 5Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1ReadOrder -8 and -15 from least to greatest.
    2. 2AttemptThe student wrote -8, -15, because 8 is smaller than 15.
    3. 3Check-15 is farther left than -8 on the number line, so -15 is the least. The correct order is -15, -8.

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:

Explain your thinkingHow does plotting on the number line help you compare and order integers?

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

Lesson 7.4Compare and Order Integers and Rational Numbers

ChallengeExtension

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

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

Why This Matters Lucy and Yuzuki are playing a trivia game with these rules: if a player answers a question correctly, they receive 1 point; if they answer incorrectly, they lose 0.25 point. The player with the greatest score wins the game. The final scores for two games are shown in the table. Who is the winner of each game?

Part 1Understand the ideamodels and meaning
  1. 1Write the name of the correct group on each line.

    These integers represent bank account changes. Sort from the WORST change (biggest loss) to the BEST change (biggest gain).

    Groups:
    • +50 deposit
    • -25 withdrawal
    • +10 deposit
    • -100 withdrawal
    • 0 no change
    • -5 fee
Part 2Explain and correctreasoning
  1. 2Find the mistake. Explain it, then show the correct work.

    Find the Comparison Error

    1. 1ProblemCompare -3 and -8. Which is greater?
    2. 2Student thinking8 is bigger than 3, so -8 must be greater than -3
    3. 3Student answer-8 > -3

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:
  2. 3Answer in complete sentences.

    A student says: 'Negative numbers are always less than positive numbers, so -100 is less than 1.' Is this correct? Now the student says: '-100 is less than -1 because 100 is greater than 1.' Is THIS correct? Explain the difference.

    Write your answer

Explain your thinkingHow does plotting on the number line help you compare and order integers?

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